University of Southern California Dissertations and Theses

Essays in political economics

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Essays in political economics

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Content ESSAYSINPOLITICALECONOMICS A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2008 Copyright 2008 Francesco Sobbrio i Dedication To my parents Giuseppe and Giusy and my sister Paola ii Acknowledgements I have spent ve wonderful and very productive years during my Ph.D. at USC. Such great learning and life experience would not have been possible withoutthehelpandsupportofthemanypeopleIhavemetandtheoneswho have supported me despite being on the other side of the world (and of the clock). Firstandmostofall,Iwanttodeeplythankmymainadvisor,JuanCarrillo. Juan has been advising, guiding, helping, listening, pushing and supporting me since I arrived at USC ve years ago. Juan is the kind of mentor I have been always wishing to meet and the one I will always want to emulate. In theseyears, wehavejustarguedoverourdi¤erentphilosophicalviewsofwhat good socceris about. I have also been greatly benetted from the support and help of my other advisors, Guofu Tan, Simon Wilkie and Andrea Mattozzi. Guofuprovidedmewithmanygreatsuggestiononhowtoimprovemywork and made me think about my research in very original ways. Simon has been tremendously supportive of my work. Working next to him at the USC Center for Communication, Law and Policy has been an outstanding and unique educational experience. Andrea gave me many great research insights which signicantly improved my dissertation. I also want to thank Andrea for the endless times I bugged him to read my papers, to ask him suggestions or simply to talk about my concerns or doubts. Most importantly, I am really grateful to Andrea for his uniquefunwaytomakeeverythingsimplerandlessdramaticandforhaving supported me as only a real friend could do. Grazie di cuore Andrea. For valuable advice, help and support I also thank Isabelle Brocas, Amit Gandhi, Daniela Iorio, Micheal Magill, Pietro Navarra, Je¤ Nugent, Geert Ridder, Guillame Roger and Kenneth Wilburn. iii I could not have done my Ph.D. at USC, without the initial support of my undergraduatedissertationadvisor,AlbertoZanardi,whostronglyencouraged the rst steps of my career as a researcher. I also want to express my gratitude to Young Miller or the angel of our departmentas I call her. Young has solved an innite amount of administra- tive issues for me in these years. Most of all she always did it with a smile. Similarly, I want to thank Arlene Luck for having been so kind and helpful to me in my fellowship years at the Center for Communication, Law and Policy. One of the things that made my years at USC so great was the company of many friends and colleagues. In particular I want to thank Jad, studying buddy, o¢ ce mate and especially great friend; Burcu who has always been willing to share with me co¤ee breaks and friendly chats and Umanga who made the rst year of the Ph.D. a more unconventional and intellectually stimulating experience. Ialsowanttothankmyroommatesandfriends,EleonoraandSalvatore,my americanfamily, with whomI spent three fun years searching every shop in LA for the closest thing to decent Italian food. For many and diverse reasons I also want to thank my friends Adam, Fab- rizio, Matteo, Nicola, Nino, Luciana, and Riccardo. Last but denitively not least, I want to thank my family. I do not know howIwouldhavedonethiswithouttheirconstantandunconditionalsupport. My dad has always believed in me much more than I did myself. Most of all, this dissertation is dedicated to him, to his life example, to his passion for knowledge, to his intellectual curiosity which have always been a great inspiration to me. The love of my mother has brightened my more pessimistic moments. MysisterPaolaisonethemostfun,creativeandbrightpersonthat I know. Her positive attitude to life has greatly helped me in these years. iv Table of Contents Dedication i Acknowledgments ii List of Tables vi List of Figures viii Abstract ix Chapter 1: Indirect Lobbying and Media Bias 1 1.1 Introduction 1 1.1.1.Empirical Evidence 5 1.1.2 Related Literature 7 1.2 The Model 9 1.2.1 The game 14 1.3 The Interactions among Lobbies, the Media Outlet,Voters and Parties 17 1.3.1 Voters 18 1.3.2 Parties 19 1.3.3 The Media Outlet 20 1.3.4 Lobbies 24 1.4 Informative Equilibria 26 1.4.1 Symmetric Equilibria 26 1.4.2 Distortion in the Policy Outcome and Welfare 30 1.4.3 Media Bias, Policy Distortion and Welfare 34 1.4.4 Limiting Cases 37 1.5 The State Contingent Contest between Lobbies 39 1.5.1 Racing for Evidence 39 1.5.2 Comparative Statics 41 1.6 Extensions 43 1.6.1 Know direction of media outlet's bias 43 1.6.2 Single Lobby 44 1.6.3 AccuracyIncreasing Lobbies 45 1.7 Conclusions 45 v Chapter 2: Electoral Participation and Communicative Voting in Europe 49 2.1 Introduction 49 2.1.1 Related Literature 52 2.2 Model Specification 56 2.2.1 The TwoStage Electoral Choice Model 56 2.2.2 The ThreeStage Electoral Choice Model 59 2.3 Data and Descriptive Statistics 61 2.3.1 Data 61 2.3.2 Descriptive Statistics 67 2.4 Electoral Participation andCommunicative Voting in Europe 70 2.4.1 Electoral Participation 70 2.4.2 Communicative Voting 77 2.5 Conclusions 84 Chapter 3: HeterogeneousPreferences and Endogenous Acquisition of Costly Information 86 3.1 Introduction and Motivations 86 3.2The Model 90 3.3Optimal Acquisition of Costly Information 94 3.4. Alternative Applications of the Model 102 3.4.1.Consumers decision over two alternative products 102 3.4.2 Individual decision over investing in a safe or risky asset 103 3.5. Conclusions 105 References 107 Appendix A 118 Appendix B 141 Appendix C 155 vi List of Tables Table 1: Voters and Abstentionist 68 Table 2: Communicative and Strategic Voters 69 Table 3: Estimates of Electoral ParticipationTwo Stage Model 71 Table 4: Estimates of Electoral ParticipationThree Stage Model 75 Table 5: Estimates of Communicative VotingTwo Stage Model 79 Table 6: Estimates of Communicative VotingThree Stage Model 82 Table A1.1: SmallHsiao test for the IIA assumptionWhole Sample 141 Table A1.2: SmallHsiao test for the IIA assumptionSubsample of CSLP voters 142 Table A1.3: SmallHsiao test for the IIA assumptionSubsample of CLWP voters 142 Table A2.1: Description of Variables 144 Table A2.2: Summary Statistics 147 Table A3.1: Estimates of Electoral ParticipationRobustness Checks (1) Regression without "expressive" dummies (2) Regression with country fixed effectsTwo Stage Model 148 Table A3.2: Estimates of Electoral ParticipationRobustness Checks No media and Institutional Dummies–TwoStageModel 149 Table A3.3: Estimates of Electoral Participation–Robustness Checkson the swing voter's curse: alternative definitions of swinger and informative votersTwo Stage Model 150 Table A3.4: Estimates of Communicative VotingRobustness Check Regression with country fixed effectsTwo Stage Model 151 Table A3.5: Estimates of Communicative VotingRobustness Checks No Media and Institutional Dummies Two Stage Model 152 vii Table A4.1: Estimates of Electoral Participation and Communicative Voting– Subsampleof countries with low discrepancybetween actual and sample turnout –TwoStage Model 153 Table A4.2: Estimates of Electoral Participation and Communicative Voting– Subsample of countries with extreme right and left loser parties Two Stage Model 154 viii List of Figures Figure 1.1:Distribution of voters’ preferences with no uncertainty 12 Figure 1.2:Timing of the game 17 Figure 1.3:Media Bias and Informative Equilibria 29 Figure 1.4:Equilibria with Biased News Media Outlet 39 Figure 2.1:The Two Stage Electoral Choice Model 57 Figure 2.2: The Three Stage Electoral Choice Model 60 Figure 3.1: Expected utility of voter i for x i <1/2 93 Figure 3.2: Expected utilities of voters iand j for x j =1/2< x i 94 Figure 3.3: Optimal Strategy of voter i after msignals 96 ix Abstract Three essays compose the dissertation. The rst essay entitled Indirect LobbyingandMediaBiasanalyzesamodelwherevotershavestate-contingent preferencesoverpoliciesandlobbiesengageininuenceactivitiestoa¤ectthe information that a media outlet collects on the state of the world. The media outlet acts as a lterbetween lobbies and voters. It has to decide what to communicate to voters given the information it collects and its idiosyncratic bias. We show that, by targeting voters, lobbies are able to indirectly inu- encethepoliticaloutcomeandthuscreateadistortioninthepoliticalprocess. Whenthemediaoutlethasasmallidiosyncraticbiasthe(unique)equilibrium is characterized by a large level of lobbiesinuence activities and no news- slantingby the media outlet. When the media outlet s idiosyncratic bias is large, the (unique) equilibrium involves a low level of lobbiesinuence activi- ties and a high probability of news-slantingby the media outlet. Moreover, weshowthatahigheridiosyncraticbiasofthemediaoutletmaybeassociated withalowerpolicydistortionandahighervoterswelfare. Ontheotherhand, publicpolicymeasuresaimedatincreasingthecostof lobbiesinuenceactiv- ities would decrease the distortion in the policy outcome and increase voters welfare. Finally, asymmetries in lobbiesinuence activities lead to di¤erent probabilities of news-slantingby di¤erent media outlet s types. ThesecondessayentitledElectoralParticipationandCommunicativeVot- inginEurope(jointwithPietroNavarra)providesanempiricalinvestigation of electoral participationandcommunicativevotingin14Europeancountries. Weestimateamulti-levelvotingprocesswhereindividualsfaceaparticipation decision (whether to vote or abstain) and a voting decision (whether to vote strategically for a likely winner party or as communicating for a sure loser party). Our main ndings can be summarized as follows. First, uninformed x individuals and independent ones are less likely to turnout. However, being independent and uninformed does not have any statistically signicant e¤ect on electoral participation. Thus our results do not provide empirical support to the swing voters curse theory. Second, expressive motivations have a pos- itive and signicant e¤ect on electoral participation. Third, the probability of voting as communicating is positively related with the level of education and the degree of dissatisfaction with the political system. Fourth, right wing ex- tremists have a signicant lower probability of voting as communicating than moderate or left wing extremists. Finally, institutional features characteriz- ing the functioning of the political system and of the media market have a signicant e¤ect both on the participation and on the voting decision. The third essay entitled Heterogeneous Preferences and Endogenous Ac- quisition of Costly informationinvestigates how individuals acquire costly information. We analyze a model of endogenous acquisition of costly informa- tioninaframeworkwheredecisionmakershavetochoosebetweenxedalter- natives with state-dependent payo¤s. The decision makerspreferences are a combinationofaprivatevaluecomponent(theiridiosyncraticpreferences)and astate-dependentpublicvaluecomponent(thequalityoftheselectedalterna- tive). More specically, we focus on the case where decision makers have the same ex-post ranking over alternatives but they instead di¤er in their ex-ante ranking over such alternatives. We apply this model to a policy environment where voters can acquire costly information on the quality of candidates. We show that the optimal information acquisition strategy of a voter is slanted toward her ideologically closer candidate. A small amount of information in favor of the leftist candidate would be su¢ cient to induce a leftist voter to stop investing in information acquisition and choose that candidate. Instead, a rightist voter would nd optimal to keep acquiring information and then choose the leftist candidate only if the evidence in favor of such candidate xi becomes very large. Hence, the more a voter is ideologically close to a can- didate the higher her probability of mistakenly choosing such candidate when he is the low quality one. Moreover, the more voters care about the quality of candidates and the lower is the cost of acquiring information, the larger the amount of information that voters will acquire and the closer the behavior of extremist and moderate voters will be. Finally, every voter expects to gain fromacquiringcostlyinformationbutmoderatevotersaretheoneswhoexpect to gain the most. 1 1 ChapterI:IndirectLobbyingandMediaBias Oneofthemostpotentandcunninglobbyingtacticsofthepast decade, grassroots campaigning, will also probably escape oversight. This secretive hybrid of telemarketing, data mining and spin doc- toring is used to generate public support for otherwise unpopular corporations caught in a legislative battle - A tap on the wrist, The Economist, May 18th 2006 1.1 Introduction What are the e¤ects of lobbiesinuence activities on the political outcome? Theeconomicliteraturehaslongbeinginterestedinthisquestion. Inaseminal paper, Becker (1985) introduced the concept of inuence functionsuggest- ing that by exerting some kind of political pressure interest groups are able to a¤ect the tax or subsidy that they pay/receive. In the twenty years that have followed, many scholars have analyzed this issue by focusing on the relation- shipsbetweenlobbiesandpoliticians. Thisextensiveliteraturehasshownthat special interest groups may directly inuence the policy outcome by targeting politicians. 1 Indeed, lobbies allocate large amount of resources in trying to inuence politicians. 2 Nevertheless, such direct channel of policy inuence is not always e¤ective or feasible for lobbies. First of all, in the case of direct democracy (i.e., referenda, ballots, propositions, etc.), politicians are simply not the policy-makers. Moreover, there are issues where the political cost that any politician would incur by endorsing a lobby and deviating from the median voter s preferred policy would be extremely high. Examples of such non-pliableissues are abortion, death penalty, gun control and gay mar- 1 See among the others Austen-Smith (1993), Baron (1994), Grossman and Helpman (1994, 1996, 2001), Lohmann (1998), Coate (2003, 2004), Prat (2002a, 2002b), Felli and Merlo (2006). 2 In the 2004 presidential elections, George W. Bush and John Kerry received around 274 and 227 million dollars, respectively, from individuals and Political Action Committees contributions. Source: http://www.opensecrets.org/presidential/index_2004.asp 2 riage. 3 Therefore, whenever lobbies cannot directly a¤ect the policy outcome by inuencing politicians, they have to try to do so indirectly by targeting voters. In the US, 527 groupsconstitute a clear example of special interest groups whose activities are explicitly focused on voters. 4 Thus, the question that remains to be addressed is whether and how lobbies can create a policy distortion when they cannot directly inuence politicians. Moreover, given that media represent the main communication channel between lobbies and voters, another question arises. How are lobbiesinuence activities and me- diabiasrelated? Finally, whatistheoveralle¤ectoflobbiesandmediaonthe e¢ ciency of the political outcome and on voterswelfare? In this paper we provide a theoretical framework to investigate these ques- tions by considering an environment where lobbies do not have any direct relationship with politicians and voters acquire information through media. We analyze a multistage game where two parties compete on a single issue and voterspreferences are a combination of a private value component (their idiosyncratic preferences) and a state-dependent public value component (the expected benets and costs that alternative policies deliver in di¤erent states of the world). In the rst stage of the game, two opposing lobbies compete to inuence the information that a media outlet collects on the state of the world. The media outlet represents a lter between lobbies and the public (i.e., voters and parties): it has to decide what to communicate to people given the information it collects and its own idiosyncratic bias. That is, the 3 Matsusaka (2007) nds that the congruence (i.e., the correlation) between policy and public opinion in US states is 88% for gay marriage and higher than 70% for public funding of abortion and death penalty. 4 A 527 group is "a tax-exempt group organized under section 527 of the Internal Rev- enue Code to raise money for political activities including voter mobilization e¤orts, issue advocacy and the like.[...] Many 527s run by special interest groups raise unlimited "soft money," which they use for voter mobilization and certain types of issue advocacy, but not for e¤orts that expressly advocate the election or defeat of a federal candidate or amount to electioneering communications" (http://www.opensecrets.org/527s/types.asp) 3 mediaoutlet sreportistheresultofthreedi¤erentcomponents: thetruestate of the world, lobbiesinuence activities and the media outlet s idiosyncratic bias. Afterhavingobservedthereportofthemediaoutlet,votersupdatetheir beliefs on the state of the world. Then, in the nal stage, parties choose their platforms to maximize the number of votes. Hence, lobbies try to indirectly a¤ectthepolicyoutcomebyinuencingvotersbeliefsonthestateoftheworld (i.e., on the costs and benets of alternative policies). By providing a micro-foundation for this indirect lobbying process, our model o¤ers new insights on the e¤ects of lobbiesinuence activities and media bias on the political process. First, we show that by targeting voters special interest groups are indeed able to indirectly a¤ect the policy outcome and thus create an ex-ante policy distortion. That is, even if the policy that o¢ ce-motivated candidates choose and implement is the one preferred by a majority of voters, this policy is not the one that the median voter would have chosen if lobbies were not to engage in inuence activities. Therefore, ouranalysissuggeststhatrestrictingtheattentiononlytotherelationshipsbe- tweenpoliticiansandlobbiesmayleadtoalimitedunderstandingoftheactual impact of special interest groups on the policy outcome. Indeed, while there seems to be a general consensus on the idea of limiting the extent to which special interest groups can lobby politicians, there are yet no boundaries on howmuchlobbyistscantrytoinuencevoters. 5 Second,therearetwointrinsi- callyrelatedsourcesofslantintheinformationthatvotersreceive. Lobbies inuence activities introduce a source-drivenslant in the information that the media outlet collects (lobbies-induced slant). At the same time there is a supply drivenslant resulting fromthe idiosyncratic bias of the media outlet (media-induced slant). When the media outlet has a small idiosyncratic bias, 5 In the US, for example, the 2002 McCain-Feingold campaign nance law prohibited parties from accepting soft money but it left unregulated 527 groupsactivities. 4 there will be a unique equilibrium characterized by a large level of lobbies inuence activities (high lobbies-induced slant) and no news-slantingby the media outlet (no media-induced slant). When the media outlet idiosyncratic bias is large, the unique equilibriuminvolves a low lobbies-induced slant and a high media-induced slant (in a probabilistic sense). As a consequence, di¤er- ences in the level of lobbiesactivities and in the bias of the media outlet lead to di¤erences in votersbeliefs and thus to di¤erent policy outcomes. Hence, ouranalysisprovidesapossibleeconomicrationaletoexplaindi¤erencesinthe median voter positions across countries in presence of the same idiosyncratic preferencesofvoters. Moreoverweshowthatbydiscouraginglobbiestoengage in inuence activities, a higher media outlet s bias may lead to a lower policy distortion and a higher voterswelfare. On the other hand, our comparative statics results on the State Contingent Contest-Success Function (SCCSF) suggestthatpublicpolicymeasuresaimedatincreasingthecostoflobbiesef- forts(e.g.,aproportionaltaxonlobbying)woulddecreasethedistortioninthe policyoutcomeandhenceincreasevoterswelfare. Finally,asymmetriesinthe direction of the media outlet s bias do not generate asymmetric incentives for lobbiestoengageininuenceactivities. Viceversa,asymmetriesinlobbiesin- uence activities lead to di¤erent probabilities of news-slantingby di¤erent media outlet s types. More specically, when only the leftist (rightist) lobby is present, for a given ex-ante bias, a rightist (leftist) media outlet will have higherincentivestoslantitsreportsthanaleftist(rightist)one. Thissuggests that,inpresenceofasymmetriesbetweenlobbies,acorrectmeasureofthebias of a media outlet should take into account the equilibrium di¤erence between the ex-post slant in a media outlet s reports and the ex-ante bias of the media outlet itself. 5 1.1.1 Empirical Evidence Thereisaconsiderableamountofevidenceshowingthatspecialinterestgroups do not limit their activities to politicians but they also care about inuencing voters. In the US, lobbies use three main types of instruments to inuence voters: advocacy groups, issue advertising and think tanks. 6 According to the Center for Responsive Politics, in the 2004 election cycle advocacy groups (527 groups) spent more than 600 million dollars in trying to inuence how voters look at the issues they are interested in. In particular, ideologicalandsingleissueadvocacygroupsspentbetween400and500million dollars. 7 Issue advertisementsare ads run by political action committees (PACs), advocacy groups and other kinds of lobbies (e.g., private rms), about public policy issues (i.e., not products or candidates). Falk et al. (2006) estimate that more than 400 million dollars were spent on print and television issue advertisements just inside the Washington DC metropolitan area, between 2003 and 2004. 8 Think tanks are non-prot research organizations which analyze public pol- icy issues and advocate solutions. 9 The number and the importance of think tanks have been growing over time. Rich (2004) estimates that in 1996 there 6 In other countries (e.g., western Europe) the lobbying sectors are typically informal (i.e., not institutionalized). Thus, while there is anecdotal evidence on lobbiesinuence over voters in many countries, it is di¢ cult to know the exact amount of money spent in indirect lobbying outside the US. 7 Source: http://www.opensecrets.org/527s/527cmtes.asp?level=E&cycle=2004 8 More specically, their estimates report that 79% of the total spending in issue ads was done by corporations. Notice that, issue advertisements are not regulated under federal campaign nance laws. Thus, it is not possible to exactly quantify the amount of resources spent on this type of political expenditure. 9 Think tanks are tax exempt organizations (regulated under section 501(c)(3) of the IRS code). The main advantage of such exemption is to allow think tanks to receive unlimited contributions from private foundations. Moreover, contributions to think tanks are tax deductible. For a comprehensive description and discussion of think tankslegal status and activities see The Political Activity of Think Tanks: The Case for Mandatory Contributor Disclosure, Harvard Law Review, March 2002, 115(5): 1502-1524. 6 were 306 think tanks operating in the US. 10 While some think tanks are non- partisan,someothersengageinideologicallyorientedresearch. Asdepictedby a2002NoteoftheHarvard Law Review,thinktanksoftenprovideaplatform for particular viewpoints by packaging and popularizing policy proposals. 11 Out of the 306 think tanks listed by Rich (2004), 165 were identied as being ideologically oriented (i.e., either conservative or liberal). 12 While in the case of issue advertisingthe communication between lobbies and voters is unltered, in other instances lobbiesinuence activities are channeled through the media. 13 A clear example of such lteredcommuni- cation is media reports over think tanksresearch. While an unbiased media outlet would report the research of di¤erent think tanks in a balanced way, a biased media outlet may slant its reports by selective omitting relevant infor- mation(i.e.,emphasizetheresultsofathinktank sresearchandhidetheones ofanother). Indeed,thereisanemergingempiricalevidenceshowingthepres- ence of this kind of bias in the media. Groseclose and Milyo (2005) propose a measure of media bias by comparing the number of times a media outlet cite a think tank with the number of times members of the congress cite the same thinkthank. Theyndthat,withfewexceptions,mostofUSnewsmediaout- lets are more leftist than the average member of the congress. 14 At the same time, the recent empirical literature on media have shown that media bias matters. Thatis,mediadoinuencevotersbehavior(DellaVignaandKaplan 10 Rich also shows that the 80% of the think tanks in existence in 1996 were formed after 1970 and their number has been steadily growing over time. Other studies use di¤erent classicationofthinktanksandreportanevenhighernumberofthinktanks(e.g.,Hellebust (1996) lists 1,212 think tanks operating in 1996). 11 Source: The Political Activity of Think Tanks: The Case for Mandatory Contributor Disclosure, Harvard Law Review, 2002, page 15203. 12 See Pepper (2005) for a discussion of ideologically-oriented research on gun control. 13 The case of unlteredcommunication is formally analyzed in section 1.4.4. 14 For additional evidence on the presence of bias in the media see Gentzkow and Shapiro (2007). See also Anderson and McLaren (2007) for anecdotal evidence and a discussion on the political motivations of media corporations and how media can bias their reports by selective omitting information. 7 2006, Gerber et al. 2006). Della Vigna and Kaplan (2006) study the e¤ect of theentryofFoxNewsinthecablemarketandtheyndthatbetween3to8 percentofitsviewerswereindeedconvincedtovoteRepublican. Gerberetal. (2006) conduct a natural eld experiment to measure the e¤ect of exposure to the Washington Times and Washington Post in the month before the 2005 Virginia Gubernatorial election. They nd that individuals assigned to the Washington Post treatment group were eight percent more likely to vote for the democratic candidate than those belonging to the control group. 15 This emerging empirical literature is, thus, highlighting the importance of consid- ering and analyzing in our theoretical framework, the presence of biased news media acting as a lterbetween lobbies and voters. 1.1.2 Related Literature The economic literature seems to have largely overlooked the issue of grass- roots activities and special interestsinuence on voters. 16 The papers that are most closely related to our work are Baron (2005) and Yu (2005). Baron (2005) considers a model of hard information where an activist lobby and an industry search for evidence on the true state of nature, and if they nd such information they have to decide whether to conceal it or report it to the me- dia. Baron shows that the activist lobby has an incentive to conceal while the industry does not, moreover the media will nd optimal to bias its report in favorofthepolicypreferredbytheactivistlobby. Thismodel,whileanalyzing a more complex structure of the media market, restricts lobbiesstrategic de- cisions to be binary (conceal/not conceal) while we construct a more general 15 Foradditionalevidenceonthee¤ectofmediaonpolicy-makingseeBesleyetal. (2002), and Stromberg (2004b). 16 The rst contribution looking at this issue is Grossman and Helpman (2001). In their model a lobby wants to educate the public by sending a costless message. They show that the median voter is likely to be harmed by such communication whenever her preferences are not close to the ones of the lobby. 8 (and symmetric) framework where lobbiesinuence activities are a continu- ous function of the incentives structure of the game and in particular of the idiosyncratic bias of the media. Moreover, such framework allows us to derive adirectmeasureofthepolicydistortionarisingfrominterestgroupsinuence activities and media bias and then analyze the e¤ects of such distortion on voterswelfare. InYu(2005),lobbiescompetebyinuencingbothpoliticiansandvoters. Yu showsthatsuchinuenceactivitiesarecomplementary. Moreover, anincrease in the e¤ectiveness of voterspersuasion or awareness induces a substitution e¤ectbetweentheinuenceactivitiestargetedtopoliticiansandtheoneaimed towards voters. However, contrary to our work, Yu assumes an exogenous relation between votersposterior beliefs and lobbiese¤orts and does not analyze the role played by media. Our paper is also related to the literature on media bias. This literature has,sofar,identiedtwodi¤erentforcescreatingabiasinmediareports. The rst one is a supply-drivenone: media bias is the result of the idiosyncratic preferences of journalists (Baron 2006), owners, editors (Djankov et al. 2003, Anderson and McLaren 2007), governments (Besley and Prat 2006) or adver- tisers(EllmanandGermano2007). Thesecondoneisademand-drivenbias. Part of this literature assumes that voters like to receive information conrm- ingtheirbiasandthusmediajustreectandconrmthebiasoftheiraudience (Mullainathan and Shleifer 2005, Bernhardt et al. 2006). On the other hand, Gentzkow and Shapiro (2006) show that even when voters do not like biased information, if media have reputation concerns and there is uncertainty on the quality of the media, a bias towards consumer prior beliefs will arise in equilibriumeveninabsence of anyexogenous mediabias. Ourmodel suggests that even when media do not have any biased preferences or any incentive to produce biased reports, their reports may still be biased since the information 9 they collect may be biased itself. That is, there is a source-drivenbias in mediareportsduetothedistortionininformationcreatedbylobbiesinuence activities. Finally, our paper is related to the literature on cheap-talk where the Re- ceiver is uncertain about the Sender s preferences. 17 Our model considers an environment where the Receiver (voters and parties) does not know whether the Sender (media outlet) is biased and at the same time does not know the direction of the possible bias. Moreover, the probability distribution of the signal that the Sender receives on the state of the world is also endogenously dependentonthesizeandprobabilityofitsbias. Weshowthatdi¤erenttypes of informative equilibria may arise depending on the size of the bias and on the probability of the Sender being biased. Thischapterisorganizedasfollows. Section1.2describesthestructureand timing of the game. Section 1.3 analyzes the interactions among the media outlet, voters, parties and lobbies. Section 1.4 derive the perfect Bayesian equilibria of the game and discuss the results of the model. Section 1.5 in- troduces a characterization of the competition between lobbies and derives a closed form solution for the di¤erent equilibria of the game. Section 1.6 dis- cusses some extensions to the basic model. Section 1.7 concludes. All the proofs are provided in Appendix A1. 1.2 The Model The political process involves a single issue or policy P. Without loss of generality we assume the policy space to be = [0;1]: The political system is characterized by two o¢ ce-motivated parties L and R that choose their platforms, P L and P R respectively, in order to maximize their votes. There 17 See Morris (2001), Morgan and Stocken (2003), Li (2004) and Dimitrakis and Saradis (2005). 10 are two possible states of the world s2 fA;Bg: The prior probability of the stateoftheworlds =Aisassumedtobecommonknowledgeanditisdenoted by : There is a continuum of voters of measure one with quadratic utility func- tion: U i (P;d i ) =(P d i ) 2 (1) Voteri policypreferenced i isacombinationofaprivatevaluecomponentand a state-dependent public value component, i.e., d i (x i ;v) =x i +v; where v = 8 < : if s =A if s =B (2) The private value component x i represents the idiosyncratic policy preference of voter i. The state-dependent public value component v captures the fact that, regardlessoftheiridiosyncraticpolicypreferences, votersvaluethecosts and benets that di¤erent policies deliver in di¤erent states of the world. In other words, by convention, if the state of the world is A then the public benets of a policy P = 0 are assumed to be higher than the public costs and asP increasesthebenetsdecreaseandthecostsincrease(viceversa ifs =B). Thatis,ifthestateoftheworldisAindividualsprefer,ceterisparibus,apolicy closer to the left end of the political space. Instead if the state of the world is B individuals prefer a policy closer to the right end of the political space: 18 Theparameter measurestheimportanceofthestate-dependentpublicvalue component in individualsutility functions. The private value component of voter i s preferences, x i ; can be seen as the policy that voter i would choose 18 This specication of the votersutility function is similar to the one of bidders in an a¢ liated value auction. In the same way the valuation of the object is correlated across bidders in an a¢ liated value auction, the valuation of the policy is correlated across voters in our setting. 11 if she were to believe that both states of the world are equally likely. 19 Such idiosyncratic preferences are distributed with a common knowledge c.d.f F(x) with density function f(x). Without loss of generality we restrict the support off(x)tobe[ ;1 ];sothattheex-ante supportofvoterspolicypreferences is (i.e., suppf(d i ) = [0;1];8i). 20 We denote the median of f(x); that is the idiosyncratic preference of the median voter, as x m : Anexamplewillhelpclarifythemeaningofthisvoter sutilityspecication. Suppose the issue on which voters have to decide is whether to implement or not the Kyoto s Protocol. Let the states of the world be A =strong ef- fects of pollution on global warmingand B =mild e¤ects of pollution on global warming. Each voter has some idiosyncratic preferences about the importance of protecting the environment. Nevertheless, in order to choose her optimal policy, each of them will also take into account the information she receives on the likelihood of the state of the world. For example, if voters receive (credible) reports saying that pollution does not have a strong impact on global warming (s = B), each of them will revise downward her idea of the benets deriving from the Kyoto s protocol. Instead, if voters receive the opposite report they would revise upward their beliefs on the importance of implementing the Kyoto s protocol. Figure 1 below, illustrates an example of the distributions of voterspolicy preferences in the two polar cases where there is no uncertainty regarding the state of the world (i.e., Pr(s = A) = 1 19 Notice that having a more general specication of votersutility functions would not change our results in any signicant way. For example as an alternative specication we could have the following: d i (x i ;v) = (x i ) v ; with v = if s =A 1= if s =B and the support of f(x) being [0;1] and 1: That is the policy preferences of more centrist voters would have a higher correlation with the true state of the world with respect to the ones of more extremistsones. Notice also that the presence of stubbornvoters (i.e., voters whose preferences are not state-contingent), would not change our results. 20 Note that for ! 0; we are in a pure private value setting. Viceversa, if ! 1 2 we are in a pure public value environment. We are going to focus our attention on the general case where 2 (0; 1 2 ): 12 and Pr(s =B) = 1). 21 f(d i |Pr(s=B)=1) x m +γ (No ratification of Kyoto’ s protocol) 1 (No regulation of industry) x m γ (Full implementation of Kyoto’ s protocol) 0 (No pollution allowed) f(d i |Pr(s=A)=1) Figure 1.1: Distribution of voterspreferences with no uncertainty. There is one media outlet whose quadratic utility function is: U n (P;d n ) =(P d n ) 2 (3) where d n contains a private value component and a state-dependent public value component, i.e., d n (' n ;v) = ' n +v; where v is dened as in (2). The idiosyncratic preference parameter ' n takes values in =f' l ;' 0 ;' r g and is private information of the media outlet. We assume the following ordering of the possible media outlet idiosyncratic preferences: Assumption 1. ' l <' 0 =x m <' r x m ' l =' r x m That is if the media outlet has idiosyncratic preferences ' l (' r ) it prefers a more leftist(rightist) policy than the median voter. On the other hand, 21 Clearly, in presence of uncertaintythedistributionofvoterspreferencewillbeaconvex combination of such two extremedistributions. 13 a media outlet of type' 0 has preferences over policies equal to the median voter s ones. More specically, in the following analysis a media outlet will be said to be unbiasedif ' n =' 0 : 22 A media outlet will be said to be leftist (rightist) if ' n = ' l (' n = ' r ): Moreover, we assume the possible bias of the leftist and rightist media outlet types to be symmetric. The probability distribution of the media outlet s preferences, g(' n ); is common knowledge and it is such that Pr(' n =' l ) = Pr(' n =' r ) =y. That is, the media outlet is unbiased with probability (1 2y) and has instead a bias j' n x m j in a direction or another with probability y. 23 It is important to point out that the fact that the media outlet is just a political actorin our model (i.e., it is not explicitly maximizing prots) is without loss of generality. If the media outlet was a prot maximizer, given that in our model voters value unbiased information, it would have a strictlydominantstrategyofnotslantingitsreports. Themodelwouldthusbe equivalenttothecasewherethemediaoutletisunbiasedwithprobabilityone. Ontheotherhand,ifthemediaoutletwasmaximizingprotsandatthesame timeithadapoliticalagenda,thenitwouldcarebothaboutthetruestateof theworld(whichisreectedinthestate-contingentpublicvaluecomponentof its utility function) and about its idiosyncratic preferences (which is reected in the private value component of its utility function). Thus we can think of our specication of the media outlet utility function as a reduced form of a modelwherethemediaoutletisaprotmaximizerandatthesametimeithas (possibly)anexogenousbias. Sincewearemainlyinterestedonhowthemedia 22 Notice that our results would not change assuming the presence of an unbiased media outlet with a purely public valueutility function. That is, we could have dened as unbiaseda media outlet with no idiosyncratic preferences, thus having preferences d 0 = 0 if s =A 1 if s =B ; That is our denition of unbiased media outlet does not have to be rely on the median voters idiosyncratic preferences. 23 Similarly to what we have specied regarding the distribution of votersidiosyncratic preferences, we assume that supp g(' n ) = [ ;1 ]: Nevertheless, notice that our results would generalize to the case where supp g(' n ) = [0;1]. 14 outlet s bias interacts with the endogenous bias arising fromlobbiesinuence activities, we will consider the media outlet preferences, and hence the media outlet s bias, as exogenous. Following the literature on media bias we can think of such exogenous bias as just arising from journalists, editors, owners oradvertisersidiosyncraticpreferences(e.g., Djankovetal. 2003, Baron2006, Anderson and McLaren 2007, Ellman and Germano 2007). 1.2.1 The game There are two lobbies a and b who, by exerting e¤orts e a and e b respectively, competetoa¤ectthedistributionofabinarysignalz i 2fz a ;z b gthatthemedia outlet receives on the state of the world. Lobbies a and b s bliss points are a and b ; respectively. We assume lobbiespreferences to be extreme, a = 0 and b = 1: That is lobby a always prefers a policy close to the left-hand side ofthepoliticalspaceregardlessofthestateoftheworldandsimilarlybalways prefersapolicyclosetotheright-handsideofthepoliticalspace. Then, lobby i quadratic utility function is: W i (P; i ;e i ) =(P i ) 2 C(e i ) (4) Where C is the cost function of e¤ort, which is assumed to be linear (i.e., C 0 (e) =c> 0): 24 The likelihood of the signal z i 2 fz a ;z b g received by the media outlet de- pends on the true state of the world and on lobbiesinuence activities. We can interpret this as a situation where both lobbies spend resources to pro- duce favorable evidence. The signal can be seen as a reduced form of media outlet s investigative journalism. In other words, the signal that the media outlet receives can be interpreted as indicating whether the evidence that it 24 Notice that considering a convex cost function, C 0 > 0; C 00 > 0; would not change our results. 15 collectedinfavorofastateoftheworldisstronger thantheoneinfavorofthe other state. As we have pointed out in the previous section, from a public valueperspective in both states each policy has costs and benets, however the amount of such costs and benets di¤er in the two states of the world. Thus lobbies are able to produce evidence on the benets and costs of each policy in both states. Indeed for many issues we have mixedevidence on the e¢ ciency of a given policy (e.g., the costs and benets of implementing the Kyoto s protocol, the e¤ectiveness of death penalty in preventing crime, the e¤ects of gun control on citizenssecurity and so on). At the same time, the truthplays a role in this evidence production process. That is, ceteris paribus, the lobby on the correctside is more likely to produce stronger evidence in its favor. More specically, the probability that the media outlet receives the correctsignal in a given state of the world is characterized by the following functions: h a (e a ;e b ;) = Pr(z a js =A;e a ;e b ;) (5) h b (e a ;e b ;) = Pr(z b js =B;e a ;e b ;) (6) where the parameter denotes the importance of the truthin this game. In other words, the higher is the greater the likelihood that the evidence in favor of the true state of the world will be stronger than the one in favor of the other state. 25 The assumptions on the properties of the signal probability function h i (e i ;e j ;) are summarized by Condition 1. 26 25 How much stronger such evidence will be depends on the specic issue. We can think that issues where the di¤erence between the cost-benet ratio of the "bad" policy and the one of the "good" policy is very high are the ones were the evidence in favor of the correct state of the world is likely to be much stronger. These are the issues where is likely to be large (notice that also is likely to be large since voters would probably care more about knowing the true state of the world). 26 Section 1.5 provides a characterization of a signal probability function satisfying this condition. 16 Condition 1 For 8i;j 2fa;bg such that i6= j; h i (e i ;e j ;) and h j (e i ;e j ;) are assumed to satisfy the following properties: i) h i (~ e; e;) =h j ( e;~ e;); 8 e;~ e ii) h i (e i ;e j ;)> 1h j (e i ;e j ;) iii) @h i @e i > 0; @h i @ > 0; @h i @e j < 0 iv) @ 2 h i @ 2 e i @ 2 h i @ 2 e j < 0 v) @h i @e i e i =e j < @h i @e j e i =e j Property i) is just a symmetry assumption on the signal probability func- tions. Property ii) requires the signal to be informative. 27 Property iii) is a straightforward necessary condition to have an interior solution. Property iv) signies decreasing marginal productivity of e¤ort. Finally, property v) implies that, when lobbies exert the same e¤ort, an equal increase in their e¤orts increases the noiseof the signal. 28 Afterhavingreceivedthesignal,themediaoutletdecidesuponthe(costless) message m n 2 fm a ;m b g to send to the public (voters and parties). 29 Given thismessage, votersupdatetheirbeliefsonthestateoftheworldaccordingto Bayesrule. That is, they discount for the possible slant present in the media outlet sreportarisingfromlobbiesinuenceactivitiesandmediaoutlet sbias. Parties L and R take into account the e¤ect that media outlet s report has on votersbeliefs and then choose their political platform to maximize the number of votes. In the last stage of the game, voters choose their most 27 Notice that property i) and ii) imply that h i (e;e;) =h j (e;e;)> 1 2 28 That is for e i =e j =e, denoting h i (e;e;) =h j (e;e;) =h; given that is constant, it must be the case that: dh(e;e;) de < 0: 29 It could appear restrictive to have a message space with just two elements given the uncertainty on media outlets type. However, given that there are just two states of the world and the media outlet can receive just two signals, votersuncertainty is just relative to such signals. For a similar cheap-talk model where there is uncertainty on the senders type see Morris (2001). 17 preferred policy between the platforms proposed by the parties. The timing of the game is summarized below: Lobbiesa andb exert e a and e b The media outlet observes z a or z b and sends m a or m b to voters and parties Voters and parties observe m n and update their beliefs PartiesL and R announce P L and P R Voters cast their ballot.Winning policy is implemented and payoffs are realized Nature decides s=A ors=B and φ n. Figure 1.2: Timing of the game In what follows, we will refer to media outlets bias as the di¤erence be- tween the media outlet and the median voter idiosyncratic preferences (i.e., j' n x m j). We will denote as information slant the noise in the information that agents receive due to the presence of media outlet s bias and/or lobbies inuence activities. Finally, we will indicate as policy distortion the di¤erence between the policy outcome with and without information slant. Wenowturntotheanalysisof thestrategicinteractions amonglobbies, the mediaoutlet,votersandpartiesandthenderivethepropertiesoftheequilibria of the game. 1.3 TheInteractionsamongLobbies,theMediaOutlet, Voters and Parties Sincelobbiese¤ortsareunobservable,wemustsolveforarationalexpectation equilibrium (REE) in which the media outlet, voters and parties correctly anticipate the optimal level of e¤ort exerted by lobbies in equilibrium and all playersstrategies maximize their expected utilities given their beliefs. A rational expectation equilibrium of this game is a perfect bayesian equi- librium. In the last stage voters update their beliefs according to Bayesrule, choosetheirmostpreferredpolicyandvotefortheplatformclosertoit. Parties 18 anticipate such behavior and propose platforms that maximize their chances of winning. The media outlet chooses its optimal strategy taking into account howthemessagethatitisgoingtosendtothepublic(votersandparties)will a¤ect the policy outcome. Finally, lobbies anticipating all such interactions decide upon the e¤ort to exert in order to try to inuence the beliefs that voters will hold on the state of the world. 30 1.3.1 Voters Given the message received by the media outlet, m n 2fm a ;m b g; voters form their posterior beliefs using Bayesrule and then decide their preferred policy platform. Thus, voters have the following expected utility: U i (x i ;m n ) = Pr(s =Ajm n ) (P (x i )) 2 +Pr(s =Bjm n ) (P (x i + )) 2 (7) Thusthepolicythatmaximizesvoteri sexpectedutilityisP i (m n ) = argmax P U i (x i ;m n ) that is: P i (m n ) =x i + [12Pr(s =Ajm n )] (8) Individuals will, thus, simply vote for the proposed platform that is closer to their preferred one. As usual, we assume that when the voter is indi¤erent between the two platforms, she simply randomizes between voting for partyL and party R: 31 30 Notice that we do not have to care here about out-of-equilibria beliefs simply because in such REE none would be able to change the other playersbeliefs by deviating from their optimal strategy. 31 Abstention is not allowed. However, given that voting is costless and all voters receive the same information there would be no strategic abstention here. Moreover, even in pres- ence of a positive cost of voting, our model would still apply to the portion of population that would turnout in equilibrium (i.e., the median voter policy would be dened on the subset of voters). 19 Thusdenotingasr i (P L ;P R )theprobabilitythatindividualivotesforparty L given the set of proposed platforms by the two parties, we have that a strategy for a voter is a function: r i :P P ! 0; 1 2 ;1 1.3.2 Parties Since the median voter is going to be pivotal in this model, parties platforms will simply converge to the expected median voter position: In other words, parties L and R both know that given message m n ; the policy platform that maximizesthemedianvoter sexpectedutilityisP m (m n ) = argmaxU m (P;x m ;m n ); where U m (P;x m ;m n ) is the median voter s expected utility. That is: P m (m n ) =x m + [12Pr(s =Ajm n )] (9) ThusP L (m a ) =P R (m a ) =P m (m a )andP L (m b ) =P R (m b ) =P m (m b ):Inother words,bothpartiesplatformsconvergetotheexpectedmedianvoterpreferred policy and they both have probability of winning equal to 1 2 . 32 Notice that, in anyequilibriumwherethemessagessentbymediaoutletareinformative,such platforms are going to be contingent on the specic message that the public (voters and parties) receives. 33 32 Thefactthatpartiesarejusto¢ ce-motivatedandconvergetothemedianvoterposition is without loss of generality. Having parties that are both policy-motivated and o¢ ce- motivated would not change our results in any signicant way. 33 Again, using our example on the Kyotos protocol, this means that parties will choose platforms more or less in favor of the protocol, depending on the message sent by the media outlet. Parties know that if the media outlet sends a (credible) message stating that pollution has strong e¤ects on global warming, ceteris paribus, voters will be more likely to vote for a policy in favor of Kyotos protocol. 20 1.3.3 The Media Outlet The media outlet acts as a lterin this game. The private cost that any individual should bear in order to acquire direct information is assumed to be higher than any private benet. Hence, voters rely on media to receive information on a given issue. 34 The expected utility for a media outlet having idiosyncratic preferences ' n is: U n (' n ;z i ;P) = Pr(s =Ajz i ) (P (' n )) 2 +Pr(s =Bjz i ) (P (' n + )) 2 Themediaoutletobserves thesignal onthestateof the worldandupdates its beliefs according to Bayesrule. It then decides on the message to be sent to voters. Since the media outlet has rational expectations, its posterior beliefs uponreceivingsignalz a orz b dependontheexpectede¤ortthatlobbiesexert, ^ e a and ^ e b : Therefore the media outlet posterior beliefs are as follows: Pr(s =Ajz a ) = h a (^ e a ;^ e b ;) h a (^ e a ;^ e b ;)+(1h b (^ e a ;^ e b ;))(1) Pr(s =Ajz b ) = (1h a (^ e a ;^ e b ;)) (1h a (^ e a ;^ e b ;))+h b (^ e a ;^ e b ;)(1) The interaction between the media outlet and voters assumes here the typical structure of a cheap-talk game. Denote the signal space as Z =fz a ;z b g and the message space as M = fm a ;m b g: 35 The media outlet will choose the 34 We believe that this assumption is realistic. Any single individual would nd too costly to read the Kyoto protocol and evaluate whether its costs are higher than the benets or not. The opportunity cost or simply the knowledge required to analyze such information would far exceed any private benet. News media thus constitute the most e¢ cient (even though not perfect) way to acquire information for any single citizen. 35 Given that this is a cheap-talk game, messages are going to be meaningful only ex-post. We can think that a possible "ex-post" interpretation of the message space could be given by the posterior beliefs of the news media outlet. Thus message m a may indicate that the news media has collected information more in favor of state A and m b is instead indicating that the news media outlet has found information more in support of s =B: 21 message to be sent to voters in order to maximize its expected utility. The media outlet can slant its reports by selectively omitting relevant information (i.e., emphasize the benets and hide the costs of a given policy). In this way the media outlet is able to slant the evidence collected and send the message that will make the median voter choose a policy as close as possible to its preferred policy P ' n (z i ): Where P ' n (z i ) is simply the policy that maximizes U n (P;' n ;z i ); that is: P ' n (z i ) =' n + [12Pr(s =Ajz i )] (10) The, possibly mixed, strategy for a media outlet with preferences ' n is a mapping from the signal space into a probability distribution over the set of possible messages: (' n ) :Z ! (M) Where is the space of probability distribution over the message space M: More specically, a media outlet with preferences ' n can have two di¤er- ent kinds of pure strategies, pooling or separating respectively. We will say that a media outlet with preference ' n plays a pooling strategy if (' n jz a ) = (' n jz b ) = m : Instead, a media outlet with preference ' n is said to play a separating strategy if (' n jz a ) = ^ m and (' n jz b ) = ~ m; with ~ m 6= ^ m: A mixed strategy will simply specify the probability that a media outlet plays a separating strategy. Let s start classifying our possible equilibria as informative and uninforma- tive. In an uninformative equilibrium the public (voters and parties) is not goingtolearnanythingaboutthestateoftheworld. Wehavetwokindsofun- informative equilibria that we are going to dene as completely uninformative and state uninformative: Denition 1 Anequilibriumissaidtobecompletelyuninformativeif 8' n 2 22 ; (' n jz a ) = (' n jz b ) = m : An equilibrium is said to be state uninforma- tiveifeverypossiblemediaoutlettypeisplayingapoolingstrategybut9' n ;' h 2 with ' n 6=' h such that (' n )6=(' h ) Itisveryeasytoseehowourcompletelyuninformative equilibriumisnothing elsethanthebabbling equilibriumofthisgame,whichalwaysexistsinacheap- talk game. An equilibrium is a state uninformative equilibrium if all media outlet types adopt a pooling strategy but these strategy is di¤erent across media outlet types. That is, at least two di¤erent media outlet types pool on di¤erent messages. Notice that the state uninformative equilibrium could not be considered a proper babbling equilibrium. Even though in a state uninformative equilibrium the receivers (voters) do not learn anything about the state of the world, they will still learn something about the sender s type (mediaoutletpreferenceparameter),eventhoughtheydonotcareaboutsuch information in this setting. 36 Indeed any state uninformative equilibrium is going to be an equilibrium here since, as for the babbling equilibrium, voters willignorethemediaoutlet smessageandthusmediaoutletwillnothaveany incentive to change its strategy. There are three possible kinds of informative equilibria: two pure strat- egy equilibria (partially informative, maximally informative) and one mixed strategy equilibrium (semi-separating). Denition 2 An equilibrium is said to be partially informativeif 9' n 2 such that (' n jz a ) = (' n jz b ) and 9' h 2 with ' h 6= ' n such that (' h jz a )6= (' h jz b ): An equilibrium is said to be maximally informativeif 8' n 2 ; (' n jz a )6=(' n jz b ): Thatisinapartiallyinformative equilibriumsomemediaoutlettypeschoose 36 Notice that in a repeated game, such information could instead be valuable to voters. Nevertheless, the incentives of lobbies to exert e¤ort would not change and so the main results of our model (see section 1.6.1). 23 a pooling strategy and some others adopt a separating strategy. From these denitions,itisclearthattheonlymaximally informative equilibrium(thatis the one where all agents in our economy have the same information regarding the state of the world and thus share the same beliefs) is the one where all media outlet types play a separating strategy. Denition 3 An equilibrium is said to be semi-separatingif9' n 2 such that, for p;q2 [0;1]: (' n jz a ) = 8 < : m a with prob. q m b with prob. (1q) ; (' n jz b ) = 8 < : m a with prob. p m b with prob. (1p) Clearly for p;q 2 f0;1g; a media outlet with idiosyncratic preferences ' n plays a degenerate mixed strategy and the semi-separating equilibrium con- verges to a pure strategy equilibrium. The following lemma provides a characterization of the possible types of symmetric informative equilibria that can arise in this cheap-talk subgame. Lemma 1 9~ '; ' l 2 [ ;1 ] such that: i) For all ' l < ~ ' l ; there exists a partially informative equilibrium where the leftist media outlet type pools on m a ; the rightist media outlet type pools on m b and the unbiased media outlet type adopts a separating strategy. ii) For all ' l > ' l ; there exists a maximally informative equilibrium where the leftist and the rightist media outlet types adopt the same separating strategy of the unbiased media outlet type. iii) If ' l > ~ ' l ; for all ~ ' l < ' l < ' l there exists a semi-separating equi- librium where the leftist media outlet type sends message m a upon receiving signal z a and sends m a with probability q and m b with probability (1q) upon receiving signal z b , the rightist media outlet type sends message m b upon re- ceivingsignalz b andsendsm b withprobabilityq andm a withprobability (1q) 24 upon receiving signal z a and the unbiased media outlet type adopts a separating strategy. That is, ~ ' l and ' l represent the leftist media outlet no-deviation thresh- oldsinapartially informative andmaximally informative equilibrium, respec- tively. 37 Theabovepropositionisthusshowingthattheunbiasedmediaoutlet type will never try to deceivethe median voter by sending out a message thatwouldinduceherbeliefstoberevisedinadirectionoppositetothemedia outlet sones. Moreover,uponreceivingasignalfavorabletothelobbyoftheir side, the two biased media outlet types do not have any incentive to slant their reports. Thus which equilibrium will ultimately arise in this cheap-talk subgame depends on whether the biased media outlet types will nd optimal to adopt a separating strategy, send the same message regardless of the signal received or mix between a separating and a pooling strategy. 38 AppendixA2containsadiscussionandcharacterizationoftheseequilibria. 39 Assection1.4.1willshow, thesizeofthemediaoutlet sidiosyncraticbiasand the endogenous level of e¤ort exerted by lobbies will, ultimately, determine which of these equilibria will arise. 1.3.4 Lobbies Lobbiesanticipatethattheplatformthewinningpartywillimplementinequi- librium is the one that maximizes the median voter s utility. That is, lobbies know that the equilibrium policy will depend on votersposterior beliefs and thus on the message of the media outlet. Since voters have rational expecta- tionstheirposteriorbeliefsuponreceivingmessagem n dependontheexpected 37 Symmetric no-deviation thresholds exist for the rightist media outlet. 38 Note that restricting the media outlet to always send a message is without loss of generality. Allowing the media outlet to not send any message would not change our results inanysignicantway. Aformalanalysisofthiscaseisavailableuponrequesttotheauthor. 39 A formal characterization of the other two possible asymmetric equilibria that could emerge in this symmetric game is available upon request to the author. 25 e¤ort that lobby a and b exert in a given equilibrium, ^ e a and ^ e b respectively. Inotherwords, themedianvoter spolicyisafunctionofsuchexpectede¤orts levels: P m (m n ;^ e a ;^ e b ) =x m + [12 (s =Ajm n ;^ e a ;^ e b )] (11) Thus from lobbiesex-ante perspective, conditional on the media outlet mes- sage, theimplementedpoliciesarenota¤ectedbytheire¤ortdecision. There- fore, lobbieschoosetheire¤ortsinordertoinuencethesignalthatthemedia outlet receives and hence the message that voters get. In other words, lob- biesexpectedutilitiesdependontheexertede¤orts(whicha¤ect Pr(m a ) and Pr(m b ))andontheexpectede¤orts(whicha¤ectthemedianvoter spreferred policy). Thus, from (4) lobby a and lobby b expected utilities are: W a (e a ;e b ;^ e a ;^ e b ;) = Pr(m a je a ;e b ;)(P m (m a ;^ e a ;^ e b ;)) 2 (12) Pr(m b je a ;e b ;)(P m (m b ;^ e a ;^ e b ;)) 2 C(e a ) W b (e a ;e b ;^ e a ;^ e b ;) = Pr(m a je a ;e b ;)(1P m (m a ;^ e a ;^ e b ;)) 2 (13) Pr(m b je a ;e b ;)(1P m (m b ;^ e a ;^ e b ;)) 2 C(e b ) In their optimization problem lobbies take into account that the nal policy outcome,P m ;willdependonwhichmessagevoterswillreceivefromthemedia outlet. Moreover,lobbiesanticipatethatsuchmessagedependsonthepossible mediaoutlet sbiasandtheirexpectede¤orts. Thuseachlobbyfacesadi¤erent optimization problem depending on whether it is expecting the equilibrium of the cheap talk game between media outlet and voters to be a partially informative, semi-separating or maximally informative equilibrium. 26 1.4 Informative Equilibria We now derive and characterize the possible equilibria of our game. Since we focus on symmetric equilibria, from now on we assume = 1 2 and x m = 1 2 : 1.4.1 Symmetric Equilibria Let s analyze the optimal strategies of lobbies. From (11) and (12) lobby a optimality conditions in a maximally informative, partially informative and semi-separating equilibrium respectively, are: V MI a = @h a @e a @h b @e a MI (s =Ajm a ) MI (s =Ajm b ) c = 0 (14) V PI a = (12y) @h a @e a @h b @e a PI (s =Ajm a ) PI (s =Ajm b ) c = 0 (15) V SS a = (12qy) @h a @e a @h b @e a SS (s =Ajm a ) SS (s =Ajm b ) c = 0 (16) Where MI (s = Ajm a ) represents votersposterior beliefs in a maximally in- formative equilibriumgiventhattheyreceivedmessagem a andq istheproba- bilitythatabiasedmediaoutletslantsitsreportsinasemi-separating equilib- rium. 40 Notice that for q! 1; the optimality condition of the semi-separating equilibrium degenerates into the one of the partially informative equilibrium. Viceversa, for q ! 0; this optimality condition converges to the one of the maximally informative equilibrium. 41 Appendix A contains a detailed deriva- 40 A similar interpretation applies to PI (s =Ajm n ); SS (s =Ajm n ); for8m n 2M: 41 Notice that8q2 [0;1] the second order condition is: (12qy) @ 2 h a @ 2 e a @ 2 h b @ 2 e a SS (s =Ajm a ;^ e SS a ;^ e SS b ) SS (s =Ajm b ;^ e SS a ;^ e SS b ) < 0 by condition 1. Thus the stationary point is a global maximum. 27 tion of these FOCs. 42 The rst necessary step to understand the interactions betweenlobbiesinuenceactivitiesandmediaoutlet sbiasistocomparelob- biese¤orts across equilibria. Let e PI ;e SS and e MI be the level of e¤ort that lobbies a andb exert in a symmetric PI;SS andMI equilibriumrespectively. Then we have the following lemma. Lemma 2 Lobbies exert a lower e¤ort in an equilibrium where they expect the media outlet to bias its report with a higher probability. Hence, e PI <e SS <e MI Moreover: @e SS @q < 0 and lim q!0 e SS =e MI ; lim q!1 e SS =e PI Therefore, the greater the likelihood that the media outlet adopts a pooling strategy, the lower the incentives of lobbies to engage in inuence activities. Indeed, from an ex-ante perspective when the media outlet chooses to disre- gard the information it collects (i.e., the signal it receives on the state of the world), lobbies would just waste resources in trying to inuence such informa- tion (i.e., signal). Viceversa, when the media outlet does not bias its report and sends a message according to the signal it receives (maximally informa- tive equilibrium),lobbieshavestrongincentivestoexerte¤orttoinuencethe distribution of this signal. The second step is to determine how the media outlet s incentives to slant its report change as a function of lobbiese¤orts. Lemma 3 The media outlet incentives to slant its reports are increasing in 42 Aformalderivationandanalysisoflobbiesaandbsreactionfunctionsisavailableupon request to the author. 28 lobbiesexpected e¤orts. Hence: ~ ' l < ' l The higher the lobbiesexpected e¤orts the higher (in a probabilistic sense) the slant that the media outlet will introduce in its report. Moreover, by rational expectations, in equilibrium the expected e¤ort will be equal to the e¤ort exerted by lobbies. Therefore, since the higher the e¤ort exerted by lobbies the more noisythe signal that the media outlet receives, we can interpret this result as telling us that the more controversialand unclear the information that media outlet collects are, the greater the likelihood that the media outlet will slant such information. 43 When instead lobbies do not engage in inuence activities (i.e., e a = e b = 0), the media outlet receives the correctsignalwithhighprobabilityandthusitwillslantsuchinformationonly when it has very extreme preferences. 44 Therefore, since from lemma 2 we know that e PI <e MI the above reasoning implies that the leftist media outlet no-deviation threshold in a PI equilibrium is lower than the one in a MI one (i.e., ~ ' l < ' l ). Hence, lemma 1, 2 and 3 are showing that the cheap-talk game, and therefore the lobbying game, has a unique informative equilibrium depending on howlarge the possible bias of the media outlet is. We thus have the following proposition characterizing the possible types of equilibria of the 43 It is interesting to reinterpret this result in the case where the media outlets idiosyn- craticpreferencesderivefromtheadvertisersones(seeEllmanandGermano2007). Lemma 3 is suggesting that in order to be more likely to be successful in inuencing the media out- lets reports, advertisers should also try to a¤ect the signal that the media outlet receives on the state of the world. In this way, advertisers would increase the noise in the signal and thus increase the media outlets incentives to slant its reports according to the advertisers idiosyncratic preferences. 44 For example assuming that h i (0;0;) = 1 and that x i is uniformly distributed, then for = 1 4 the leftist media outlet will never slant its report upon receiving message z b (since ' l = 1 4 = andhence' l alwaysgreaterthan ' l ):Thesamereasoningappliesfortherightist media outlet. Notice that such result hold in our cheap talk setting and thus it abstracts from any cost of slanting information. 29 game: Proposition 1 For any given set of media outlet idiosyncratic preferences, there is a unique informative equilibrium. More specically: i) If ' l 2 [ ' l ;x m ] there is a unique maximally informative equilibrium where each biased media outlet type adopts a separating strategy and lobbies exert e¤ort e MI . ii) If ' l 2 (~ ' l ; ' l ) there is a unique semi-separating equilibrium where each biased media outlet type adopts a mixed strategy and lobbies exert e¤ort e SS . iii) If ' l < ~ ' l there is a unique partially informative equilibrium where each biased media outlet type pools on the message most preferred by the lobby on its side and lobbies exert e¤ort e PI : Thefollowinggraphillustratesthepossibleequilibriathatcanarisedepend- ing on where the media outlet s idiosyncratic preferences lie: SemiSeparating Equilibrium (Medium lobbies’ efforts) r φ ~ l φ ~ I l φ r φ 1 γ γ SemiSeparating Equilibrium (Medium lobbies’ efforts) Partially Informative Equilibrium (Low lobbies’ efforts) xm Maximally Informative Equilibrium (High lobbies’ efforts) Partially Informative Equilibrium (Low lobbies’ efforts) Figure 1.3: Media Bias and Informative Equilibria. Therefore, the higher the possible bias of the media outlet, the lower the equilibrium level of e¤ort that lobbies will exert. Indeed, if the media outlet turnouttobestronglybiasedintheoppositedirectionofthelobby,nomatter how much e¤ort the lobby is going to exert and whether it is lobbying for the e¢ cient policy or not, the media outlet will always send a message that drives voters induced preferences further from the lobby s optimal policy. Moreover, 30 even if the media outlet turn out to be strongly biased in favor of the lobby s optimal policy, lobby s e¤ort would be totally worthless by virtue of being unnecessary. Inthiscase,itwillbethemediaoutletthatwilltakecareoftrying to inuence votersbeliefs in a direction favorable to the lobby. Therefore, in either case, the possibility of facing a very biased media outlet lowers the incentives of lobbies to spend resources to a¤ect the signal distribution. Notice that for intermediate values of the media outlet s bias, an equilib- rium in pure strategies cannot exist. This is due to the discontinuity in the equilibrium level of e¤ort of lobbies: for ' l < ~ ' l lobbies play according to a partially informative equilibriumandputane¤ortequaltoe PI : Viceversa, for ' l = ~ ' l +"; the leftist media outlet has an incentive to deviate from its pool- ing strategy. However, this gives higher incentives to lobbies to exert a higher level of e¤ort and thus increases the incentives of the media outlet to play a pooling strategy. Therefore, for ~ ' l <' l < ' l ; the only possible equilibrium is asemi-separating equilibriumwherelobbiesexerte¤orte SS . Moreover,toany ' l inthisintervalcorrespondsauniqueoptimalprobabilityofthemediaoutlet slantingitsreports,q;whichsupportstheuniquesemi-separating equilibrium. 1.4.2 Distortion of the Policy Outcome and Welfare We now analyze the e¢ ciency and welfare implications of this game. To sim- plify the analysis we now assume, without loss of generality, the following: Assumption 2. h i (0;0;) = 1; 8i =a;b In other words, we focus on the case where in absence of lobbies, there is no noise in the signal that the media outlet receives. Thus, given Assumption 2, with no lobbiesinuence activities and no news-slantingby the media outlet the equilibrium would be a fully revealing one where voters learn the 31 true state of the world and no distortion is present in the implemented policy. Distortion in the Policy Outcome In order to evaluate the policy dis- tortion arising from this game, we should compare the policy outcomes that arise in a maximally informative (MI), partially informative (PI), and semi- separating (SS) type of equilibrium with the one of a fully-revealing (FR) equilibrium. From an ex-ante perspective, the expected policy outcome is the sameinalltypesofequilibriaofourgame. Ontheotherhand,themorevoters care about the state of the world and the higher the noise in the information that they receive, the higher will be the expected policy distortion. Proposition 2 In all types of equilibria of the game (PI; SS; MI), the ex- pected policy outcome is equal to the median voter idiosyncratic policy prefer- ence. The ex-ante policy distortion is positively related with and with the e¤ort exerted by lobbies in equilibrium (i.e., e ). Moreover, in a PI and SS type of equilibrium, the ex-ante policy distortion is also positively related with q and y: Therefore, from an ex-ante perspective, lobbiesinuence activities create an upward distortion when the state of the world in A and a downward dis- tortion when the state is B: The expected policy distortion depends on the size of the state-contingent public value component of the voter utility func- tion (i.e., ). In other words, the more voters care about the e¢ ciency of the implementedpolicy, thehigherthepolicydistortion. Thisresultsuggeststhat we should expect, ceteris paribus, a higher policy distortion in an issue like global warming than in an issue like abortion where preferences are mostly idiosyncratic. On the other hand, the expected policy distortion also depends on the overall slant in the message that voters receive from the media outlet. More specically, the media outlet s message contains two di¤erent kinds of 32 slant. Thereisasource-drivenslantintroducedbylobbiesinthesignalthat the media outlet receives (lobbies-induced slant). At the same time, in a par- tially informative and semi-separating type of equilibrium, the media outlet s message contains also a supply-drivenslant due to the idiosyncratic bias of the media outlet (media-induced slant). Hence, the expected policy distortion is positively related with the lobbies-induced slant (i.e., with the equilibrium level of e¤ort exerted by lobbies) and also with the media-induced slant (i.e., with the probability of the media outlet slanting its reports q and with the probability of the media outlet being biased y): In any case, despite the fact that parties in our model do not introduce any distortion and they simply implement the policy preferred by a majority of voters, there will be an ex-ante distortion in the policy outcome. Even though voters are rational and discount the possible presence of slant in the informationtheyreceive,thenoisethatlobbiesandthemediaoutletintroduce inthepoliticalprocesspreventsthemfromchoosingthefullyrevealing optimal policy. WinnersandLosersoftheInuenceGame Wenowanalyzethewelfare implications of the policy distortion derived in the previous section. That is, we now focus on who is winning and who is losing in this inuence game. Proposition 3 From an ex-ante perspective, all voters and the media outlet are always worse o¤ in any type of equilibrium of the game (PI;SS;MI) than in a fully revealing equilibrium. Their expected utility loss is larger the higher is the expected policy distortion. Viceversa, lobbiesexpected utility gain is positively related with the expected policy distortion. Hence, lobbies are better o¤ in any type of equilibrium of the game than in a fully revealing equilibrium whenever the expected policy distortion is large enoughrelative to the cost of e¤ort. 33 Voters, regardless of their idiosyncratic preferences, would prefer an equi- librium without any inuence activity. Moreover, their expected utility loss is larger the higher is the expected policy distortion. On the other hand, lobbies would prefer to commit to a no-lobbying equilibrium if and only if the cost of e¤ortistoohighcomparedwiththepossiblegainfromengagingininuence activities (expecteddistortionthat theycreate inthe policyoutcome). 45 Nev- ertheless,thefollowingcorollaryshowsthateventhoughlobbiesmaynotwant to commit to a no-lobbying equilibrium, they would always like to commit to a low-lobbyingone. Corollary 1 Lobbiesexpected utilities are higher: i) the lower are and (in all types of equilibria), ii) the higher is y (in a PI and SS equilibrium) Theloweris ;thesmallertheintervalinwhichtheimplementedpolicymay lieandthusthelessriskywillbethepolicyoutcome,hencethehigherlobbies expectedutilities are. Onthe otherhand, the loweris ; the more productive are lobbiesinuence activities and thus their expected utility will also be higher. Moreover,thehigheristheprobabilitythatthemediaoutletisbiased, the higher the lobbiesexpected utilities in a PI and SS equilibria. Indeed, lobbiesex-ante preferredoutcomewouldbeanuninformativeequilibrium(i.e., y = 1=2). In other words, from an ex-ante perspective a very biased media outletmayrepresentsacommitmentdeviceforlobbiestonotspendtoomany resources in this arm-wrestlegame to inuence voters. From an ex-post point of view (i.e., after the state of the world is realized), moderatevotersarestillalwayslosingfromsuchgame. Instead,extremistvot- ers maybe bettero¤whenthe policythat theylike is not the onematching 45 Notice that, if we were to consider an utilitarian social welfare function giving equal weights to all voters, the media outlet and lobbies, the net e¤ect of this inuence game on socialwelfarewouldbenegative. Indeed,sincethewelfarelossofonevotersalwayoutweighs the welfare gain of one lobby, in presence of two or more voters the total social welfare loss would always be higher than the total gain in social welfare. 34 the true state of the world as the following lemma shows. Lemma 4 LetP J m betheequilibriumpolicy outcome (whereJ =PI;SS;MI): Let x A = 1+ (P J m ) 2 and x B = 1+ (P J m + ) 2 : Then voter i is better o¤ in a fully revealing equilibriumthan in any type of equilibriumof the game (PI;SS;MI) if and only if one of the following conditions is satised: i) x A x i x B ii) x i <x A and the state of the world is A iii) x i >x B and the state of the world is B Again,wecanlookatourexampleontheKyoto sprotocoltounderstandthe intuition behind this result. Let s suppose that the state of the world is mild e¤ects of pollution on global warming. Lemma 4 is suggesting that in such caseaveryenvironmentalistvoterswouldpreferanytypeofequilibriumofthe game, where the median voter chooses a policy more in favor of the Kyoto s protocol,toafullyrevealingequilibriumwherethemedianvoterwouldchoose a policy less in favor of the Kyoto s protocol. 1.4.3 Media Bias, Policy Distortion and Welfare In the previous section we have derived and discussed the distortion in the policy outcome and its e¤ects on the expected utilities of players regardless of whichequilibriumisactuallyinplace. Thatis,wehaveanalyzedthee¢ ciency andwelfareimplicationsofthegameregardlessoftheactualsizeofthepossible bias of the media outlet. In this session we want instead to analyze the e¤ect that the media outlet s bias has on the policy distortion and on the welfare of voters,lobbiesandofthemediaoutletitself. 46 Thiswillallowustoanswerthe following questions: is a larger idiosyncratic bias of the media outlet always 46 Without loss of generality we will assume, as in the previous section, that Assumption 2 holds. 35 associated with a higher policy distortion? Moreover, if voters and lobbies could decide how large the possible bias of the media outlet should be, what would be the optimal media biasfrom their perspectives? Media Bias and Policy Distortion When there are no lobbiesinuence activitiestakingplace,thepresenceofmediabiasalwaysincreasestheexpected policydistortionhenceitalwayshasanegativeimpactonthee¢ ciencyof the political outcome. However, when lobbies come into play this is not neces- sarily true anymore. As the following proposition shows, the expected policy distortionmaybelowerinatypeofequilibriumwherethebiasedmediaoutlet types slant their reports than in one where they do not. Proposition 4 Theexpectedpolicydistortioninamaximallyinformativeequi- libriumis higher thanthe one in a partially informative equilibriumif and only if y < h PI h MI 2h PI 1 : In other words, it is not possible to say a priori whether the ex-ante policy distortion will be larger in a PI or MI type of equilibrium. 47 The expected policydistortiondependson butitalsodependsontheinformativenessofthe messagethatvotersreceivefromthemediaoutlet. Thatis,theexpectedpolicy distortion is positively related with the slant in the information that voters receive, whichisdi¤erentinthedi¤erenttypesofequilibria. Morespecically, as we have pointed out in section 1.4.2 the overall slant present in the media outlet s message derive from two di¤erent types of slants: the lobbies-induced slantandthemedia-induced slant. Votersknowthatwhenthepossiblebiasof the media outlet is low, the media outlet will always send truthfulreports (i.e.,itwillnotslanttheinformationitreceived). However,inthiscaselobbies 47 A similar intuition applies to the policy distortion in a SS equilibrium with respect to the one in a MI equilibrium. Notice that h PI also depends on y trough e PI : Therefore, whether y < h PI h MI 2h PI 1 or not will ultimately depend on the parameters of the model and on the functional form of the signal likelihood function (i.e., h(e a ;e b ;)): 36 have strong incentives to exert e¤ort. Therefore, the message that voters receiveinamaximally informative equilibriumhasnomedia-induced slantbut it incorporates a high lobbies-induced slant. Instead, the message that voters observe in a partially informative equilibrium contains a high media-induced slant (in a probabilistic sense) and a low lobbies-induced slant. Therefore the expected policy distortion in a partially informative equilibrium will be lower thantheoneina maximally informative equilibriumwhenthe lobbies-induced slant is higher than the media-induced slant. Intuitively, if lobbies introduce lots of noise in the signal that the media outlet receives, voters will discount this and thus they will not give much credit even to a report coming from an unbiased media outlet. If instead voters are in a partially informative equilibriumwherelobbiesexertalowlevelofe¤ort,theymaybuyrelatively more the media outlet report (provided that they believe the media outlet being biased with a low probability). That is, in presence of lobbiesinuence activities, a higher bias of the media outlet may ultimately lead to a lower policy distortion by lowering the lobbies-induced slant. Media Bias and Welfare At this point, a natural question to ask is the following: if voters could choose between facing a media outlet with a large possible bias (and thus be in a PI equilibrium) or one with low or no bias (and thus be in a MI equilibrium), which one would they prefer? To answer this question we should compare the welfare of voters across di¤erent types of equilibria. Proposition 5 Every voter has a higher expected utility in a PI equilib- rium than in a MI one if and only if the expected policy distortion in a PI equilibrium is lower than the one in a MI equilibrium. Lobbies have a higher expected utility in a PI equilibrium than in a MI one if and only if y > 1 2 1 p 2 (2h MI 1) 2 [c(e PI )c(e MI )] (2h PI 1) : 37 Inotherwords,itisnotpossibletosaya priori inwhichtypeofequilibrium voters would prefer to be. From proposition 3 we know that voters expected utility depends on the expected policy distortion. As we discussed in the pre- vious section, the size of the expected policy distortion depends on the overall slant contained in the media outlet s message. Therefore, since such slant is di¤erent across types of equilibria, voterswelfare would also be di¤erent in the di¤erent types of equilibria of the game. Since the strength of the lobbies- induced slant and the media-induced slant are inversely related across types of equilibria, voters would prefer a PI equilibrium to a MI one whenever the lobbies-induced slant is stronger than the media-induced one. In other words, from an ex-ante point of view, voters may prefer to face a potentially very biasedmediaoutlet. Indeed,suchtypeofmediaoutletmaydiscouragelobbies to engage in inuence activities and hence may ultimately lead to a higher quality of information and lower policy distortion. 48 On the other hand, lob- bies a and b s ranking of equilibriais opposite to the votersone. Lobbies prefer a PI equilibrium to a MI one, provided that the media-induced slant is strong enough. Moreover, the higher the cost of e¤ort the greater the like- lihood that lobbies would prefer to face a media outlet with a large possible bias (since e PI <e MI ): 1.4.4 Limiting Cases We now analyze the two limiting case where y = 0, i.e., the media outlet is unbiased with probability one, and the opposite one where y = 1=2; i.e., the media outlet is biased with probability one. 48 Notice that while ex-ante voters may prefer the possible bias of the media outlet to be large, after the media outlet has received the signal on the state of the world, voters would always want it to not slant its reports. That is, an unbiased media outlet could never credibly commit to play a pooling or mixed strategy. 38 Unbiased media outlet The case where the media outlet is unbiased with probability one is equivalent to a situation where there is no such lter as media and voters receive a direct signal on the state of the world. Thus, nestedinourmodelisthecasewherelobbiescommunicatedirectlywithvoters. An obvious example where such situation arises is when lobbies compete by engaging in informative advertising (e.g., issue advertisement). In this case, the signal that voters receive can be interpreted as which informative content of the advertisements is stronger. Fromlemma1weknowthatwhenthemediaoutletisunbiaseditwillnever slant its reports in any informative equilibrium. Therefore, the equilibrium with an unbiased media outlet is equivalent to a maximally informative one. Thus, even when the media outlet has no bias, the information that voters receive will be slanted due to the presence of lobbiesinuence activities and there will be a distortion in the policy outcome. 49 BiasedMediaOutlet Whenthemediaoutlethasalargebiasitwillalways slant its reports. Therefore, when the media outlet is biased with probability one, voters will disregardthe message comingfromaverybiasedmediaoutlet because simply uninformative. On the other hand, in such uninformative equilibrium lobbies would have no incentives to engage in inuence activities, thus the signal that a very biased media outlet receives is very likely to be correct. From lemma 3 we know that in such case the media outlet has lower incentives to adopt a pooling strategy and thus it will do so only when it has a very large bias. Therefore, when the media outlet has a very high bias with probability one, the unique equilibrium will be an uninformative one where voters do not modify their prior beliefs and lobbies exert no e¤ort. 50 49 See proposition 2. 50 This case highlights the fundamental di¤erence between a media outlet and a lobby. If themediaoutletweretohaveextremepreferences(astheonesofalobby), itsreportswould 39 Forintermediatevaluesofthemediaoutlet sbias,therewillbeauniquesemi- separating equilibriumwherelobbiesexertalowere¤ortthaninthebenchmark case because of the certainty of facing a biased media outlet. Finally, for low valuesofthemediaoutlet sbiastheuniqueequilibriumwillstillbeamaximally informative one. 51 The possible types of equilibria will thus be as follow: l φ SemiSeparating Equilibrium (Low lobbies’efforts) r φ ~ r φ 1 γ γ SemiSeparating Equilibrium (Low lobbies’efforts) Uninformative Equilibrium (No lobbies’ efforts) xm Maximally Informative Equilibrium (High lobbies’efforts) Uninformative Equilibrium (No lobbies’ efforts) l φ ~ Figure 1.4: Equilibria with Biased News Media Outlet. Inthenextsectionweproposeapossiblecharacterizationofthecompetition between lobbies and thus of the signal probability function (which satises Condition 1) and derive a closed form solution for the symmetric informative equilibria of this game. 1.5 The State Contingent Contest between Lobbies 1.5.1 Racing for evidence Following the innovation raceliterature we model the competition between lobbies as a race for evidencewhere one of them has an advantage over the other. 52 That is, lobbies have di¤erent hazard rates depending on whether simply be uninformative and thus it would neither have any policy inuence nor get any prots from readers and/or advertisers. 51 Notice that a similar intuition applies to the case where the bias of the media outlet is known (i.e., it is common knowledge). That is our model implies that a biased media outlet may a¤ect the policy outcome even in presence of rational, Bayesian consumers who know its bias (for a similar result see Anderson and McLaren 2007). 52 For an extensive review of this literature see Reinganum (1989). 40 they are lobbying for the goodcause or not. 53 To simplify notation let the state of the world be s2fa;bg:Thus assuming the time at which each lobby wins the race, ; being exponentially distributed, we have the following: Pr((e i )tjs =i) = 1expf(e i +)g (17) Pr((e j )tjs =i) = 1expf(e j )g (18) That is to say, for ! 0; if the state of the world is s = i; then lobby i will win the contest and thus have the media outlet receiving signal z i with an instantaneous probability equal to e i +; where is a positive parameter measuring the importance of the truthin the contest. Viceversa, lobby j will have an instantaneous probability of winning the contest simply equal to e j : Ifwedenev i z i (v i z j )asthenetexpectedbenetthatlobbyigetswhensignal z i (z j )isrealized,wehavethatlobbyiexpectedpayo¤inthisstatecontingent contest will be: W i (e i ;e j ;;v i z i ;v i z j js =i) = 1 Z 0 v i z i (e i +)expf(e j )tgexpf(e i +)tgdt+ + 1 Z 0 v i z j e j expf(e j )tgexpf(e i +)tg(e i +)dt That is: W i (e i ;e j ;;v i z i ;v i z j js =i) =v i z i e i + e i +e j + +v i z j e j e i +e j + (19) Thus we have the following probabilities of media outlet receiving signal z i or 53 In other words, lobbies are going to have a state contingenthazard rates: k(e i js =i) =e i + and k(e j js =i) =e j 41 z j when the state of the world is s =i: h i (e i ;e i ;) = Pr(z i js =i) = e i + e i +e j + (20) 1h i (e i ;e i ;) = Pr(z j js =i) = e j e i +e j + (21) These winningprobabilities are a straightforward generalization of the ones of the Contest-Success Function (CSF) introduced by Tullock (1980) and ax- iomatized by Skaperdas (1996). The contest success function captures a wide range of situations where players put an e¤ort to win a prize. In our setting this prize is going to be the signal received by the media outlet. 54 It is imme- diate to verify that this State Contingent Contest-Success Function (SCCSF) satises all the properties of Condition 1. 1.5.2 Comparative Statics We now discuss the e¤ects that a change in the parameters of the model has on lobbiesinuence activities and on the probability of news-slantingby the media outlet. Proposition 6 In all the equilibria of the game, a higher leads to a higher level of lobbiese¤orts and a weakly lower probability of news-slantingby the media outlet. An increase in the importance of the public value component in the vot- ersutility function has two e¤ects. A higher implies a larger space for inuence, therefore the higher is the stronger lobbiesincentives to try to inuence votersbeliefs (higher lobbies-induced slant). On the other hand, a higher also decreases the relative importance of the media outlet s idiosyn- cratic bias. Hence the higher is the lower the media outlet s incentives to 54 A detailed and formal characterization of the properties of this State Contingent Contest-Success Function (SCCSF) is available upon request to the author. 42 slant its reports (lower media-induced slant). Therefore, a higher has oppo- site e¤ects on the incentives of lobbies and of the media outlet: it increases the lobbies-induced slant and it reduces the media-induced slant. On the other hand, as the following proposition shows, an increase in the cost of e¤ort or the probability of the media outlet being biased has always a negative e¤ect on either one or both types of information slants. Proposition 7 In all the equilibria of the game, a higher c and a higher y both result in a lower level of lobbiese¤orts and/or a lower probability of news-slantingby the media outlet. This result suggests that increasing the cost of lobbiesinuence activities would have a positive e¤ect on the informativeness of the message that voters receiveandhenceonthee¢ ciencyofthepolicyoutcome. Anincreaseinc has a direct and an indirect e¤ect. It decreases lobbiesincentives to exert e¤ort and thus it increases the quality of the signal received by the media outlet. As a consequence the media outlet has lower incentives to slant its reports. However, this last e¤ect increases lobbiesincentives to exert e¤ort. Thus the direct and indirect e¤ect of an increase in c on lobbiese¤orts go in opposite directions. Nevertheless, the net e¤ect on the slant in information is always negative. Noticethatinsomecases(e.g.,inaSS equilibrium),thenete¤ectof anincreaseinc onlobbiese¤ortsisnull (thedirectandindirecte¤ectscancel each other). Thus in such cases an increase in c has a positive e¤ect on the e¢ ciency of the policy outcome not because it decreases the lobbies-induced slant but because it decreases the media-induced slant. Therefore, our result implies that public policy measures aimed at increasing the cost of lobbies inuence activities (e.g., a linear tax on lobbying) would reduce the policy distortion and increase voterswelfare. Indeed, such measures would either reduce lobbiesinuence activities or reduce news-slantingby the media (in 43 a probabilistic sense) or reduce both. Asimilare¤ectandsimilarreasoningappliestoanincreaseprobabilityofthe mediaoutletbeingbiased,i.e.,y:Thepolicyoutcomewouldbemoree¢ cientif everyonewouldattributealowprobabilitytothemediaoutletbeingunbiased. Thus knowing for sure that the media outlet is indeed biased would actually lead to a lower policy distortion. 1.6 Extensions In this section we briey describe and discuss some possible extensions of our benchmark model. 55 1.6.1 Known direction of media outlets bias A natural extension of the benchmark model is the situation where the di- rection of the media outlet s bias is common knowledge but the strength of such bias is private information. Suppose for example that the media outlet is leftist. Let the space of possible media outlet types be = ' H l ;' L l with ' H l < ' L l < x m and Pr(' n = ' H l ) = y. That is, with probability y the media outlet has a largeleftist bias and with probability (1y) it has a small leftist bias. When lobbies are ex-ante symmetric their incentives to exert e¤ort remain symmetriceventhoughthemediaoutletpossiblestrategiesarenotsymmetric. To understand why this is true, let s focus on a partially informative equilib- riumwherethesmallbiastypeadoptsaseparatingstrategyandthelarge biastypeadoptsapoolingone. Fromtherightistlobby sperspective,exerting an e¤ort to inuence the information that the media outlet collects is a waste with probability y (probability of largebias type) and is productive with probability (1y): Similarly, from the leftist lobby s point of view, exerting 55 Detailed formal proofs for these extensions are available upon request to the author. 44 e¤ort is unnecessary (and thus a waste) with probability y and it is produc- tive with probability (1y). Therefore, asymmetries in the media outlet s bias do not generate asymmetric incentives and thus the equilibrium remains symmetric. 1.6.2 Single Lobby We discuss here the case where there is just one lobby engaging in inuence activities. We can think of such situation being the limiting case where there are two asymmetric lobbies. Without loss of generality suppose the unique lobby to be the leftist one (lobby a). In such case, the rightist media outlet is more willing to slant its reports than a leftist media outlet (in a probabilistic sense), despite having the same ex-ante bias. There is a simple reason behind this asymmetry in the behavior of the leftist and rightist media outlet types. Iftheleftistmediaoutletreceivessignalz b ;thengiventhatlobbyaengagedin inuenceactivitiestodecreasethelikelihoodofsuchsignal,itwillconsiderthis signal very informative. Therefore, the leftist media outlet will have, ceteris paribus, lowincentivestodisregardsignalz b andadoptapoolingstrategy. On the other hand, if the rightist media outlet receives signal z a ; then given the presence of lobby a inuence activities, it will not consider this signal very informative. Therefore a rightist media outlet will have high incentives to disregard such signal and choose a pooling strategy. Hence, despite having the same ex-ante bias, a media outlet on the opposite side of the lobby may appear relatively more biased than the one on same side of the lobby, since it ismorelikelytoslantitsreports. Thisresulthasanimmediateimplicationfor empirical studies aimingatmeasuringmediabias. Inpresenceof asymmetries between lobbies, a reliable measure of the bias of a media outlet should take into account the equilibrium di¤erence between the ex-post slant in a media outlet s reports and the ex-ante bias of the media outlet itself. 45 1.6.3 Accuracy-Increasing Lobbies Until now we have assumed that the overall nete¤ect of lobbiesinuence activities is to increase the noise in the information that the media outlet col- lects (noise-increasing lobbies). Moreover, we have also derived endogenously this property when we have modeled the competition between lobbies as a race for evidence(see section 1.5). Now we instead discuss the other possi- ble case where lobbiese¤orts have a positive net e¤ect on the accuracyof thesignal. Thus,themoree¤ortlobbiesputina(symmetric)equilibrium,the greater the likelihood that the media outlet will collect correct information. 56 Inpresenceofaccuracy-increasing lobbies,ahigherprobabilityofthemedia outlet slanting its reports corresponds to a lower equilibrium level of lobbies e¤orts. 57 Thus, similarly to the noise-increasing case, lobbies nd more pro- ductive to engage in inuence activities in presence of a media outlet with a small bias. However, in this accuracy-increasing case, since the lower the media-induced slant the higher the lobbies-induced accuracy, multiple equilib- ria exist for intermediate values of the media outlet s bias (one with low and one with high lobbiese¤orts). 58 1.7 Conclusions Voters,parties,newsmediaandlobbiesareimportantactorsinvolvedinevery democratic political process. These actors are intrinsically related to each other and the nal political outcome will be the result of the mutual interac- 56 This is equivalent to relaxing property v) of Condition 1. Thus, in the accuracy- increasing case @hi @ei ei=ej > @hi @ej ei=ej 57 Notice that for y small enough it may also exist an alternative pattern of equilibria where there is a positive correlation between lobbiese¤orts and the probability of media outlet slanting its reports. 58 For large values of the media outlets bias, an increase or decrease in lobbiese¤orts wouldnota¤ectthemediaoutletequilibriumstrategy.Asimilarreasoningapplieswhenthe media outlets bias is small. 46 tionsamongallofthem. Wehavedevelopedasimplemodeltoanalyzesomeof these interactions that have been overlooked in the literature. Lobbies spend hundreds of millions of dollars every year to advocate their positions. This is especially true on issues where the cost of choosing a policy di¤erent from themedianvoter sonewouldbetoohighforanypolitician(ideological/single issue 527 groups). In such cases lobbiesmain channel of inuence is through voters. Given that voters decide on the optimal policy based on their idio- syncratic preferences and their beliefs on the expected benets and costs of alternative policies, lobbies will succeed in altering the implemented policy as long as they manage to alter such beliefs. In our setting the role of a media outlet is to collect information on the costs and benets of a given policy and then lter this information according to its idiosyncratic preferences. Even thoughvotersandthemediaoutletarerationalandtheyaccountforthepres- ence of lobbiesinuence activities, the ex-ante slant of information (signals) by lobbies will result in a distortion of the equilibrium policy. The policy will besub-optimalinthesensethatitwillnotbeexactlyshapedonthetruestate of the world. Thebias of the mediaoutlet andlobbiese¤orts showaquiteinterestingre- lationship. The higher the possible bias of the media outlet the lower lobbies e¤orts. This result derives from the fact that lobbiese¤orts are less produc- tivethe more likely the media outlet is to slant its reports. Indeed a very biased media outlet on the same side of the lobby will make the lobby s e¤ort unnecessary. Instead,averybiasedmediaoutletontheoppositesidewillsim- ply make lobby s e¤ort unproductive. Either way, the greater the likelihood that the media outlet will slant its reports the lower the incentives of lobbies toinuencetheinformationthatthemediaoutletcollects. Ontheotherhand, the lower the lobbiese¤orts the less likely, ceteris paribus, is the media outlet to slant its reports. Despite the fact that the media outlet does not incur 47 any cost in manipulating the information it collects (i.e., the media outlet is a cheap-talker), it still has lower incentives to slant its reports upon receiving a very informative signal (i.e., when lobbies exert a low level of e¤ort). From an ex-ante welfare point of view, this inuence game negatively af- fects all players but lobbies. All voters and every media outlet type face a net expected loss from the policy distortion generated by lobbiesactivities and media bias. Lobbies instead expect to benet from this game as long as the policy distortion induced by their inuence activities is large enough with respect to the cost of e¤ort. At the same time, our analysis shows that in presence of lobbiesinuence activities, a higher idiosyncratic bias of the media outlet is not necessarily associated with a higher policy distortion and a lower voterswelfare. On the other hand, the comparative statics results on the State Contingent Contest-Success Function (SCCSF) show that public policy measures aimed at increasing the cost of lobbiese¤orts would reduce lobbiesinuence activities and/or reduce news-slantingby the media (in a probabilistic sense). Thus, the introduction of a proportional tax on lobbying wouldreducethedistortioninthepolicyoutcomeandincreasevoterswelfare. Asymmetriesinthemediaoutlet sbiasdonotgenerateasymmetricincentives for lobbies to engage in inuence activities. Viceversa, asymmetries between lobbies (e.g., the presence of only one lobby) induces asymmetries in the be- havior of di¤erent media outlet types. When only the leftist lobby is engaging in inuence activities, for a given ex-ante bias, a rightist media outlet will be more likely to slant its reports than a leftist one. As a consequence, by just observing the news reports, the rightist media outlet may appear more biased than the leftist one. This suggests that empirical studies aimed at measuring media bias that just focus on the slant in media reports, may be misleading. In other words, such measurements may capture the ex-post slant in a media outletreports rather than the ex-ante bias of the media outlet itself. 48 This analysis is intended to be a rst step in the direction of analyzing the relationships between lobbies, voters and media. A more active role of media should probably be considered in the analysis. Nevertheless, the message of thepaperremains. Lobbiescanindeeddistortthepoliticaloutcomeevenwhen they do not interact directly with politicians. Rational voters discount the re- portstheyreceivefromthemediaoutletbytakingintoaccountthepresenceof news-slantsarising from lobbiesinuence activities and media bias. How- ever, the nal policy outcome is still suboptimal and a distortion is present in the political platform that the winning party implements. This suggests that the recent lobbying reform laws in the US, just focused on tackling the distortions deriving from the interactions between lobbyists and politicians, have overlooked a potentially large source of news-slantand, ultimately, of policy ine¢ ciency. 49 2 ChapterII:ElectoralParticipationandCom- municative Voting in Europe 2.1 Introduction Electionsindemocraciesareunanimouslyconsideredasbeingthemostimpor- tantchannelforcitizenstoexpresstheirindividualpreferencesoverleadersand public policies. Elections are generally viewed as choice mechanisms in which votersareinvolvedinadecisionprocessstructuredintotwostages: theyrstly decide whether to participate in the election (participation decision) and, sec- ondly, they choose whom to cast their vote for (voting decision). In line with otherstudies(DeaconandShapiro(1975),KahnandMatsusaka(1997),Degan and Merlo (2007)), we construct a unied empirical framework in which both theparticipationdecisionandthevotingdecisionaretakenintoaccount. Such empirical framework is instrumental to our empirical investigation of the re- cent theoretical literature concerning the role of information on voter turnout (Matsusaka (1995), Feddersen and Pesendorfer (1996), (1999)) and the trade- o¤between strategic and communicative motives for voting (Piketty (2000), Castanheira (2003), Razin (2003)). To clarify our terminology, while most of the voting literature use the term strategic votingto indicate the vote for a party di¤erent from the one most preferred by the voter (e.g., McKelvey and Ordeshook (1972)), in the present paper we will use the terms strategic votingand communicative votinga la Piketty: Voters trade-o¤two di¤erent motives when deciding howto vote: they care about current decision-making (they are strategic), but they also care about communicating their views about their most-preferred candidate so as to inuence future elections, by in- 50 uencing other votersopinion and/or party positioning(Piketty (2000), pg. 169). We will thus refer to strategic votingas the vote for a likely winner party (indicatingthat avotercaremore about current-decisionmaking) andwewill instead refer to communicative votingas the vote for a sure loser party (indicating that a voter care more about future elections). Wemodelelectionsasamulti-levelschoicemechanisminwhichvotersdecide whether to vote and whom to vote for. We employ several econometric tech- niques to test the validity of the empirical structure underlying the electoral decision process that we propose in this paper. More specically, we estimate multinomial logit, sequential logit and nested logit models and compare the relative appropriateness of each of themto deal with the research questions of this study. We evaluate how individual characteristics, the level of information and expressive motivations inuence electoral participation. Further, given that people trade-o¤strategic and communicative motivations in the voting deci- sion, we provide an understanding of the individual characteristics that make a voter more likely to greatly care about the strategic part of this trade-o¤ or, alternatively, about the communicative role of voting. At the same time, we explore how institutional features, such as those dening the working of the political systemand the characteristics of the media market, inuence the participation and the voting decision. The evidence regarding the role that information plays on electoral partici- pation does not seem to provide support to the swing voters curse theory of abstentionism. Uninformed individuals are less likely to vote as well as mod- erate and independents ones. However, being independent and uninformed at the same time does not seem to have any statistically signicant e¤ect on the decisiontovote. Ontheotherhand,ourempiricalresultssuggestthatexpres- 51 sive motivations play a signicative role in electoral participation. Individuals that belong to a political party, consider politics important and that have a good opinion on the political system of their country are more likely to vote. Asfarasthevotingdecisionisconcerned,bettereducatedpeopleseemtobe more likely to vote as communicating, rather than strategically. We interpret this evidence as indicating that higher educated people may be more likely to understand and exploit the communicative role of voting. People having a bad opinion regarding the political system are also more inclined to vote for loser parties. This result seem to suggest the presence of protest voting, i.e., individualsvoteforsureloserpartiestocommunicatetheirdissatisfaction with the overall functioning of the political system. Another interesting result concerns the electoral behavior of voters placed atthetwoextremesofthepoliticalspectrum. Left-wingextremistsseemmore likely to vote for their most preferred party regardless of whether this party is a sure loser. Therefore, they always choose to a¢ rm and communicate their partisan preference. Di¤erently, right-wing extremists seem to be very strategic (even more strategic than moderate voters). Finally, the features of the electoral system and the structure of the media market of the country where the individual is entitled to vote, have a signi- cative e¤ect both the participation and the voting decisions. From a public policy perspective, our ndings seem to suggest that a higher level of media freedom, a lower threshold for political representation and a larger number of representative elected for a given constituency size, are all elements conducive to higher levels of electoral participation. Moreover, our empirical analysis show that sure loser parties are likely to nd higher support the lower the media freedom, the fewer the elected representative for constituency size and the more fragmented the opposition parties are. 52 2.1.1 Related Literature Our study is related to two di¤erent strands of literature. The rst is the theoreticalandempiricalliteratureonvoterturnoutand, morespecically, on the e¤ect of information on the electoral participation. Participation in mass elections is a typical collective action problem: in large elections the prob- ability that a voter would cast a decisive ballot is not signicantly di¤erent fromzero. Avastliteraturehaveemergedtryingtoexplainwhypeoplevote. 59 The most recent theories on the determinants of electoral participation have focused on the role played by information both in a decision theoretic (Mat- susaka(1995))andinagametheoreticframework(FeddersenandPesendorfer (1996) and (1999)). The decision theoretic approach predicts that, since the more condent a voter is about voting for the best candidate the higher her expectedbenetfromvoting,moreinformedvotersaremorelikelytoturnout (Matsusaka(1995)).Ontheotherhand,byendogenizingtheindividualproba- bilityof beingpivotal, FeddersenandPesendorfer(1996) showthat politically independent and uninformed voters su¤er from the swing voters curse, i.e., they are better o¤by abstaining than by voting for any of the competing can- didates even when the cost of voting is zero. More specically, in presence of costless voting, both independent informed and partisans voters have a domi- nant strategy of turning out to the polls. Di¤erently, uninformed independent votersvotetocompensateforthe[presenceof]partisansandhavingachieved thatcompensationtheyabstain(FeddersenandPesendorfer(1996),pg. 414). The swing voters curse theory implies that, ceteris paribus, uninformed in- dependent voters are less likely to turn out than informed independent and partisan voters. 60 59 See Dhillon and Peralta (2002) and Feddersen (2004) for extensive surveys on the the- oretical literature on votersturnout. 60 Feddersen and Pesendorfer (1999) generalize this model to allow for a continuum of voterspreferences and a "ne" state space. They show that in such case the level of 53 Recent empirical studies on electoral participation have focused on the re- lationships between information and turnout. Lassen (2005) use data from a natural experiment where a random fraction of the electorate is exogenously informed and nds that a more informed voter is more inclined to vote in a referendum setting. Degan and Merlo (2007) show that since uninformed voters are more uncertain about the optimal candidate, their expected regret from voting is higher and therefore they are less likely to turn out. This lit- erature while analyzing the role of information on the individual decision to turnout,hasnottakenintoconsiderationtheroleofpoliticalpreferences. The evidence found in the literature regarding the positive correlation between in- formationandturnoutcanthusbeexplainedbybothdecisiontheoretic(Mat- susaka(1995))andgametheoreticmodels(FeddersenandPesendorfer(1996), (1999)). Two are the exceptions. Larcinese (2006) analyses the e¤ect of infor- mation and ideological strength on voter turnout. In line with our ndings, Larcinese s results point out that beinginformedandat thesametimehaving more extreme preferences does not have any signicative e¤ect on the voter s probability of turning out. Nevertheless, in this study the author exclude in- dependent voters from his analysis and thus his specication does not provide anappropriatetestoftheswing voters curse theory. Theonlystudythathas so far tried to directly test the swing voters curse is the experimental work by Battaglini, Morton and Palfrey (2006). The evidence emerging in such ex- perimental context is in favor of the game-theoretic approach on the e¤ect of information on turnout. Battaglini, Morton and Palfrey (2006) show that in- dividuals that are independent and uninformed strategically abstain and that they also take into account the presence of partisan bias in their decision to turnout. Our study represents the rst empirical analysis aimed at directly abstention should be closer to zero. Nevertheless, in a presence of a more realistic "coarse" state space "the more general model can produce the same comparative statics as in the 1996 paper" (Feddersen (2004), pg 105). 54 testing the swing voters curse theory using eld data both on the level of information and on the political preferences of individuals. Contrary to the ndings of Battaglini, Morton and Palfrey (2006) the results of our empirical analysis seem consistent to decision-theoretic models of information inuence on voter turnout and, instead, they do not provide empirical support to the swing voters curse theory. The second strand of literature our work relates to is the theoretical and empirical literatureoncommunicative voting. Onceanindividual hasdecided to participate in the election, she has to choose whom to cast her vote for. If voters care only about current decision-making, sure loser parties should not get any vote in equilibrium. This intuitive result seems quite conicting withsimpleempiricalobservation: sureloserpartiesandcandidateshavebeen able to reach signicant vote shares even in rst-past-the-post systems such as those present in the US and in the UK. These considerations have lead several scholars to depart from traditional voting models where voters are alwaysstrategictoanalyzetheroleofvotingasconveyinginformationforother votersandparties. Thekeyideaofthisliteratureisthatevenifinaoneperiod electionweshouldobserveonlystrategicvoting(i.e.,peoplecastingtheirvotes only for parties with a positive probability of winning), broadening the time spanoftheobjectivefunctionofthevotermayleadtodi¤erentresults. While Piketty(2000)exploresthewaycommunicativevotinginuencesothervoters, Castanheira (2003) proposes a model where rational individuals may vote for sure loser parties in order to inuence the platforms of main parties. 61 In a multi-period model, both extremist voters and core voters may want to vote for extremist parties in order to alter the beliefs of main parties and therefore 61 In the same vein, Razin (2003) points out that voters signal their private information by voting. In this perspective, a winning candidate responds to the information elicited by the vote signal by recrafting her policies and therefore by positioning more e¤ectively in the next campaign. 55 theirfutureplatforms. Corevotersmaybetemptedtomimicextremistvoters the closer the platforms proposed by the main parties are. 62 Franklin, Niemi and Whitten (1992) provide an empirical analysis of in- strumental tactical voting and expressive tactical voting, where the former indicates strategic voting of individuals whose most preferred party has no chance of winning and the latter represents communicative voting of individ- uals casting their vote for a loser party di¤erent from their preferred focal party. By analyzing individual data on the 1987 British election, they nd that instrumental tactical voting is positively related with the margin of vic- tory of the two main parties, while expressive tactical voting shows a negative relationship with it. Expressive tactical voting is also positively related with being indi¤erent among which of the main parties would win and with the level of education. Both kinds of tactical voting appear to be positively re- lated with the strength of partisanship. Degan and Merlo (2007) model the behavior of voters in a two-stage optimization problem. In the rst stage the voter chooses whether to participate in the election. In the second stage, con- ditional on participating, the voter decides whom to cast her vote for. They focus of the analysis on the split-ticket voting where individuals vote for dif- ferent parties/candidates indi¤erent elections (i.e., aRepublicancandidate in presidentialelectionsandaDemocratcandidateincongressionalelectionsand viceversa) to evaluate the extent to which sincere voting a¤ects the electoral choice of voters. Their work brings about several interesting results relevant for our study. First only a small fraction of split-ticket voting (about 20% on average in the elections investigated) can be explained by sincere voting since other considerations, such as the desire to balance the government (Fiorina 62 Castanheira (2003) argues that this may explain why some of the voters of extremist partiesmaynotberealextremistsbutrathertheyusethisinstrumenttowarnmainparties, in other words, they use a communicative voting (they would probably stop voting for extremist when those become too important). 56 (1990), Alesina and Rosenthal (1996)), may play a signicant role in inducing voters to split their ticket. Second, independent voters split their ticket more thanpartisanvoters. Third, uninformedvoterssplittheirticketmorethanin- formed voters. Fourth, the distribution of the fraction of split-ticket voters on theliberal-conservativeideologicalspacerevealsthatsinceresplit-ticketvoters account for those voters displaying more moderate positions. This chapter is organized as follows. Section 2.2 describes the empirical models used in our analysis. Section 2.3 presents the data. Section 2.4 illus- trates and discusses the empirical results. Section 2.5 concludes. 2.2 Model Specication We propose two di¤erent specications of our empirical model. In the rst we construct a two-stage decision process where the individual makes a par- ticipation and a voting decision. The second is characterized by a three-stage structure where, prior to making the above two electoral decisions, the indi- vidual takes into account the fact that her preferred party is either a likely winner or a sure loser. 2.2.1 The Two-Stage Electoral Choice Model The rst structure of the decision process that we are going to model and analyze empirically is described by gure 1. In the rst stage the individual decides whether to participate in the political process or to abstain. In the second stage, conditional on having decided to participate, the voter chooses whom to vote for. The voter may either vote as communicating for a sure loser party, or she can choose to vote strategically for a likely winner party. 57 Vote for a sure loser party First Stage: Participation Decision Abstains Second Stage: Voting decision Vote for a likely winner party Individual Votes Strategic Voting Communicative Voting Figure 2.1: The Two Stage Electoral Choice Model Di¤erentempiricalmodelsmaybespeciedtorepresentthisdecisionprocess. The rst one is a multinomial logit (ML) where the individual, rather than facingthesechoicessequentiallytakethematonce. Thus, therstandsecond stagebelongtoauniquedecisionstage. Inotherwords,individualshavethree di¤erent potential choices at their disposal: they can abstain, vote for a likely winner party (strategic voting) or vote for a sure loser party (communicative voting). We performed a Small-Hsiao test of the underlying Independence of Irrele- vant Alternatives (IIA) assumption of this multinomial logit model. The ML fails the test for the IIA assumption, suggesting that the individual decision processisindeedsequential. TheresultsofthefullyspeciedMLarereported by Table A1.1 in Appendix B1. Given the results of the Small-Hsiao tests, we propose and estimate two alternative models: a sequential logit model (SL) and a nested logit model (NL). InordertoestimatetheSLmodel,wespecifyandestimatealogitmodelfor each level of decision. We dene our dependent variable as Y = 1 if the indi- vidualchoosestoabstainandY = 2iftheindividualchoosesacommunicative 58 vote. Then, P 1 = PrfY = 1g =F( 0 1 x) (22) P 2 = PrfY = 2g = [1F( 0 1 x)]F( 0 2 x) (23) wherexrepresentsthevectorofexplanatoryvariables. Theparameters 1 can be estimated from the the entire sample of potential voters by diving it into two groups: those who vote and those who do not. The parameter 2 can be estimated from the subsample of those who vote by diving it into two groups: thosewhovotestrategicallyandthosewhovote as communicating. Assuming that the error term is distributed according to a logistic distribution, all these binary models are going to be estimated using a maximum likelihood logit model. We should notice that this sequential logit model implicitly contains the assumption that each stage is stochastically independent from the others. An alternative specication of our empirical model is the NL model. The individual has to choose whether to participate in the election, i = 1; or not, i = 2; where i = 1 contains one nest j corresponding to the voting decision. This nest contains two di¤erent choices k = 1;2 , corresponding to the decision of voting strategically or as communicating: Thus, the individual derivesautilityU ijk fromthealternative(i;j;k):Wecanexpressthisutilityas afunctionoftheindividualpersonalcharacteristicsinteractedwiththeselected alternative V ijk and a residual ijk capturing the unobserved characteristics. Assuming that the error terms ijk are i.i.d. with a type-I extreme value distribution, then the probability of the (i;j;k) alternative being chosen is given by: P ijk =e V ijk = X l X m X n e V lmn (24) 59 Wecandecomposesuchprobabilityasthefollowingconditionalprobability: P ijk =P kji;j P jji P i Moreover, V ijk can be expressed as a function of a vector of explanatory variables for the "bottom level" choices (X ijk ) and the vector of variables inuencing the choice of abstention (Z i ) as follows: V ijk = 0 X ijk + 0 Z i (25) We can therefore dene the inclusive values: IV ij = ln( X n e 0 X ijn ) (26) and IV = ln( X m e 0 z iim +I im ): (27) After having estimated the NLmodel, we performa likelihood ratio test for the hypothesis that the inclusive value parameters are equal to one. This LR test will allow us to check whether our model is indeed nested. 2.2.2 The Three-Stage Electoral Choice Model The second specication of our empirical model takes into account the fact thatindividualsfacedi¤erentchoicesetsdependingonwhethertheirpreferred partyisapotentialwinnerorasureloser. Figure2illustratesthevoter sdeci- sionprocessembeddingtheex-antedistinctioninthechoicesetsthatdi¤erent individual face. 63 63 It may appear odd that an individual ideologically closer to a likely winner party votes for a sure loser one. However as shown by Casthaneira (2003), moderate voters may nd sometimes optimal to mimick extremist ones (for example because the party platform is 60 Vote for a likely winner party Vote for a sure loser party Vote for a sure loser party Second Stage: Participation Decision Abstains Third Stage: Voting decision Vote for likely winner party Ideologically closer party is a sure loser Ideologically closer party is likely winner First Stage: Definition of the Choice Set Nature Closer to a sure loser party Closer to a likely winner party Votes Abstains Votes Strategic Voting Communicative Voting Strategic Voting Communicative Voting Figure 2.2: The Three Stage Electoral Choice Model In the rst stage the individual, given her political bliss point, observes the "shelves of political o¤er" and determines her choice set. In other words, she realizes whether the party whose platformis closer to her preferred policy is a likely winner party. We dene as "closer to a sure loser party" (CSLP) those individuals whose most preferred party is a sure loser. Instead, individuals whose preferred party is a potential winner are dened as "closer to a likely winnerparty"(CLWP).Inthesecondstage,givenherchoiceset,theindividual decides whether to participate in the political process or abstain. Finally, in the third stage, conditional on having decided to participate, the voter decides whom to cast her vote for. Put it di¤erently, in the third stage the voter chooses whether to vote strategically (vote for a likely winner party) or as communicating (vote for a sure loser party). The three-stage decision process,therefore,ischaracterizedbyarststagethatrepresentsanexogenous constraint since the individual does not actually make any choice. Assuming thatthevoterisendowedwithagivenpoliticalblisspointandthatshecannot moving far away with respect to the individual preferred policy). 61 inuence the loser-winner distribution of parties in a given country at a given time, we can think as if the choice set of each voter was chosen by nature. Therefore, the three-choice decision process allows us to analyze separately theelectoralbehaviorofthetwosubsamplesofCSLP andCLWP votersinor- der to consider the di¤erent incentives and constraints that CSLP and CLWP individuals face in their voting decisions. Similarly to what already discussed for the two-stage electoral choice mech- anism, di¤erent empirical models may be specied to estimate the three-level electoralchoicemechanism. Therstisamultinomiallogit(ML)modelwhere the individual, rather than facing the three voting choices sequentially, take them at once. Thus, in the ML the second and third stage belong to a unique decisionstage. Again, theMLmodelfailstheSmall-HsiaotestofIIAassump- tion both in the subsample of CSLP and CLWP voters (in Tables A1.2 and A1.3 in Appendix B1 we report the results for these tests). Thus, given the decision structure specied above, in order to analyze the individual s participation and voting decisions we estimate a sequential logit model (SL) and a nested logit model (NL) in the two CSLP and CLWP sub- samples. 2.3 Data and Descriptive Statistics 2.3.1 Data Thedatathatweusedinthisstudyaredrawnfromavarietyofpublishedand on-line sources. We focus our empirical investigation on the analysis of the electoralbehaviorofmorethan17.000votersinterviewedbytheWorldValues Survey association (henceforth WVS) in 14 European countries between the end of 1999 and the beginning of 2000. 64 64 The 14 European countries under investigation in our study are the following: Austria, Denmark,Belgium,Netherlands,Sweden,Finland,Portugal,Spain,Greece,Germany,Italy, 62 DependentVariables Electoral Participation. Todescribethevoter s par- ticipationdecisionweconsideredthefollowingquestioncontainedintheWVS: "Which party (if any) would you vote tomorrow?". Respondents were given the possibility of answering the question by indicating the party they would vote or by asserting that they would not vote or would cast a blank vote. Therefore, to assess whether an individual would abstain in an election, we constructed a binary dummy variable that takes the value of 1 if she would not vote or cast a blank vote in the election and the value of 0 if she would vote for one of the competing parties. One limitation of using survey data is that the sample turnout rate may di¤er from the actual one. In our data the overall sample turnout is 82.7% while the average of the actual turnout in the two elections closest to the survey is 77%. This di¤erence between the self- reportedturnoutrateandtheactualoneisinlineorevenlowerthanprevious studies. The main potential problemarising fromhaving a non-representative sample is the possibility of obtaining biased regression coe¢ cients. However, vote validation studies have also suggested that the presence of such discrep- ancy has no signicant e¤ect on the empirical results. 65 Moreover, excluding from our sample the countries where the di¤erence between the self-reported and actual turnout rates is higher then 10%, does not have any signicant e¤ect on our results. 66 Communicative Voting. In order to construct a variable that embodies the trade-o¤betweenstrategicandcommunicativemotivationsinthevotingdeci- sion, we need to distinguish between parties considered as likely winners from those perceived as sure losers. Since in most European countries the electoral system entails a proportional representation, our discriminator for classifying France, United Kingdom and Ireland. Appendix B2 contains a complete description of all the data used in our analysis. 65 See Matsusaka and Palda (1999) for a discussion on this issue. 66 See Table A4.1 in Appendix B4 for the regression results obtained from the subsample of countries with low dicrepancy between sample and actual turnout rates. 63 a party as a "likely winner" or a "sure loser" is not given by its dimension (share of votes). Rather, by using the information contained in Koole and Katz(2000),wemakesuchaclassicationdependingonwhetheragivenparty in 1999 was perceived by voters as a party with the potential to participate in a government coalition. More specically, "likely winner" parties are dened as being those that belong and/or support a government coalition or that be- longtoacoalitionthatopposesthegovernmentandrepresentsapotentialand crediblealternativetothegoverningcoalition. Di¤erently, "sureloser"parties are the ones with no chance of being in a winning coalition. This information allows us to generate a binary dummy variable taking the value of 1 if the party that the individual would vote is a sure loser and the value of 0 if it is a likely winner. "Closer to a sure loser party" vs "Closer to a likely winner party" (CSLP vs CLWP).Inordertoclassifyindividualsaccordingtowhethertheirideologically closer party was a sure loser or a likely winner, we combined the information drawn fromthree di¤erent data sources. First, we used WVS data to take the self-reported positions of individuals on a single-dimensional political space structured in a ten-point political scale where 1 indicates the extreme left and 10 the extreme right. Second, we used the Marks and Steenbergen (1999) party dataset to assess the positions held by political parties on the Left- Right political spectrum in each country included in our analysis. Finally, to distinguish between parties considered as likely winners from those sure losers, we took the information contained in Koole and Katz (2000). These three di¤erent pieces of information were then combined with each other to determine which party was the closest to the preferences of each individual in oursampleandwhetheritwasalikelywinnerorasureloserparty. Therefore, we were able to construct a binary dummy variable for being CSLP, taking thevalueof1ifthepartywhoseideologicalpositionwasclosertotheoneself- 64 reported by the individual was a sure loser and 0 if it was a likely winner. 67 Independent Variables Individual Characteristics of Voters. In order to analyze the determinants of voters turnout and communicative voting, we have included several individual-level explanatory variables. Along with the usual demographics such as age and gender, we added variables indicating the education level, the level of income, the marital status and information about the job and the employment of the respondents as proxies that dene the individual s socioeconomic status. We have also included a series of variables regarding the level of interest of the individual in political matters such as the extent to which she believes that politics is important and/or how good she considers the working of the political system in her country and whether she belongs to a political party and/or to a special interest group. Such variables are meant to investigate thepossiblepresenceof"expressive"motivationsintheparticipationdecision. These kind of variables have been criticized due to the possible presence of endogeneity (Matsusaka and Palda (1999)). Nevertheless, these proxies are somehowcapturingthepotentialheterogeneityacrossindividualintheunder- lying disposition to participate in the political process. Moreover, excluding thesevariables fromourempirical analysis does not haveanysignicant e¤ect on our results. 68 Information and Political Preferences. Inordertotest forthe empirical rel- evanceoftheswing voters curse theorywefocusedonthequestionscontained 67 Obviously, relyingonsuchself-reportedpoliticalpreferencesimpliesimplicitlyassuming that all individuals have the same mapping between political preferences and numbers on the 10 points left-right spectrum. This constitutes a very strong assumption behind the three-stage electoral choice model and thus represents a potential source of measurement errors. Nevertheless, as long as the measurement error is small, the three-stage model may bring additional insights to the analysis not captured by the benchmark model (two stage model). 68 See table A3.1 in Appendix B3. 65 in the WVS regarding the level of information and the political preferences of individuals. First, we constructed a proxy of the individual s level of informa- tion about politics by classifying an individual as uninformed when she does notfollowpoliticsinthenews. Then,wecreatedavariableindicatingwhether the individual is moderate or independent (when she does not have a political position on the left-right spectrum) in order to have a proxy of the swinger quality of the individual. Finally we computed the interaction term between these two variables. Controlling for being uninformed and independent, if the swing voters curse theory holds true, we should observe this interaction term being positively correlated with the probability of abstaining. We should point out that in general it is di¢ cult to draw sound conclu- sions on the causal relationship between being uninformed and deciding not to participate in the voting process. As observed by Lassen (2005): The problem is that information acquisition is endogenous and, therefore, both the decision to vote and the decision to ob- tain an education or become informed about political issues can be caused by some third, unobservable, factor. Hence, to make a statement about causal e¤ects in order to empirically evaluate the theoretical work, it is necessary to address the endogeneity problem(Lassen (2005), pg. 104). In other words, if the information variable is endogenous we may have that the econometric relationship between voting and information may simply rep- resent a correlation rather than a casual link. Nevertheless, we argue that such endogeneity problem is not really worri- some in our analysis. First of all, our dataset is constructed on the basis of a general survey rather than an election poll. This implies that, since the information collected is not specically related to a given election, the indi- 66 vidual decision to be informed about political issues is not determined by the decision of participating in a specic voting process. Second, the set of our independent variables is quite rich and extensive so that it is unlikely that some variables not considered in the analysis could actually determine both the decision to vote and the decision of being informed about politics. More- over and most importantly, even if information were to be endogenous, if the swing voters curse theory holds we should still observe a positive correlation betweenbeingindependentanduninformedandtheprobabilityof abstaining. Therefore, althoughwecannotexcludethepresenceofsuchendogeneityprob- lem, webelievethatourresultsarenotseriouslyunderminedbythispotential problem. Country-Level Statistics. Since the electoral behavior of voters may be af- fectedbycountry-levelvariablesthatdenetheworkingofpoliticalinstitution and the functioning of the media system, we collected information that relate to these two dimensions of the European countries under investigation. From the international IDEA Handbook of Electoral System Design (2004) we col- lected data on the electoral systems. 69 Other variables such as the Herndahl index of opposition parties, the district magnitude and the threshold level of representation help us to dene the political system governing the elections in the European countries considered in this study (Beck, Keefer and Clarke (2004)). At the same time we have included two variables to account for the impact of the country media system on voting behavior: an index of the free- dominthemediatakenfromthereport"Pressfreedom1994-2001"releasedby The Freedom House and the Herndahl Index of media concentration drawn 69 Noticethatwehaveincludedsuchdummiesonelectoralsystemjustascontrolvariables in some of the robustness-check regressions in appendix B3. The reason for not including them in the our main regressions is that we do not have enough variability in our sample. For example, the rst-past-the-post system is used only in UK and the single transferable vote only in Ireland, thus it is not possible to separate the e¤ect of such variables on the probabily of participating and on the voting decision, from the country xed e¤ect. 67 from Sanchez-Tabernero (2004). 2.3.2 Descriptive Statistics In Tables 1 and 2 we provide a preliminary description of our variables of interest. More specically, Table 1 displays the di¤erences in terms of indi- vidual characteristics between the samples of voters and non-voters in the 14 European countries under investigation. We notice that, on average, individ- uals who decide to participate in the election seem to give more importance to politics, have a better opinion of the working of the political system and are more likely to belong to a political party compared to non-voters. This suggests that expressive motivations may play an important role in electoral participation. Further, in line with the swing voters curse theory, individuals whodo not participate inthe votingprocess are generallyless informedabout politicsandhavemoremoderatepoliticalpreferencesthanthosewhodecideto vote. Moreover, voters seem also to earn, on average, higher levels of incomes andaremorelikelytobelongtoaspecialinterestgroupthannon-voters. This indicates that the potential private benets from voting are likely to a¤ect electoral participation. 68 Voters Abstentionists Average level of information about politics : 1 (highest) to 5 (lowest) 1.910 2.510 Prob>|t| = 0,0000 Average level of importance given to politics: 1 (highest) to 4 (lowest) 2.690 3.110 Prob>|t| = 0,0000 Frequency of discussions about politics (1 to 3) 1.910 1.670 Prob>|t| = 0,0000 Average valuation of the political system (1 to 10) 5.490 4.900 Prob>|t| = 0,0000 Percentage of Women 51.56% 60.95% Prob>|t| = 0,0000 Average age 46.150 42.024 Prob>|t| = 0,0000 Average level of education (1 to 8) 4.400 4.230 Prob > |t|=0,0001 Average level of income (1 to 10) 5.200 4.670 Prob>|t| = 0,0000 Percentage of individuals belonging to a Special Interest Group (SIG) 59.38% 43.75% Prob>|t| = 0,0000 Percentage of individuals belonging to a political party 6.70% 1.50% Prob>|t| = 0,0000 Percentage of individuals close to a "sure loser" party 37.58% 44.94% Prob > |t| =0,0000 Percentage of independents and moderate voters 44.88% 72.38% Prob>|t| = 0,0000 ttest H0: Vectors of means are equal for the two samples Table 1. Voters and abstentionist 69 Table 2. Communicative and strategic voters Strategic Voters Communicative Voters Average level of information about politics : 1 (highest) to 5 (lowest) 1.900 1.960 Prob > |t| = 0,0395 Average level of importance given to politics (1 to 4) 2.699 2.670 Prob > |t| = 0,1849 Frequency of discussions about politics (1 to 3) 1.900 1.940 Prob > |t| = 0,0062 Average valuation of the political system (1 to 10) 5.630 4.900 Prob > |t| = 0,0000 Percentage of Women 51.38% 52.33% Prob > |t| = 0,3910 Average age 46.770 43.460 Prob > |t| = 0,0000 Average level of education (1 to 8) 4.280 4.890 Prob >|t| = 0,0000 Average level of income (1 to 10) 5.210 5.170 Prob > |t|= 0,5601 Percentage of individuals belonging to a Special Interest Group (SIG) 59.45% 59.09% Prob>|t|= 0,7414 Percentage of individuals belonging to a political party 6.96% 5.85% Prob > |t|= 0,0457 Percentage of individuals close to a "sure loser" party 34.78% 49.80% Prob > |t| = 0,0000 Percentage of independents and moderate voters 44.78% 45.33% Prob > |t| = 0.6161 Percentage of Leftist extremists 7.20% 11.59% Prob > |t|= 0,0000 Percentage of Rightist Extremists 12.28% 11.90% Prob > |t|= 0.5987 ttest H0: Vectors of means are equal for the two samples Table2reportstheindividualcharacteristicsofstrategicandcommunicative voters, respectively. By observing the t-test for the di¤erences in means, we note that individuals voting for a sure loser party seem to have, on average, a worse opinion regarding the working of the political system than those who vote for a likely winner party. This suggests the presence of the so-called "protest-voting", i.e., people decide to vote for a sure loser party as a signal 70 to express their dissatisfaction with the functioning of the political system. Communicative voters seem also to be generally more educated and more likely to be politically extremists. Further, individuals whose ideologically closer party is a sure loser are, on average, less inclined to vote for a likely winner party. Such a di¤erence may be explained by the fact that sincere voting is one of the driving forces in the voting decision. 2.4 Electoral Participation and Communicative Voting in Europe InthissectionweimplementtheeconometricmethodologydescribedinSection 2 and comment on the results obtained. We carry on our empirical investiga- tion as follows. We rst analyze the determinants of electoral participation in the two-stage and the three-stage electoral choice models. Then we examine the determinants of communicative voting. Again the estimation is carried out for the two-stage and the three-stage electoral choice models. 2.4.1 Electoral Participation The Two-Stage Electoral Choice Model: Estimation and Results We report in Table 3 the estimation results on the determinants of electoral participation in the two-stage electoral choice model. As already discussed in Section 2.2, two are the specications adopted: Sequential Logit and Nested Logit. 71 0.019 0.214 ( 0.062 ) ( 0.216 ) 0.146 * 0.427 ( 0.079 ) ( 0.298 ) 0.199 ** 0.200 ( 0.086 ) ( 0.146 ) 0.264 ** 0.357 ** ( 0.111 ) ( 0.186 ) 0.875 *** 1.000 *** ( 0.158 ) ( 0.227 ) 0.206 *** 0.210 ** ( 0.053 ) ( 0.100 ) 0.435 *** 0.720 *** ( 0.052 ) ( 0.273 ) 0.507 *** 0.483 *** ( 0.061 ) ( 0.101 ) 0.168 *** 0.202 ( 0.057 ) ( 0.129 ) 0.413 *** 0.580 ** ( 0.121 ) ( 0.234 ) 1.009 *** 0.963 *** ( 0.060 ) ( 0.064 ) 0.018 0.022 ( 0.133 ) ( 0.136 ) 0.235 *** 0.623 ** ( 0.050 ) ( 0.335 ) 0.025 *** 0.048 *** ( 0.006 ) ( 0.019 ) 0.020 0.064 ( 0.033 ) ( 0.069 ) Plurality System 0.009 0.113 ( 0.090 ) ( 0.310 ) Threshold for representation 0.090 *** 0.070 * ( 0.017 ) ( 0.040 ) Herfindal Index Opposition Parties 0.035 1.962 ( 0.223 ) ( 1.937 ) 0.004 *** 0.007 *** ( 0.001 ) ( 0.003 ) Pseudo R2 Number of Observations Percentage of Correct Predictions LR test of homoskedasticity (IV for the nested logit = 1) *Significant at 0.10 level **Significant at 0.05 level ***Significant at 0.01 level Note. Dependent variable is whether the individual would not vote in a general election. All regression include age, gender, occupation, marital status and size of urban area dummies. Robust standard errors are in parenthesis 17072 chi2(1)= 8075.28 Prob > chi2 = 0.000 17072 80.37% Believe politics is important Discuss politics frequently or occasionally Uninformed about politics Moderate or indipendent Inverse Index of Media Freedom HH Index of Media Concentration 0.14 Moderate/Indipendent x Uninformed Middlehigh level of income High level of income Belong to a political Party Good opinion about the political system of the country Table 3. Estimates of Electoral Participation Two stage model Middle level of education Mean District Magnitude Closer to a "sure loser" party High level of education Belong to a Special Interest Group Sequential Logit Nested Logit 72 People with higher incomes are less likely to abstain. Similarly, individuals belongingtoaspecialinterestgrouparemorelikelytovote. Wecanthinkthat thesepeoplehavehigherpotential privatebenets fromvoting. Thecombina- tionofthesetworesultstogetherseemtosuggestthat,asextensivelyshownby the empirical literature on turnout, private benets play an important role in electoral participation (see Lijphart (1997)). On the other hand, the positive correlation between probability of turnout and belonging to a special interest groupisalsoconsistentwiththeideathatvotersincludeothergroupmember s welfare in their own utility function (Feddersen and Sandroni (2006), Coate and Conlin (2004)). The educational level, quite unexpectedly and in contrast with previous studies (Carter and Guerette (1992), Fisher (1996)), seems to have no e¤ect on the probability of voting. We can explain this result by considering that the level of education inuences the cost of acquiring information and thus indirectlytheprobabilityofvoting. Therefore, oncecontrollingforthelevelof information this e¤ect of education on voterselectoral participation vanishes away. People belonging to political parties display higher inclination to vote (Fio- rina (1976) and Riker and Ordeshook (1968)). Voters having a good opinion of the political system operating in their country as well as those who think thatpoliticsisimportantaremorelikelytovote(Downs(1957)andRikerand Ordeshook(1968)). Therefore, the e¤ect exercised on the individual s elec- toral participation by the variables indicating the extent of voter s interest in politics and her evaluation of the functioning of the political system seems to bringempiricalsupporttotheideathatexpressivemotivationsplayanimpor- tant role in the individual s decision to turnout (Riker and Ordeshook (1968), Fiorina (1976)). 73 As far as the e¤ect of information on the voter s turnout is concerned, we note that being uninformed increases the probability of not voting. Simi- larly, moderate or independent individuals are less likely to turn out. How- ever, the interaction term indicating whether the individual is uniformed and moderate/independent does not seem to be statistically signicant. These results seem to suggest that being at the same time uninformed and moder- ate/independentdoesnota¤ecttheindividual sdecisiontoturnout,butrather both characteristics contribute to a di¤erent extent to the choice of whether to vote or abstain. Such results are robust to all the di¤erent specication of our empirical model and to di¤erent classication of uninformed and swinger voters. 70 Consequently, our empirical ndings do not provide empirical sup- port to the swing voters curse theory. On the other hand, our results seem supportiveof theempiricalpredictionsonthee¤ectofinformationonturnout implied by decision theoretic models of voting behavior (Matsusaka (1995)). Therefore, our ndings seem to go in the opposite direction of the results ob- tained by Battaglini, Morton and Palfrey (2006) on the empirical relevance of the swing voters curse in an experimental context. Ontheotherhand,individualswhoseideologicallycloserpartyisasureloser are less likely to vote. This results suggests that voters do take into account their expected benet from voting when deciding whether to cast a vote or not (Riker and Ordeshook (1968)). The country-level characteristics seem to play an important role on the voter s decision of whether to participate in the elections. From the perspec- tive of the functioning of the media system, we nd that a reduction in the level of freedom in the media has a negative e¤ect on turnout. This evidence isconsistentwiththeideathathigherlevelsofpoliticalcontroloverthemedia a¤ect the political accountability of parties and muddle up the overall func- 70 See table A3.3 in the Appendix B3. 74 tioningofthedemocracy(Besley,BurgessandPrat(2002)). Atthesametime, this result is also supportive of the informational theories on electoral partic- ipation suggesting that in presence of more "noisy" informations, individual incentivestoturnoutdecrease(Matsusaka(1995), FeddersenandPesendorfer (1999)). Finally, some characteristics of the institutional system seems also to have a signicant e¤ect on votersparticipation decisions. Di¤erences between plu- rality (winner-takes-all) and other forms of electoral systems as well as the degree of concentration of opposition parties do not appear to a¤ect the vot- ersdecision of whether to vote. On the other hand, a higher threshold for representationreducesthevotersparticipationintheelection(Powell(1986)). Districtmagnitudealsoa¤ectstheprobabilityofturnout: thehigherthenum- ber of representatives elected out of a given constituency size, the more likely that an individual will turn out. This evidence seems to suggest that voters take into account their probability of being pivotal in deciding whether to participate in the electoral process (Riker and Ordeshook (1968), Palfrey and Rosenthal (1983), (1985)). The Three-Stage Electoral Choice Model: Estimation and Results In Table 4 we report the empirical results regarding the determinants of elec- toral participation for the subsamples of individuals "closer to a sure loser party" (CSLP) and "closer to a likely winner party" (CLWP), respectively. 75 Table 4. Estimates of the Electoral Participation Three stage model 0.073 0.244 0.072 0.175 ( 0.098 ) ( 0.171 ) ( 0.081 ) ( 0.106 ) 0.046 0.578 ** 0.193 * 0.340 ** ( 0.123 ) ( 0.242 ) ( 0.103 ) ( 0.140 ) 0.159 0.265 0.244 ** 0.232 * ( 0.131 ) ( 0.225 ) ( 0.115 ) ( 0.127 ) 0.198 0.312 0.287 ** 0.352 ** ( 0.168 ) ( 0.275 ) ( 0.147 ) ( 0.160 ) 0.763 *** 0.896 *** 1.000 *** 1.069 *** ( 0.221 ) ( 0.325 ) ( 0.232 ) ( 0.259 ) 0.202 ** 0.224 * 0.222 *** 0.207 *** ( 0.080 ) ( 0.136 ) ( 0.069 ) ( 0.076 ) 0.393 *** 0.870 *** 0.475 *** 0.635 *** ( 0.081 ) ( 0.159 ) ( 0.068 ) ( 0.116 ) 0.463 *** 0.322 ** 0.517 *** 0.527 *** ( 0.096 ) ( 0.148 ) ( 0.078 ) ( 0.082 ) 0.218 *** 0.312 ** 0.122 0.146 * ( 0.088 ) ( 0.149 ) ( 0.076 ) ( 0.084 ) 0.377 ** 0.512 ** 0.467 *** 0.536 *** ( 0.194 ) ( 0.209 ) ( 0.152 ) ( 0.157 ) 1.388 *** 1.336 *** 0.876 *** 0.891 *** ( 0.107 ) ( 0.112 ) ( 0.077 ) ( 0.081 ) 0.104 0.142 0.050 0.053 ( 0.206 ) ( 0.194 ) ( 0.169 ) ( 0.165 ) 0.074 *** 0.140 *** 0.004 0.003 ( 0.011 ) ( 0.023 ) ( 0.007 ) ( 0.010 ) 0.101 ** 0.276 *** 0.113 ** 0.156 ** ( 0.049 ) ( 0.105 ) ( 0.051 ) ( 0.065 ) Plurality System 0.302 * 0.762 *** 0.092 0.338 ( 0.174 ) ( 0.263 ) ( 0.112 ) ( 0.205 ) Threshold for representation 0.047 * 0.135 *** 0.119 *** 0.079 ** ( 0.028 ) ( 0.050 ) ( 0.022 ) ( 0.036 ) Herfindal Index Opposition Parties 1.135 *** 5.153 *** 1.386 *** 0.582 ( 0.319 ) ( 1.187 ) ( 0.342 ) ( 0.665 ) 0.003 * 0.012 *** 0.004 *** 0.005 *** ( 0.002 ) ( 0.003 ) ( 0.001 ) ( 0.001 ) Pseudo R2 0.16 0.13 Number of Observations 6676 1036 1036 Percentage of Correct Predictions 82,15% 6676 chi2(1)= 3858.05 LR test of homoskedasticity (IV for the Nested Logit= 1) Prob > chi2 = 0,0000 Good opinion about the political system of the country Believe politics is important 78,82% Mean District Magnitude Moderate/Indipendent x Uninformed Middlehigh level of income High level of income Belong to a political Party Belong to a Special Interest Group Sequential Logit Inverse Index of Media Freedom HH Index of Media Concentration Discuss politics frequently or occasionally Uninformed about politics Moderate or indipendent Middle level of education High level of education *Significant at 0.10 level **Significant at 0.05 level Sequential Logit Subsample of closer to a "sure loser" party voters Subsample of closer to a "likely winner" party voters Note. Dependent variable is whether the individual would not vote in a general election. All regression include age, gender, occupation, marital status and size of urban area dummies. Robust standard errors are in parenthesis Nested Logit Prob > chi2 = 0.000 chi2(1)= 4142.82 ***Significant at 0.01 level Nested Logit 76 We can notice that most of the results of the two-stage electoral choice modelholdtruealsointhemodiedstructureoftheelectoraldecisionprocess that takes into account that individuals face di¤erent choice sets depending on whether their most preferred party is a likely winner (CLWP voters) or a sureloser(CSLP voters).Expressivemotivationsforparticipationinthevoting processcontinuetoplayanimportantandsignicantrolebothinthesubsam- ple of CSLP and CLWP voters. As before, being uninformed as well as being moderate or independent is positively correlated with the probability of non- voting. At the same time, being uninformed and moderate/independent does not have a signicant impact on the probability of voting for both CSLP and CLWP individuals. As far as individual-level characteristics are concerned, the only di¤erence that it is worth noticing regards the role of income. In the subsampleofCSLP voters,incomedoesnothaveanysignicantimpactonthe probability of voting. On the contrary, in the subsample of CLWP voters, a higher level of income is positively and signicantly correlated with the prob- ability of voting. This di¤erence can be explained by the di¤erent potential private benet that CSLP and CLWP voters derive from participating in the electoral process. Since their preferred party is a likely winner, CLWP voters havearealpotentialprivatebenetfromvoting. Thehighertheirincome, the highersuchpotentialbenet. Di¤erently, forCSLP individualsthepossibility of deriving a private benet from voting is very limited since their most pre- ferred party is a sure loser. Therefore, their decision to vote does not depend on the level of their income. For what concerns the country-level variables, as in the previous two-stage electoralchoicemodel,lowerthresholdsforrepresentationandahighernumber of elected representatives are both conducive to higher turnout probabilities forbothCSLP andCLWP voters. Moreover,concentrationinthemediaown- ership seems also to be positively correlated with the probability of voting. 77 This result seems in line with the ndings of Oberholzer-Gee and Waldfogel (2005) of a "political mobilization" e¤ect due to the structure of media mar- kets. Since the media market is characterized by xed costs and economies of scale, a more concentrated media market is more e¤ective at reaching large groups. Therefore candidates nd easier to mobilize voters. For the same reason, we can think that a more concentrated media market can lower the cost that individuals have to incur in order to learn candidates positions and thus increase the probability of turnout (Matsusaka (1995), Oberholzer-Gee and Waldfogel (2005)). On the other hand, our results show that a higher freedom of the media, the presence of a winner-takes-all system and higher concentrationofoppositionpartiesdonotseemtohaveasignicantimpacton CLWP votersbutinsteadincreasestheprobabilityofturnoutofCSLP voters. 2.4.2 Communicative Voting TheTwoStageElectoralChoiceModel: EstimationandResults In Table 5 we report the empirical results regarding the determinants of commu- nicative voting. Before analyzing the results regarding communicative voting, it is important to highlight that the likelihood ratio tests reported in Tables 3 and 5 on the Nested Logit models show that we cannot accept the null hy- pothesis of the inclusive value parameters being equal to one. This seem to suggest that our empirical model is indeed nested. Better educated people seem to be more likely to vote as communicating rather than strategically. This result, although it may appear surprising, can be understood by referring to the direct and signicant e¤ect of education on electoral participation observed in the empirical literature on turnout. As pointed out by Lijphart (1997): At the endof the 19thcenturyandthe beginningof 20thcen- tury,whenuniversalsu¤ragewasbeingadoptedinmanycountries, 78 political analysts tended to assume that it would be the better ed- ucated and more prosperous that would make the rational choice not to bother to vote. [...] But empirical studies soon showed that socioeconomic status and voting were positively, not negatively, linked(Lijphart (1997), pg. 1). Probably something similar is happening here. We would have expected more educated people to "make the rational choice" of not voting for a sure loser party. However, as the recent literature on communicative voting shows, thevoteforloserpartiescouldbeexplainedinanentirelyrational framework. Therefore, a possible interpretation of this result may indeed lie on the higher awareness that better educated individuals may have on the communicative role of their vote. In other words, higher educated voters may realize that by voting as communicating they can inuence other individuals (Piketty 2000) or the political platforms of likely winner parties (Castanheira 2003). 79 Table 5. Estimates of Communicative Voting Two stage model 0.283 *** 0.284 *** ( 0.070 ) ( 0.097 ) 0.389 *** 0.379 *** ( 0.081 ) ( 0.114 ) 0.056 0.001 ( 0.093 ) ( 0.128 ) 0.158 0.151 ( 0.112 ) ( 0.144 ) 0.217 * 0.195 ( 0.111 ) ( 0.126 ) 0.034 0.016 ( 0.061 ) ( 0.087 ) 0.488 *** 0.449 *** ( 0.056 ) ( 0.095 ) 0.039 0.035 ( 0.059 ) ( 0.077 ) 0.011 0.073 ( 0.067 ) ( 0.104 ) 0.212 ** 0.222 ** ( 0.080 ) ( 0.114 ) 0.101 0.073 ( 0.087 ) ( 0.084 ) 0.347 *** 0.473 *** ( 0.088 ) ( 0.148 ) 0.717 *** 0.665 *** ( 0.057 ) ( 0.148 ) 0.048 *** 0.037 ** ( 0.006 ) ( 0.017 ) 0.071 * 0.037 ( 0.038 ) ( 0.061 ) Plurality System 0.080 0.242 ( 0.110 ) ( 0.241 ) Threshold for representation 0.041 ** 0.037 ( 0.019 ) ( 0.028 ) Herfindal Index Opposition Parties 3.168 *** 3.203 *** ( 0.259 ) ( 0.438 ) 0.005 *** 0.004 *** ( 0.001 ) ( 0.001 ) Pseudo R2 Number of Observations Percentage of Correct Predictions LR test of homoskedasticity (IV for the nested logit = 1) 64.59% 13548 Sequential Logit Nested Logit 0.07 HH Index of Media Concentration *Significant at 0.10 level **Significant at 0.05 level ***Significant at 0.01 level 13548 Note. Dependent variable is whether the individual would vote for a "sure loser" party. All regression include age, gender, occupation, marital status and size of urban area dummies. Robust standard errors are in parenthesis chi2(1)= 8075.28 Prob > chi2 = 0.000 Right wing extremist Mean District Magnitude High level of income Belong to a political Party Left wing extremist Belong to a Special Interest Group Inverse Index of Media Freedom Closer to a "sure loser" party Uninformed about politics Good opinion about the political system of the country Believe politics is important Middle level of education High level of education Middlehigh level of income Discuss politics frequently or occasionally 80 A voter s positive attitude toward the working of the political system oper- ating in her own country is positively related with the probability of casting a strategic vote. This nding seems to reveal that voters dissatised with the way the political system functions in their respective country are more likely to vote for sure loser parties (what is generally referred in political science as protest voting). Quite interesting appears to be the relationship between being either a left wing or a right wing extremist and strategic voting. Right-wing extremists seem more likely to vote strategically for a likely winner party than moderate voters do. On the other hand, leftist extremists do not behave statistically di¤erently from moderate voters. A rst possible explanation of this asym- metry between the behaviors of left wing and right wing extremists may lie in the presence of a "supply e¤ect". In some of the countries of our sample there are no extreme right loser parties and/or extreme left loser party. Since in such case extremist voters may have a restricted choice set, the results may be a¤ected by this "supply e¤ect". However, restricting our sample only to countries that have extremist loser parties do not chance our results in any signicant way. 71 Thus such "supply e¤ect" does not seem to account for the presence of such asymmetry. Another possible interpretation of this empirical result may simply involve the presence of heterogeneity in the votersprefer- ences. In this perspective, the utility functions of right wing extremist seem tohaveahigherdegreeof"concavity"and/oralowerdiscountfactor. Finally, wemayinterpretthisresultasa"stigmae¤ect". Inotherwords,rightextrem- ist voters may not report that they would vote for extremist rightist parties since in western Europe, for historical reasons, extreme rightist parties have a negative public image. Another interesting result is given by the fact that voters displaying pref- 71 See table A4.2 in Appendix B4. 81 erences closer to the platform of a sure loser party show a greater probability of casting a communicative vote. This nding seems to suggest the presence of sincere voting even by individuals whose ideologically closer party is a sure loser. Country-level institutional variables seem also to have a signicant impact oncommunicative voting. The lowerthe freedomof the mediathe more likely thevotercastshervoteforasurlyloserparty. Wemightinterpretthisresultas acaseofprotestvoting. Thegreatertheconcentrationofthepartiesbelonging to the opposition, the less likely individuals vote for losers. This seems to suggest that if opposition parties are more fragmented (less concentrated), it is more likely that a loser party may receive a signicative amount of votes and thus enter sooner or later in a winning coalition. Finally, the higher the number of representatives elected for a given constituency size, the less likely individuals vote for losers. This nding can be understood in the light of the fact that the higher the number of representatives to be elected, the higher the probability of being pivotal and thus the higher the incentives to vote strategically. The Three Stage Electoral Choice Model: estimation and results In Table 6 we report the empirical results regarding the determinants of com- municativevotingforthesubsamplesof "closer to a sure loser party" (CSLP) and "closer to a likely winner party" (CLWP) voters. 82 Table 6. Estimates of Communicative Voting Three stage model 0.252 ** 0.283 *** 0.295 *** 0.285 *** ( 0.102 ) ( 0.097 ) ( 0.098 ) ( 0.095 ) 0.391 *** 0.419 *** 0.403 *** 0.384 *** ( 0.126 ) ( 0.122 ) ( 0.108 ) ( 0.114 ) 0.040 0.078 0.059 0.039 ( 0.139 ) ( 0.137 ) ( 0.126 ) ( 0.130 ) 0.075 0.106 0.223 0.203 ( 0.169 ) ( 0.162 ) ( 0.153 ) ( 0.162 ) 0.155 0.064 0.267 0.298 * ( 0.152 ) ( 0.159 ) ( 0.169 ) ( 0.175 ) 0.036 0.037 0.085 0.043 ( 0.089 ) ( 0.083 ) ( 0.085 ) ( 0.086 ) 0.533 *** 0.424 *** 0.491 *** 0.485 *** ( 0.084 ) ( 0.086 ) ( 0.076 ) ( 0.077 ) 0.150 * 0.105 0.050 0.030 ( 0.086 ) ( 0.085 ) ( 0.084 ) ( 0.081 ) 0.014 0.100 0.045 0.076 ( 0.098 ) ( 0.093 ) ( 0.094 ) ( 0.093 ) 0.242 ** 0.117 0.179 0.196 * ( 0.113 ) ( 0.104 ) ( 0.113 ) ( 0.105 ) 0.408 *** 0.097 0.696 *** 0.486 ( 0.108 ) ( 0.089 ) ( 0.223 ) ( 0.292 ) 0.199 * 0.310 *** 0.635 ** 0.549 *** ( 0.110 ) ( 0.079 ) ( 0.198 ) ( 0.207 ) 0.069 *** 0.059 *** 0.022 ** 0.019 * ( 0.010 ) ( 0.012 ) ( 0.009 ) ( 0.011 ) 0.094 * 0.089 0.197 *** 0.151 ** ( 0.052 ) ( 0.056 ) ( 0.064 ) ( 0.076 ) Plurality System 0.642 *** 0.297 0.570 *** 0.658 *** ( 0.184 ) ( 0.183 ) ( 0.147 ) ( 0.143 ) Threshold for representation 0.027 0.054 ** 0.094 *** 0.106 *** ( 0.029 ) ( 0.028 ) ( 0.027 ) ( 0.026 ) Herfindal Index Opposition Parties 3.443 *** 4.014 *** 1.979 *** 2.197 *** ( 0.362 ) ( 0.441 ) ( 0.450 ) ( 0.540 ) 0.009 *** 0.008 *** 0.002 ** 0.002 ** ( 0.001 ) ( 0.001 ) ( 0.001 ) ( 0.001 ) Pseudo R2 0.08 0.06 Number of Observations 8442 8442 Percentage of Correct Predictions 42.44% *Significant at 0.10 level **Significant at 0.05 level 22.50% LR test of homoskedasticity (IV for the nested logit = 1) Middlehigh level of income Discuss politics frequently or occasionally Uninformed about politics Belong to a political Party Belong to a Special Interest Group Good opinion about the political system of the country Believe politics is important High level of income High level of education Middle level of education Subsample of closer to a "sure loser" party voters 5092 Left wing extremist Right wing extremist 5092 Mean District Magnitude Inverse Index of Media Freedom HH Index of Media Concentration Subsample of closer to a "likely winner" party voters Sequential Logit Nested Logit Sequential Logit Nested Logit Note. Dependent variable is whether the individual would vote for a "sure loser" party. All regression include age, gender, occupation, marital status and size of urban area dummies. Robust standard errors are in parenthesis Prob > chi2 = 0.000 chi2(1)= 4142.82 ***Significant at 0.01 level chi2(1)= 3858.05 Prob > chi2 = 0,0000 83 WecannoticethatmostoftheresultsofcommunicativevotingintheCSLP andCLWP subsamplesaresimilartothoseobtainedinthetwo-stageelectoral choice model. Education and "protest voting" continue to play an important role in de- termining communicative voting. As before, right wing extremists seem to be very strategic: they are more likely to vote for a likely winner party than moderate voters, regardless of whether their preferred party is a likely winner (when they are CLWP) or a sure loser (when they are CSLP). Di¤erently, left wing extremists are more likely to vote for a winner party than moderate voters when their preferred party is a likely winner and more likely to vote for a loser party when their preferred party is a sure loser. We can interpret this result as suggesting that leftist extremists are more likely to vote sincerely, regardless of whether their preferred party is a winner or a loser. The functioning of the media system seems to exercise a signicative e¤ect on communicative voting. Both CSLP and CLWP voters are more likely to vote for sure loser parties if the extent of freedom in the media market is low. Thisresultcanbeinterpretedasasignalofprotestvotinginbothsubsamples. As in the two stage model, higher concentration of opposition parties and a higher number of elected representatives for constituency size leads to a higher probability of voting strategically in both subsamples. On the other hand,thehighertheconcentration,themorelikelyCLWP individualswillvote strategically. Againwe caninterpret this result inthe light of Oberholzer-Gee and Waldfogel (2005). An higher media concentration implies that the larger groupsandthuslarger(likelywinner)partiesaremorerepresented. Therefore, smaller (likely loser) party will nd less space in the media and thus, ceteris paribus, people will be less inclined to vote for them. Plurality (winner-takes-all) electoral system seems to a¤ect positively the probability that voters whose most preferred party is a likely winner vote as 84 communicating. As far as the threshold level for getting representation is concerned, this does not appear to produce any signicant impact on commu- nicative voting of CSLP voters. 2.5 Conclusions Elections are widely recognized as decision mechanisms where voters are in- volved in two di¤erent decisions. Voters face a participation decision in which they have to decide whether to go to the polling stations and cast their vote. At the same time, voters face a voting decision in which they have to decide whom to vote for. We constructed a unied empirical framework in which both the participa- tiondecisionandthevotingdecisionaretakenintoaccount. Weproposedtwo di¤erentspecicationsofourempiricalmodel. Therstisatwo-stagedecision processwheretheindividualmakesaparticipationandavotingdecision. The second is characterized by a three-stage structure where, prior to making the above two electoral decisions, the individual takes into account the fact that her preferred party is either a likely winner or a sure loser. The results from the Small-Hsiao tests on the IIA assumption underlying the multinomial logit model suggest that voters decision process is indeed sequential. The empirical analysis was thus carried over using two alternative empirical models: a sequential logit model and a nested logit model. The results that we obtained do not di¤er signicantly neither across electoral choice models nor across model specications. The results in fact are similar in both the signs and the signicance of the coe¢ cients. Nevertheless, the likelihoodratiotestontheinclusivevalueparametersofthenestedlogitmodel seems to point out that the empirical model is indeed nested. Our main ndings can be summarized as follows. First, the evidence re- garding the role of information show that uninformed individuals and in- 85 dependent ones are less likely to turnout. However, being independent and uninformed does not have any statistically signicant e¤ect on electoral par- ticipation. Thus our results do not provide empirical support to the swing voters curse theory. Second, the empirical investigation seems to conrm the presence of expressive motivations in electoral participation. Third, the level of education and the degree of extremism play a signicant role on the voter s decision of whether to vote strategically or as communicating. Finally, our empirical results show that a higher level of media freedom, a lower threshold for political representation and a larger number of representative elected for a given constituency size are associated with a higher electoral participation. Moreover, individualsaremorelikelytovoteforsureloserpartythelowerthe media freedom, the fewer the elected representative for constituency size and the more fragmented the opposition parties are. 86 3 Chapter III: Heterogenous Preferences and Endogeous Acquisition of Costly Informa- tion 3.1 Introduction and Motivations How do individuals acquire costly information? Should a rational decision maker attribute the same informational value to similar pieces of information orwouldbeoptimalforhertoacquireinformationinaslantedfashion? This paper explores these questions by considering a model of endogenous acquisi- tion of costly information. More specically, we analyze a policy environment where voters have to choose between xed alternatives with state-dependent payo¤s. We assume voters to care both about their idiosyncratic preferences and the quality of di¤erent candidates (or the e¢ ciency of the implemented policies). Thatis, ex-ante votershavedi¤erentordinalpreferencesovercandi- dates due to the heterogeneity in their idiosyncratic preferences. At the same time, we focus on the case where ex-post voters have the same ordinal prefer- encesovercandidates(orpolicies). Inotherwords,weconsiderthecasewhere voters would all rank candidates (or policies) in the same order provided that they know which candidate is of higher quality (or which policy is most e¢ - cient). Therefore, if information was costless all voters would acquire as much information as possible, learn the quality of candidates and then end up all choosing the same one. Our model shows that when information is costly to acquire di¤erent voters attribute di¤erent values to similar pieces of informa- tion. As a consequence, their optimal strategy will be to acquire information in a slantedway. That is, a small amount of information in favor of the leftist candidate would be su¢ cient to induce a leftist voter to stop investing ininformationacquisitionandchoosethatcandidate. Instead, arightistvoter 87 would nd optimal to keep acquiring information and then choose the leftist candidate only if the evidence in favor of such candidate becomes very large. The intuition for such result is straightforward. From voter s i perspective in- formation is valuable only as long as it can inuence her decision. Therefore, for a liberal voter a small amount of evidence in favor of a liberal candidate would be enough to convince her to vote for such candidate. However, weak evidence in favor of the conservative candidate would not be enough to make her choose such candidate. In this case, it would be optimal for a liberal voter to keep acquiring (costly) information up to the point where the evi- dence in favor of the conservative candidate is very strong and then she will be persuaded that the conservative candidate is indeed the high quality one. In other words, a rational voter would nd optimal to slanther information acquisition strategy in favor of her ex-ante preferred alternative. As a conse- quence, voters will be systematically inclined to choose the candidate closer to their idiosyncratic preferences. On the other hand, moderate voters tend to give a similar value to evidence in support of either candidates and, thus, they end up being less likely to choose the low quality candidate. Moreover, the more voters care about the quality of di¤erent candidates and the lower is the cost of acquiring information; the more we should expect voters to be- haveas if theyweremoremoderate(i.e.,tohavemoresymmetricinformation acquisition strategies). On the other hand, we show that when the cost of acquiring information is highvotersmayhavealowerexpectedutilitywhenchoosingtheirideologically closer candidate. More specically, the expected utility that each voter gets from choosing a candidate depends on two di¤erent components. There is an ideology component such that every voter has, ceteris paribus, a higher utility when voting for her ideologically closer candidate. At the same time, there is a valence component such that the expected utility from voting for a 88 given candidate is higher the more condent a voter is regarding the quality of that candidate. When acquiring information is very costly, the optimal information acquisitionstrategyis veryslanted. That is, veryfewsignals in favoroftheideologicallyclosercandidatewouldbeenoughtoconvinceavoter tochoosethatcandidate. Viceversa,avoterwouldrequiremuchmoreevidence in favor of the ideologically more distant candidate in order to vote for him. Therefore, when voting for the ideologically least preferred candidate, a voter willberelativelyverycondentabouthisqualitywithrespecttothesituation where she votes for the ideologically closer candidate. That is, when the cost ofacquiringinformationishigh,thevalencecomponent dominatestheideology component,henceeachvoterwouldhaveahigherexpectedutilitywhenvoting for the ideologically least preferred candidate. Exploring a similar underlying intuition, we also showthat when acquiring information is very costly, a voter ideologicallyclosetoacandidatemaygetalowerexpectedutilitywithrespect to an ideologically less close voter, when voting for that candidate. Finally we show that the expected gross benet and the expected cost of acquiring information are both higher for more moderate voters. This is due to the fact that moderate voters acquire relatively more information than extremistvotersbeforemakingadecision. Moreover, whileeveryvoterexpect togainfromacquiringinformationpriortomakingadecision,moderatevoters are the ones who expect to gain the most from the endogenous acquisition of costlyinformation. Atthesametime,weshowthatthemorevoterscareabout the quality of di¤erent candidates, the higher the expected gross benet, the expected cost and the expected net benet of acquiring information will be. While our main application of the model of optimal acquisition of costly information focuses on the voterschoice between alternative candidates, we argue that the model has a more general scope. As we discuss in Section 3.4, themodelcanbeeasilyappliedtoanyconsumerdecisionbetweentwoalterna- 89 tives involving idiosyncratic and quality characteristics (e.g., choice between buying a PC or a MAC). We also reinterpret our theoretical framework in the context of the decision by an agent on whether to invest in a risky asset or not. Formally, our paper is related to the one of Brocas and Carrillo (2007b) on systematic errors in decision making. In their setting individuals have to decide how much (costly) information they want to collect before taking an action whose utility depends on the state of the world. Given any exogenous amountofinformation,allindividualswouldchoosethesameaction. However, in presence of endogenous information acquisition di¤erent individuals would have di¤erent probabilities of choosing a given action. More specically, they show that individuals favor actions with large payo¤-variance. Our setting di¤er in that we assume that all actions have the same variance in payo¤s for any individual and such variance is equal across voters. At the same time we assume that individuals have the same ex-post preferences over actions but they instead di¤er in their ex-ante ranking of actions. Our paper is also related to Suen (2004) on the self-perpetuation of biased beliefs. This model focus on a situation where information acquisition is not costly but the presence of heterogenous subjective beliefs and coarse informa- tion lead to a short-runpolarization of beliefs. Our setting focus instead on a situation where information is not coarse, people share the same subjective beliefs but the presence of a cost in information gathering and heterogenous idiosyncratic preferences lead to long-runpolarization of beliefs. The paperis organizedas follows. Section2describes the model of informa- tionacquisitionbyindividuals. Section3presentsanddiscussestheresultson optimalacquisitionofcostlyinformation. Section4describessomealternative applications and interpretations of our model. Section 5 concludes. 90 3.2 The Model We analyze a model where individuals have to make a decision regarding a singleissueorpolicyP. Withoutlossofgeneralityweassumethepolicyspace to be = [0;1]. There are only two possible alternative candidates/policies L and R (i.e., P =fL;Rg) where L = 0 and R = 1: There are two possible states of the world s2 fl;rg; where the prior probability of the state of the world being s = r is assumed to be common knowledge and it is denoted by q: There is a continuum of voters of measure one who want to minimize the euclidean distance between their policy preferences and the winning candi- date/implemented policy. That is, voter i s utility function is: u i (P;d i ) =jP d i j (28) where voter i s policy preference d i is a combination of a private value com- ponent and a state-dependent public value component, i.e., d i (x i ;v) = x i +v where: v = 8 < : if s =l if s =r The private value component x i represents the idiosyncratic policy preference of voter i. The state-contingent public value component v captures the fact that, regardlessoftheiridiosyncraticpolicypreferences, votersvaluethecosts andbenets thatdi¤erentcandidates/policieswoulddeliverindi¤erentstates of the world. In other words, if L and R represents the alternative political platforms of two candidates, v can be seen as the di¤erence in the valence of the two candidates in two di¤erent states of the world. If L and R are two alternativepolicies,v justindicateswhichpolicyismoree¢ cientfromapublic 91 value perspective. 72 As a consequence, candidate L gives a higher utility to voterswhenthestateoftheworldisl thanwhenthestateisr. Theparameter measures the importance of the public value component in the individuals utilityfunctions. Theprivatevaluecomponentofvoteri spreferences, x i ; can beseenasthepolicythatvoteriwouldregardasoptimalifsheweretobelieve that both states of the world are equally likely. Such idiosyncratic preferences are distributed with a common knowledge c.d.f. F(x) with density function f(x). Withoutlossofgeneralitywerestrictthesupportoff(x)tobe [ ;1 ]; so that the ex-ante support of voterspolicy preferences is [0;1]. 73 Thus the state contingent utilities of voter i are as follows: u i (L) = 8 < : x i if s =l x i if s =r and u i (R) = 8 < : x i 1 if s =l x i + 1 if s =r (29) Notice also that for any voter i the two alternatives have the same variance in payo¤s and such variance is equal across voters since: u i (Ljs =l)u i (Ljs =r) =u i (Rjs =r)u i (Rjs =l) = 2 8i Let = f l ; r g be the signal space. The signal likelihood function is as follows: Pr( l js =l) = Pr( r js =r) = (30) where 2 (1=2;1) represents the precision of the signal. Moreover and most importantly, we assume that each voter has to incur a cost c any time she decides to get a signal on the state of the world. 72 That is by convention, if the state of the world is l then the public benets/cost ratio of policy L is higher than the one of R (viceversa if s =r). That is, if the state of the world is l policy L is the most e¢ cient one. 73 Note that for ! 0; we are in a pure private value setting. Viceversa, if ! 1 2 we are in a pure public value environment. 92 We denote by i;m the decision of voter i given that she has already drawn m = f0;1;:::::1g: Given any m; the choice set of voter i is m = fL;R;dg: Thus she canchoose candidateL orR orshe canpayc andget anothersignal on the state of the world (i.e., choose i;m = d; where d stands for draw). Let n l the number of signals l and n r the number of signals r , that voter i obtained by sampling m = (n l +n r ) times. Then the voter posterior beliefs are: Pr(s =rjn l ;n r ) = Pr(n l ;n r js =r)Pr(s =r) Pr(n l ;n r js =r)Pr(s =r)+Pr(n l ;n r js =l)Pr(s =l) Thus Pr(s =rjn l ;n r ) = q nrn l q nrn l +(1q)(1) nrn l Therefore, denoting n =n r n l we can write voters posterior beliefs as: (n) = 1 1+ 1q q 1 n (31) Hence, voter i prefers candidate R to candidate L whenever: (n)> 1 4 (2 2x i +1) = ^ i (n) (32) That is ^ n i is the di¤erence in the number of signals in favor of state r which makesvoteribeingindi¤erentbetweencandidatesRandL:Itisimmediateto showthatfor > 1 4 wealwayshavethat ^ i (n)> 0. Hencefor > 1 4 all voters would prefer candidate L when (n) = 0 and candidate R when (n) = 1: Since for 0 < < 1 4 some voters would always prefer the same candidate regardless of the state of the world, from now on we will focus on the more interesting case where > 1 4 : That is, ex-post (after knowing the state of 93 the world) all voters have the same ranking of preferences over candidates. 74 Moreover: @u i (R) @(n) = @u i (L) @(n) = 2 , 8i that is, the expected utility functions of voter i and j are always parallel. At the same time: ^ i ^ j = jx i x j j 2 >jx i x j j; for 8 2 ( 1 4 ; 1 2 ) That is, ^ i ^ j = jx i x j j if and only if = 1 2 (i.e., pure public value model).We can thus represent the expected utility of voters as follows: 0 u i (L) u i (R) | 1 μ i x - γ | i μ ˆ 1/2 1 - + i x γ Figure 3.1: Expected utility of voter i for x i < 1=2 For any exogenously given (n) 2 (0;1); di¤erent voters may have di¤erent ranking of preferences regarding candidates L and R. More specically: ^ 1 2 (n) = 1 2 and @^ i (n) @x i < 0 (33) Thus voters with more rightistpreferences require less evidence in favor of R in order to choose that candidate with respect to moderate voters. Notice 74 Notice that this restriction is without loss of generality. Considering < 1 4 would just imply the presence of some stubbornextremists voters but would not a¤ect our results on the other voters. 94 also that: u i (Lj^ i (n)) =u i (Rj^ i (n)) = 1 2 8i Hence the expected utilities of voters i and j for x j = 1=2<x i are as follows: i x - γ 2 1 - γ ) ( 2 1 L u ) ( 2 1 R u u i (L) 2 1 0 u i (R) | 1 μ 1 - + i x γ | i μ ˆ 1/2 Figure 3.2: Expected utilities of voters i and j for x j = 1=2<x i Noticealsothatwhenavotercaresmoreaboutthetruestateoftheworld(i.e., when the state-contingent public value component is larger), her indi¤erence threshold is closer to the one of a moderate voter. That is: @^ i (n) @ = (2x i 1) 4 2 8 < : < 0 if x i < 1 2 > 0 if x i > 1 2 (34) In other words, the more voters care about the quality of di¤erent candidates, the more evidence infavorof the ideologicallyclosercandidate theyrequire in order to vote for him. 3.3 Optimal Acquisition of Costly Information The model specied above highlights the trade-o¤ that each voter faces be- tweenthecostofacquiringasignalandtheutilityshegetsfromtheinformative content of each signal. The problem is thus to nd the optimal stopping rule 95 for each voter i and analyze its properties. The value function that voter i maximizes afterm draws; given a current di¤erence of signals in favor of state r equal to n; is the following: V i (n) = 8 > > > > > > > > < > > > > > > > > : max 8 < : (12(n))x i ; v(n)V i (n+1)+(1v(n))V i (n1)c 9 = ; if (n)< ^ i max 8 < : (2(n)1)(1x i ); v(n)V i (n+1)+(1v(n))V i (n1)c 9 = ; if (n) ^ i (35) wherev(n) =(n)+(1(n))(1): Inotherwords, if afterm draws voter i has a posterior (n) < ^ i (n) she will choose between alternative L with an expected payo¤of (1(n))( x i )+(n)( x i ) or paying c and getting another signal. In this case, with probability v the voter will get signal r in whichcasethevaluefunctionbecomesV i (n+1)andwithprobability(1v)she willgetsignal l inwhichcasethevaluefunctionbecomesV i (n1):Viceversa, if after m draws voter i has a posterior (n) ^ i (n) she will choose between alternativeRwithanexpectedpayo¤of(1(n))(x i 1)+(n)(x i + 1) or paying c and getting another signal. In this case, with probability v the voter will get signal r in which case the value function becomes V i (n + 1) and with probability (1 v) she will get signal l in which case the value function becomes V i (n1): Notice also that the value function of voter i does not depend on how many draws she has already done (i.e., m), since the only variabledeterminantforherdecisionisthecurrentdi¤erenceofsignalsinfavor of r (i.e., n): The following Proposition characterizes the properties of the optimal infor- mation acquisition strategy. Proposition 8 For all c > 0 and x i 2 [ ;1 ]; with 2 1 4 ; 1 2 ; there exist (n ¯ i ; n i ) such that for8m;8i: 96 1. i;m =L if n< n ¯ i ; i;m =R if n> n i and i;m =d if n2 (n ¯ i ; n i ): 2. @n ¯ i @x i < 0; @n ¯ i @ < 0 and @n ¯ i @c > 0 3. @ n i @x i < 0; @ n i @ > 0 and @ n i @c < 0 Moreover @ n i @x i 8 > > > < > > > : < @n ¯ i @x i for x i < 1 2 = @n ¯ i @x i for x i = 1 2 > @n ¯ i @x i for x i > 1 2 and @ n i @ 8 > > > < > > > : < @n ¯ i @ for x i < 1 2 = @n ¯ i @ for x i = 1 2 > @n ¯ i @ for x i > 1 2 ; @ n i @c 8 > > > < > > > : < @n ¯ i @c for x i < 1 2 = @n ¯ i @c for x i = 1 2 > @n ¯ i @c for x i > 1 2 Proof. See Appendix. Thefollowinggraphillustratestheoptimalstrategyofvoteriaftermdraws: * i n L m i = , τ * * i n ∞ - ∞ d m i = , τ R m i = , τ Figure 3.3: Optimal Strategy of voter i after msignals In other words, n ¯ i is the threshold below which voter i does not sample any- moreandchoosecandidateL;and n i isthethresholdabovewhichvoteridoes not sample anymore and choose candidate R: For any given n a more rightistvoter is always more willing to choose candidate R and less willing to choose L than a more leftistvoter. Thus x i >x j implies that n ¯ i < n ¯ j and n i < n j : Moreover, given voters j and i with 97 x j < x i < 1 2 ; then n j n ¯ j < n i n ¯ i : That is, a leftist voter requires even less signal in favor of L than more in favor of R with respect to a moderate voter. Similarly, given voters j and i with x j > x i > 1 2 ; then n j n ¯ j < n i n ¯ i : That is, a rightist voter requires even less signal in favor of R than more in favor of L with respect to a moderate voter. Hence, the more moderate a voter is, the larger is her information acquisition setN i = fnj i;m =dg (i.e., the set of the di¤erence in the number of signals in favor of r such that individual i will keep sampling). At the same time, an increase in the importance of the state- contingent public value component of the voter s utility function ( ) makes voters sample more in both directions (i.e., N i becomes larger). Moreover, an increase in induces a leftist voter to increase her leftiststopping rule more than her rightiststopping rule (i.e.,jn ¯ i j increases more than n i ). The opposite is true for a rightist voter. That is, a higher is associated with more sampling in both directions and a more symmetric stopping rule for every voter. Finally, when the cost of each signal is higher, it is optimal for each voter to make her mindsooner (i.e., N i shrinks). Moreover, when c is larger the stopping rule of each voter is also more asymmetric. Hence, when information acquisition is more costly, each individual nds optimal to devote moreresourcesinacquiringinformationinthedirectionthatcouldchangeher ex-ante decision(i.e., in the direction of persuading her not to vote for the ideologically closer candidate). Therefore, proposition 8 suggests that when is higher and c is lower we should expect voters: i) to acquire more information; ii) to behave as if they were more moderate (i.e., to have more symmetric stopping rules). Notice that, for x i = 1 2 ; n i ^ n i = ^ n i n ¯ i and thus ( n i ) = 1 (n ¯ i ): Moreover for x i >x j : (n ¯ i )<(n ¯ j )<q <( n i )<( n j ) (36) 98 Moreover, given the comparative statics results of Proposition 8, we can di- rectly derive some comparative statics results on the probability of choosing the wrongcandidate. Corollary 2 @Pr( i =Ljs=r) @c > 0 and @Pr( i =Rjs=l) @c > 0 @Pr( i =Ljs=r) @ < 0 and @Pr( i =Rjs=l) @ < 0 @Pr( i =Ljs=r) @x i < 0 and @Pr( i =Rjs=l) @x i > 0 Moreover, the more moderate a voter is, the lower is her overall probability of making errors. Thusasexpected,whenthecostofsamplingishighervoterswillmakemore errorsinthesensethattheywouldbelesslikelytochoosethecandidatethat maximizes their ex-post utility. Viceversa, when people care more about the quality of candidates their probability of mistakenly choosing the low quality candidate decreases (since as shown by proposition 8, when is higher voters acquire more information). On the other hand, more rightistvoters are less likely to choose candidate L when the high quality one is R and are instead more likely to choose candidate R when the high quality one is L: However, overall, moderatevotersarelesslikelytovoteforthewrongcandidate. This is due to the fact that, as shown by proposition 8, the more moderate a voter is,themoresymmetrichersamplingstrategyisandalsothemoreinformation sheacquiresbeforemakingadecision. Therefore,bytakingonaverageamore informeddecision moderate voters are less likely to vote for the low quality candidate. The following corollary shows that in presence of endogenous acquisition of costly information, voters may end up having a lower expected utility when voting for their ideologically closer candidate. 99 Corollary 3 The expected utility of a leftist (rightist) voter when stopping at n ¯ i and choosing L is higher (lower) than the one she obtains when stopping at n i and choosing R if and only if the cost of sampling is low. The expected utility that each voter gets from choosing one of the two candidates depends on how close her idiosyncratic preferences are with the ones of the candidate and how condent she is that the chosen candidate is thehighqualityone. Thusthedi¤erenceintheexpectedutilityofchoosingone candidate over the other depends on two di¤erent components, an ideological one and a qualitative one. Let s focus on a leftist voter to understand the intuition behind this: 1) Ideology component: For the same level of information regarding the quality of each candidate, a leftist voters would obviously get a higher utility from voting for the leftist candidate since this is the ideologically closer one. 2) Valence component: Since a leftist voter has a higher rightiststopping threshold(i.e., n i >jn ¯ i j);shewouldberelativelymorecondentofthequality of R when reaching n i rather than of the quality of L upon reachingjn ¯ i j. By proposition 8 we know that the lower the cost of sampling, the more symmetric is the optimal stopping rule of each voter. Therefore, when the cost of sampling is low, the level of condence of each voter on the quality of candidate R upon stopping n i is relatively similar to the one regarding the quality of candidate L upon stopping at n ¯ i : Hence when the cost of sampling is low, a voter has a higher expected utility when she ends up voting for her ideologically closer candidate (i.e., the ideology component dominates the va- lence component). Viceversa, when the sampling cost is high, the stopping rules of voters become very asymmetric. Hence a leftist voter will be much more condent that the rightist candidate is the high quality one upon reach- ing n i than the leftist candidate is indeed the best one when reaching jn ¯ i j: Therefore, when c is high voters have a higher expected utility when they 100 end up choosing their ideologically least preferred candidate (i.e., the valence component dominates the ideology component). Byexploitingasimilarintuition,thefollowingcorollaryshowsthataleftists voter gets a higher expected utility than a rightist voter from voting for the leftist candidate only when acquiring information is not very costly. Corollary 4 A more rightist (leftist) voter has a lower expected utility when choosing L (R) than a more leftist (rightist) one if and only if the cost of sampling is low. Theintuitionbehindthiscorollaryisverysimilartotheonebehindcorollary 3. An increase in the voter s idiosyncratic preferences (i.e., a more rightist voter), hastwoe¤ectsontheexpectedutilityofchoosingLuponreachingn ¯ i : 1) A direct negative e¤ect @U i (Lj(n ¯ i )) @x i < 0, due to the fact that, ceteris paribus, the more rightist a voter is, the lower is her utility from choosing the leftist alternative. 2) An indirect positive e¤ect @U i (Lj(n ¯ i )) @n ¯ i @n ¯ i @x i > 0, due to the fact that the more rightist a voter is, the higher is her leftiststopping threshold jn ¯ i j, hence the more condent she is about the quality of the leftist candidate. Hencewhencissmall,morerightistvotershavealowerexpectedutilitywith respect to more leftist ones when choosing L upon reaching n ¯ i : Instead, when cislarge,morerightistvoterswouldacquirerelativelymuchmoreinformation to make sure that L is the high quality candidate. Therefore, voting for L upon reaching n ¯ i when c is large gives a relatively higher expected utility to more rightist voters with respect to more leftist ones: We can also decompose the expected utility from sampling as the di¤erence between the expected benet of sampling and the expected cost of sampling. The following proposition summarizes the comparative statics results on the expected benet and expected cost of acquiring information. 101 Proposition 9 LetB i ,C i andB NET i be, respectively, theexpectedgrossbenet of acquiring information, the expected cost of acquiring information and the expected benet of acquiring information net of the cost of individual i. Then 8i: 1. B i > 0 and dB i d > 0; dB i dc < 0; dB i dx i 8 > > > < > > > : > 0 for x i < 1 2 = 0 for x i = 1 2 < 0 for x i > 1 2 2. C i > 0 and dC i d > 0; dC i dc > 0; dC i dx i 8 > > > < > > > : > 0 for x i < 1 2 = 0 for x i = 1 2 < 0 for x i > 1 2 3. B NET i > 0 and dB NET i d > 0; dB NET i dc < 0; dB NET i dx i 8 > > > < > > > : > 0 for x i < 1 2 = 0 for x i = 1 2 < 0 for x i > 1 2 Moderate voters have a higher expected gross benet of sampling with re- spect to less moderate voters. This is due to two e¤ects both going in the same direction. The rst is a direct e¤ect, due to the fact that holding the sampling sizeconstant, moderate voters are the ones that are most likely to gain from acquiring information since their nal decision is more likely to be a¤ected by the information they acquire. The second is an indirect e¤ect due to the fact that, as proposition 8 above showed, moderate voters have more symmetric stopping rules and they also tend to acquire more informa- tion (i.e., the set N i is larger for moderate voters). Therefore, by getting a highernetexpectedbenetfromsamplingandbysampling(onaverage)more than extremist voters, moderate voters end up having a higher expected gross benet of sampling. Notice that moderate voters also have a higher expected cost of sampling since the indirect e¤ect makes moderate voters have a higher expected number of draws. Nevertheless, overall moderate voters are the ones 102 withthehighernet benetofsampling. Thatis, moderatevotersaretheones who are expecting to gain more from acquiring information. Ontheotherhand,asexpected,theexpectedgrossbenetandtheexpected costofsamplingarehigherthemorevoterscareaboutthequalityofcandidates (i.e., the higher is ); since in such case they acquire more information before making a decision. Notice, however, that the net e¤ect is positive. The more voters care about the quality of candidates rather than about their idiosyn- craticpreferencesthehigherwillbetheirnet benetofacquiringinformation. Viceversa, the higher is the cost of sampling the higher will be the expected cost of sampling and the lower will be the expected benet of sampling (since the optimal sampling strategy involves a lower n i and a lower jn ¯ i j). Hence, the higher is the cost of sampling the lower is the net benet of sampling. 3.4 Alternative Applications of the Model Until now we have applied the model described in section 3.2 to the voters decision between alternative candidates or policies. Nevertheless, the same settingcanbenaturallyextendedtootherenvironments. Wenowpresentand discuss some of them. 3.4.1 Consumers decision over two alternative products ConsiderconsumerdecisionssuchaswhethertobuyaPCoraMAC,whether to buy a SUV or a convertible car or whether to watch a drama or an action movie. Theparameterx i couldnowbeinterpretedastheidiosyncraticprefer- encesofindividualiforagivenalternative(e.g.,idiosyncraticpreferencesover PC rather than MAC). The parameter , instead, represents how much the consumer cares about the overall quality of the chosen alternative regardless ofitsidiosyncraticcharacteristics. Allourresultsontheoptimalacquisitionof 103 costly information naturally translates to these types of consumersdecision. 3.4.2 Individual decision over investing in a safe or risky asset Consider a situation where before deciding whether to invest or not in a risky asset, an agent can acquire costly information on the expected value of such asset. We can thus reinterpret our model as follows. Each agent is endowed with one unit of capital. She has to decide whether to invest this unit of capital intheriskyassetP = 1 ornot investP = 0: Theriskyasset has state- contigent returns. More specically, there are two possible states of the world s 2 fA;Bg: When the state is A; the risky asset yields a return of r A > 0: Instead,whenthestateisB;theriskyassetgivesareturnof (r B )< 0:Ifthe agentdecidesnottoinvest,shewilljustconsumetheunitofcapital. Theprior probabilityofthestateoftheworlds =Aisassumedtobecommonknowledge and it is denoted by q: Without information acquisition the expected return from investing in the asset will be: q(1+r A )+(1q)(1r B ) To simplify the analysis and without loss of generality, suppose that agents have a linear utility function but at the same time have an idiosyncratic disu- tility from investing in the risky asset. 75 That is, agents have the following utility: u i (P = 0) = 1 and u i (P = 1) = 8 < : (1+r A )x i if s =A (1r B )x i if s =B (37) Assuming that x i 2 (0;r A ) 8i; every agent i wants to invest in the asset if the state is A and does not want to invest if the state is B: Thus ex-post 75 This could be simply be interpreted as a reduced form of their risk aversion. 104 every agent would choose the same action. However, ex-ante agents di¤er in theirpreferredactiondependingontheiridiosyncraticdisutilityfrominvesting in the risky asset (i.e., depending on their degree of risk aversion). More specically, without information acquisition, agent i would invest if and only if: x i <q(r A +r B )r B Nowassumeasbeforethateachvotercangetasmanysignalsasshewantson the state of the world and that she has to incur a cost c any time she decides to get a signal. Denote as (n) the posterior beliefs of the state being A after n =n A n B signals. Then agent i will invest whenever: (n)> x i +r B r A +r B = ^ i (n) Notice that ^ i (n) = 1 2 for x i = 1 2 (r A r B ): Moreover, @^ i (n) @x i > 0; @^ i (n) @r A < 0; @^ i (n) @r B > 0 (38) That is more risk averse agents require more evidence in favor of state A to invest. At the same time, the higher is the return of the asset in the good state the lower the evidence that the agent will require to invest in the asset. Viceversa, the higher is the negative return in the badstate the higher the threshold that agent i will require to invest. Notice also that: u i (P = 1j^ i (n)) = 1 2 (r A r B ) 8i Therefore, applying the same intuition behind the results of the previous sec- tion, we should expect very risk averse individual to invest in the risky asset only when collecting lots of evidence in favor of state A. Instead, we should 105 expectveryriskadverseindividualtodecidenottoinvestafterreceivingsome- how weak evidence in favor of state B: Hence, more risk averse individual are more likely to not invest when they should and less risk averse individual are more likely to invest when they should not. Overall, our results suggest that individuals with an intermediate degree of risk aversion are the one less likely to make mistakes and also the ones who will have the highest net benet of acquiring information. 3.5 Conclusions The economics literature has long been recognized yet not fully explored the di¤erent values attached by di¤erent individuals to similar pieces of infor- mation. This paper has analyzed this issue by considering a setting where individuals have to decide how much costly information to acquire prior to make a choice. More specically, we have analyzed a model where voters preferences over candidates are a combination of an idiosyncratic component and a state-contingent public value component. Individuals have the same ex-post preferences order over candidates but they instead di¤er in their ex- ante ranking oversuch candidates. We have shown that the optimal sampling strategy of a voter is slantedtoward the candidate closer to her idiosyn- cratic preferences. That is after having acquired few evidence in favor of the leftistcandidate,leftistvoterswouldndoptimaltostopsamplingandsimply vote for that candidate. Instead, rightist voters would nd optimal to keep sampling and they would eventually stop acquiring information and choose the leftist candidate only when the evidence in favor of such candidate be- comes very strong. We have also shown that more moderate voters have a more symmetric optimal sampling strategy: they require a similar amount of evidence to be induced to choose either the leftist or the rightist candidate. Moreover, themorevoterscareaboutthequalityof thecandidates(i.e., when 106 their state-contingent public value component is larger) and the lower is the cost of acquiring information, the more their behavior will resemble the one of moderate voters (i.e., the more symmetric their optimal sampling strategy will be). At the same time, we showed that moderate voters are overall less likely to vote for the low quality candidate than less moderate ones. The cost of acquiring information plays an important role in determining whether in equilibrium voters get a higher expected utility when voting for their ideologically closer candidate or not. More specically, when the cost of sampling is high, choosing the ideologically least preferred candidate implies that a voter is very condent of the quality of such candidate. Hence, when information is very costly to acquire a voter would have a higher expected utility when voting for the ideologically least preferred candidate. This is true since the higher utility from being more condent about the quality of such candidate more than compensate the disutility from not voting for the ideologically closer candidate. Finally we have shown that the more moderate voters are and the more they care about the quality of candidates, the more they expected to gain from acquiring information. While we have analyzed the endogenous acquisition of costly information in thecontextofvoterschoiceoveralternativecandidates,wehavealsosuggested that our theoretical framework may be applied more generally. 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New York: Harper and Row. [108] Yu, Z. (2005) Environmental Protection: A Theory of Direct and Indi- rect Competition for Political Inuence, Review of Economic Studies, 72(1): 269286. 118 AppendixA AppendixA1 Derivation of lobbiesrst order conditions. The utility function of lobby a from (11) and (12), can be written as: W a (e a ;e b ;^ e a ;^ e b ;) = 4 Pr(m a je a ;e b ;)[ (s =Ajm a ;^ e a ;^ e b ) (s =Ajm b ;^ e a ;^ e b )] (x m + [ (s =Ajm a ;^ e a ;^ e b )+ (s =Ajm b ;^ e a ;^ e b )]) (P m (m b ;^ e a ;^ e b ;)) 2 C(e a ) where (s = Ajm a ;^ e a ;^ e b ) is the votersposterior belief that the state of the worldisA giventhat theyreceivedmessagem a andtheyexpect lobbiesa and b to have exerted e¤orts ^ e a and ^ e b respectively. Thus the rst order condition for an optimum for lobby a is: V a = W a (e a ;e b ;^ e a ;^ e b ;) @e a = 4 Pr(m a je a ;e b ;) @e a [ (s =Ajm a ;^ e a ;^ e b ) (s =Ajm b ;^ e a ;^ e b )] (x m + [ (s =Ajm a ;^ e a ;^ e b )+ (s =Ajm b ;^ e a ;^ e b )])c = 0 Notice that in any symmetric equilibrium (s = Ajm a ;^ e a ;^ e b ) + (s = Ajm b ;^ e a ;^ e b ) = 1: Therefore the above expression simplies to: V a = 4 x m Pr(m a je a ;e b ;) @e a [ (s =Ajm a ;^ e a ;^ e b ) (s =Ajm b ;^ e a ;^ e b )]c = 0 Moreover: Pr(m a je a ;e b ;) = Pr(m a js =A)+Pr(m a js =B)(1) 119 Thus for = 1 2 ; Pr(m a je a ;e b ;) = 1 2 (Pr(m a js = A)+Pr(m a js = B)): More- over, given that in any equilibrium expectations are correct, i.e., ^ e a = e a and ^ e b =e b : (s =Ajm a ;^ e a ;^ e b ) = (s =Ajm a ;e a ;e b ) (s =Ajm b ;^ e a ;^ e b ) = (s =Ajm b ;e a ;e b ) To simplify notation we will simply denote (s = Ajm a ;e a ;e b ) = (s = Ajm a ); (s = Ajm b ;e a ;e b ) = (s = Ajm b ): Therefore since in a maximally informative equilibrium Pr(m a js = A) = Pr(z a js = A) and Pr(m b js = B) = Pr(z b js =B) : V MI a = 2 x m @h a @e a @h b @e a MI (s =Ajm a ) MI (s =Ajm b ) c = 0 Similarly, given (A1) and (A2) (from appendix B): V PI a = 2 x m (12y) @h a @e a @h b @e a PI (s =Ajm a ) PI (s =Ajm b ) c = 0 Then, given (A6) and (A7) (from appendix B): V SS a = 2 x m (12qy) @h a @e a @h b @e a SS (s =Ajm a ) SS (s =Ajm b ) c = 0 A similar derivation applies for lobby b s FOCs. Proof of Lemma 1 Let us rst introduce the following notation: Let the posterior beliefs of voters upon having received message m a and m b respectively be: (s =Ajm a ) =r and (s =Ajm b ) =t: Assume without loss of generality that r > t: Then in any informative equilibrium an unbiased media outlet will always adopt a separating strategy 120 as follows: (' 0 jz a ) =m a and (' 0 jz b ) =m b We prove this by contradiction. Suppose not. That is assume that upon receiving signal z a the unbiased media outlet sends message m b : Thus the posterior beliefs of voters will be (s = Ajm b ) = t: Thus the policy that will be implemented in equilibrium (median voter policy) will be: P m (m b ) = x m + (12t). The unbiased media outlet preferred policy will instead be P ' 0 (z a ) =' 0 + [12Pr(s =Ajz a )]: Viceversa, if media outlet were to send messagem a ;thepolicyoutcomewouldbeequaltoP m (m a ) =x m + (12r): Notice that since by assumption r >t, then P m (m a )<P m (m b ): The unbiased media outlet will send message m b instead of m a as long as: P m (m b )P ' 0 (z a ) < P m (m a )P ' 0 (z a ) Given that P m (m a ) < P m (m b ) by monotonicity this condition will be equiva- lent to: P m (m b )+P m (m a )2P ' 0 (z a )< 0 and since by denition ' 0 =x m ; this reduces to: 2Pr(s =Ajz a )<r+t and we know from Condition 1 that Pr(s =Ajz a )> Pr(s =Ajz b ): Thus since r is going to be a convex combination of Pr(s = Ajz a ) and Pr(s = Ajz b ) then r 2 [0;Pr(s = Ajz a )]: However since by assumption t < r then (r + t) 2 [0;2Pr(s = Ajz a )); which contradicts the above condition. At the same time theunbiasedmediaoutletwillneverbeindi¤erentbetweensendingoutthetwo messages. Suppose that instead it is. From the reasoning above the following 121 condition must hold: 2Pr(s =Ajz a ) =r+t which again is impossible since r 2 [0;Pr(s = Ajz a )] and t < r: Thus we have proved that in any informative equilibrium the unbiased media outlet typeplaysalwaysaseparatingstrategyaccordingtotheorderingofitsbeliefs. Given that the unbiased media outlet always plays this separating strategy, we just need to analyze what are the possible equilibrium strategies of the leftist and rightist media outlet. 76 Again, assume without loss of generality that r > t: Then in any informative equilibrium the leftist (rightist) media outlet will always send message m a (m b ) upon receiving z a (z b ). That is: (' l jz a ) =m a and (' r jz b ) =m b Weprovethisfortheleftistmediaoutlet. Bycontradiction. Supposethatupon receiving z a , the leftist media outlet sends message m b : For such strategy to be optimal it must be the case that: P m (m b )P ' l (z a ) < P m (m a )P ' l (z a ) : Where P ' l (z a ) =' l + [12Pr(s =Ajz a )] Given that P m (m a ) < P m (m b ) by monotonicity this condition will be equiva- lent to: P m (m b )+P m (m a )2P ' l (z a )< 0 76 Noticethatgiventhatthisisacheap-talkgameasetofequilibriatotallyspeculartothis one always exists. That is equilibria where (s =Ajm a )<(s =Ajm b ) and (' 0 jz a ) =m b and (' 0 jz b ) =m a : Given that the results from such alternative equilibria are strategically equivalent to the one we derive, we just focus on one set of equilibria. 122 That is: 2(x m ' l )+2 +2 (2Pr(s =Ajz a ))(t+r))< 0 and we know from Condition 1 that Pr(s = Ajz a ) > Pr(s = Ajz b ): Thus since r is going to be a convex combination of Pr(s =Ajz a ) and Pr(s =Ajz b ) then r 2 [0;Pr(s = Ajz a )]: However since by assumption t < r then (r +t) 2 [0;2Pr(s =Ajz a )); and given that x m >' l the condition will never hold. A similar proof applies to the rightist media outlet. Thus we have shown that in any informative equilibrium: (' 0 jz a ) = m a and (' 0 jz b ) =m b (' l jz a ) = m a and (' r jz b ) =m b Q.E.D. Proof of Lemma 2 We show here that e MI < e SS ; a similar proof applies to show that e SS < e PI : In a symmetric equilibrium since e a = e b = e then h a (e ;e ;) = h b (e ;e ;) = h ; where h denote the probability of receiving the correct signal given that both lobbies exert e¤ort e : Moreover, by rational expecta- tions, in any equilibrium ^ e a = ^ e b = e . Therefore, given equations (A11) and (A12)inAppendixB,theposteriorbeliefsofvotersinasymmetric maximally informative equilibrium are such that: MI (s =Ajm a ;^ e MI a ;^ e MI b ) MI (s =Ajm b ;^ e MI a ;^ e MI b ) = 2h MI 1 Similarlyfrom(A8)and(A9)inAppendixB,inasemi-separating equilibrium: SS (s =Ajm a ;^ e SS a ;^ e SS b ) SS (s =Ajm b ;^ e SS a ;^ e SS b ) = (12qy) 2h SS 1 123 Thus the equilibrium conditions become: V MI a = @h a @e a @h b @e a 2h MI 1 c = 0 V SS a = (12yq) 2 @h a @e a @h b @e a 2h SS 1 c = 0 Nowwecanprovethate MI >e SS . Supposenot,thatise MI <e SS . Wedenote L a (e MI ) = @h a (e MI ;e MI ;) @e a @h b (e MI ;e MI ;) @e a 2h MI 1 and L a (e SS ) = @h a (e SS ;e SS ;) @e a @h b (e SS ;e SS ;) @e a 2h SS 1 InaninteriorequilibriumwemusthavethatV MI a =V SS a = 0:Thusgiventhat themarginalcostofe¤ortisconstantandthat(12yq)< 1itmustbethecase that L a (e MI ) < L a (e SS ): 77 Moreover, by Condition 1 d @h i (e;e;) @e i @h j ((e;e;) @e i de < 0. 78 Thus since e MI <e SS : @h a (e MI ;e MI ;) @e a @h b (e MI ;e MI ;) @e a > @h a (e SS ;e SS ;) @e a @h b (e SS ;e SS ;) @e a 77 Notice that a similar proof would apply with a convex cost function, that is c 00 (e)> 0 78 Indeed we have that since is a constant: d @h i (e;e;) @e i @h j ((e;e;) @e i = @ 2 h i @ 2 e i de i + @ 2 h i @e i @e j de j @ 2 h j @ 2 e i de i @ 2 h j @e i @e j de j : Therefore for de i =de j =de and since in a symmetric equilibrium @ 2 hi @ei@ej = @ 2 hj @ei@ej : d @h i @e i @h j @e i = @ 2 h i @ 2 e i @ 2 h j @ 2 e i de< 0,de> 0 (by condition 1, property iv)). 124 therefore it must be the case that: 2h MI 1 < 2h SS 1 Thustheaboveconditionimpliesthatanecessaryconditiontohavee MI <e SS is h SS >h MI ; but this contradicts Condition 1 (property v)). A similar proof applies to show that e SS > e PI . Moreover, lim q!0 L a (e SS ) = L a (e MI ); and @V SS a @q < 0; thus it must be the case that @e SS @q < 0. Q.E.D. Proof of Lemma 3 Consider: ~ ' l =x m PI (s =Ajm a )+ PI (s =Ajm b )2Pr(s =Ajz b ) Now let s focus on the term inside the brackets. Since in a symmetric PI equilibrium we have that: h a (^ e PI a ;^ e PI b ;) =h b (^ e PI a ;^ e PI b ;) =h(^ e PI ;^ e PI ;) with a slight abuse of notation we denote h(^ e PI ;) = h PI : Hence by the symmetry of the equilibrium PI (s =Ajm a )+ PI (s =Ajm b ) = 1 and: Pr(s =Ajz b ) = (1h a (^ e PI a ;^ e PI b ;)) ((1h a (^ e PI a ;^ e PI b ;)))+(h b (^ e PI a ;^ e PI b ;)) = (1h PI ) Thus: ~ ' l =x m 12(1h(^ e PI ;^ e PI ;)) Similarly: ' l =x m 12(1h(^ e SS ;^ e SS ;)) ' l =x m 12(1h(^ e MI ;^ e MI ;)) 125 In other words, the equilibrium no-deviation thresholds of the media outlet depends on the parameters of the model and on the expected e¤ort exerted by lobbies. It is straightforward to see that by Condition 1: @~ ' l @^ e > 0; @ ' l @^ e > 0; @ ' l @^ e > 0: Now we want to show that8q2 (0;1) ' l > ' l and ' l > ~ ' l . Suppose not. 8q2 (0;1) ' l < ' l )x m 12(1h MI ) )<x m 12(1h SS ) , (1h MI )< (1h SS ),h MI >h SS Moreover, by rational expectations, in equilibrium ^ e MI = e MI and ^ e SS = e SS . Therefore since from lemma 2 e MI > e SS and from Condition 1 (property v) we know that in a symmetric equilibrium for e a = e b = e it must be the case that dh(e;e;) de < 0: Thus: e MI >e SS )h MI <h SS Contradiction. A similar proof applies to the other cases. Q.E.D. Proof of Proposition 1 It follows directly from lemma 1, 2 and 3. Q.E.D. Proof of Proposition 2. The expected policy outcome in an equilibrium J =MI;PI;SS given by: P J m = Pr(s =A)E(P J m js =A)+Pr(s =B)E(P J m js =B) where E(P J m js = A) represents the expected median voter policy when the state is A and E(P J m js = B) is the expected median voter policy when the 126 state is B: That is: E(P J m js =A) = J (m a js =A)P J m (m a )+ J (m b js =A)P J m (m b ) Then by the symmetry of the equilibrium: J (m a js =A)+ J (m a js =B) = J (m b js =B)+ J (m b js =A) = 1 Thus P J m = 1 2 P J m (m a )+P J m (m b ) =x m ; 8J The ex-ante policy distortion is given by: Dist = Pr(s =A) P FR m (s =A)E(P J m js =A) +Pr(s =B) P FR m (s =B)E(P J m js =B) where P FR m (s =A) =x m and P FR m (s =B) =x m + . Thus: Dist = + 1 2 2 4 P J m (m a ) J (m a js =A) J (m a js =B) P J m (m b ) J (m b js =B) J (m b js =A) 3 5 Now let s consider the expected policy distortion in a semi-separating equilib- rium. Then, since in a symmetric equilibrium h SS a =h SS b =h SS : SS (m a js =A) SS (m a js =B) = SS (m b js =B) SS (m b js =A) = (12qy)(2h SS 1) and: P SS m (m a ) =x m + 12 h SS (12qy)+qy P SS m (m b ) =x m + 12 (1h SS )(12qy)+qy Thus: Dist SS = 1(12qy) 2 (2h SS 1) 2 127 Similarly: Dist MI = 1(2h MI 1) 2 Dist PI = 1(12y) 2 (2h PI 1) 2 Thus: @Dist SS @ > 0; @Dist SS @q > 0; @Dist SS @y > 0; @Dist SS @h SS < 0 Q.E.D. Proof of Proposition 3 Let s compare the ex-ante expected utilities of voters, media outlet and lobbies in a fully revealing equilibrium (i.e., no lobbies-induced slant and no media-induced slant) with the ones that they derive in this game. 1) FULLY REVEALING: a) Expected utility of voter i : U i (x i ) = Pr(s =A) (x m x i + ) 2 +Pr(s =B) (x m + x i ) 2 thus U i (x i ) =(x m x i ) 2 b) Expected utility of media outlet. U n (' n ) =(x m ' n ) 2 c) Lobby a : W a ( a ) = Pr(s =A) (x m ) 2 +Pr(s =B) (x m + ) 2 128 thus W a ( a ) = x 2 m + 2 d) Lobby b : 79 W b ( b ) = (1x m ) 2 + 2 2) EX-ANTE MI;PI;SS EQUILIBRIA: a) Expected utility of voter i in a semi-separating equilibrium is: U i (x i ) = Pr(s =A) 8 < : Pr(m a js =A) x i 1 2 + 2(qy +(12qy)h SS )1 2 + Pr(m b js =A) x i 1 2 2(qy +(12qy)h SS )1 2 9 = ; Pr(s = B) 8 < : Pr(m a js =B) x i + 1 2 + 2(qy +(12qy)h SS )1 2 + Pr(m b js =B) x i + 1 2 2(qy +(12qy)h SS )1 2 9 = ; Thus U SS i (x i ) =( 1 2 x i ) 2 4 2 qy +h SS (12qy) 1 qy +h SS (12qy) Hence, the expected loss from voter i perspective is: (DU i ) SS = 2 1(12qy) 2 (2h SS 1) 2 Thus from the proof of proposition 2 we get that: (DU i ) SS = (Dist SS ) That is the expected utility loss is proportional to the expected policy dis- 79 Noticesincex m = 1 2 isanecessaryconditiontohaveasymmetricequilibrium,W a ( a ) = W b ( b ): 129 tortion. Thus from the proof of proposition 2, we conclude that (DU i ) SS is positively related to ;y and q and negatively related with h SS : b) The expected utility of lobby a in a semi-separating equilibrium is: W SS a ( a ) =Pr(s =A) 8 < : h SS a (12qy))+qy 1 2 h 2( qy+(12qy)h SS a qy+(12qy)h SS a +qy+(12qy)(1h SS b ) )1 i 2 + 1h SS a (12qy))qy 1 2 h 2 (qy+(12qy)(1h SS a ) qy+(12qy)(1h SS a )+qy+(12qy)h SS b 1 i 2 9 = ; Pr(s =B) 8 < : 1h SS b (12qy))qy 1 2 h 2( qy+(12qy)h SS a qy+(12qy)h SS a +qy+(12qy)(1h SS b ) )1 i 2 + h SS b (12qy))+qy 1 2 h 2 (qy+(12qy)(1h SS a ) qy+(12qy)(1h SS a )+qy+(12qy)h SS b 1 i 2 9 = ; c(e SS a ) Thus, lobby a s expected utility in a SS equilibrium is: W SS a ( a ) =( 1 4 + 2 )+4 2 qy +h SS (12qy) 1 qy +h SS (12qy) c(e SS a ) thus from lobbiesperspective the expected benetnloss from this game with respect to a fully revealing equilibrium is: (DW j ) SS = 2 1(12qy) 2 (2h SS 1) 2 c(e SS j ); 8j =a;b thusitisimmediatetoseethattheexpectedgainofeachlobbyfromengaging in inuence activities is directly related with the expected loss of voters. (DW a ) SS = (DU i ) SS c(e SS a ) (DW b ) SS = (DU i ) SS c(e SS b ) 130 Thus the higher the expected loss of voters, the higher the expected gain on lobbies. Q.E.D. Proof of Corollary 1 From the proof of proposition 3 we know that lobby a s expected utility in a SS equilibrium is: W a ( a ) =( 1 4 + 2 )+4 2 qy +h SS (12qy) 1 qy +h SS (12qy) c(e SS a ) Now let W SS a =W a (e SS a ;e SS b ) be the value function of lobby a: Thus by using the envelope theorem we can easily see that: @ W SS a @y = @W SS a @y e SS a =e SS b =e SS = 4 2 q 2h SS 1 2 (12qy)> 0 @ W SS a @ = @W SS a @ e SS a =e SS b =e SS =2 2h SS 1 2 (2qy1) 2 < 0 @ W SS a @h = @W SS a @h e SS a =e SS b =e SS =4 2 (2qy1) 2 2h SS 1 < 0 Thus since h is increasing in ; the results follow. A similar reasoning applies to lobby b: Q.E.D. Proof of Lemma 4 LetthestateofnaturebeA:Inafullyrevealingequilibrium,voterireceives perfectly informative message, i.e., Pr(s = Ajm a ) = 1: Thus the preferred policy of voter i in such equilibrium will be P FR i = x i : Let P J m be the median voter policy in an equilibrium J (where J =MI;SS;PI): Then voter i prefers a fully revealing equilibrium if and only if: P FR m P FR i P J m + = x i ) which implies that the above condition becomes: P J m < x m ; which is clearly impossible since P J m 2 [x m ;x m + ] 2)P J m > P FR i (thatisx i <P J m + = x i ); thusx i x m <P J m x i + ) x i < 1 2 P J m + +x m =x B Moreover notice that x B < x i : Now let the state of nature be B: In a fully revealing equilibrium, voter i receives perfectly informative message, i.e., Pr(s = Bjm b ) = 1: Thus the preferred policy of voter i in such equilibrium will be P FR i = x i + : Then voter i prefers a fully revealing equilibrium if and only if: P FR m P FR i x m ; it is obviously always the case that voter i prefers the FR policy outcome we have 2 cases to analyze: 1)P J m P J m = x i ) which implies that the above condition becomes: x i > 1 2 P J m +x m =x A Moreover notice that x A > x i : 2) P J m > P FR i (that is x i <P J m = x i ) which implies x m + <P J m which is clearly impossible since P J m 2 [x m ;x m + ] Q.E.D. 132 Proof of Proposition 4 It follows immediately from the Proof of Proposition 2 Q.E.D. Proof of Proposition 5 We know from the proof of proposition 3 that: U SS i (x i ) =( 1 2 x i ) 2 4 2 qy +h SS (12qy) 1 qy +h SS (12qy) and W SS a ( a ) =( 1 4 + 2 )+4 2 qy +h SS (12qy) 1 qy +h SS (12qy) c(e SS a ) Thus U MI i (x i )W MI a if and only if y > 1 2 0 @ 1 q 2 (2h MI 1) 2 [c(e PI )c(e MI )] (2h PI 1) 1 A Q.E.D. Proof of Proposition 6 Suppose we are in a MI equilibrium. Then e MI = 1 2 2 p c 1 and ' l = 1 2 p c . An increase in leads to a lower ' l ; thus for any initial level of the media outlet s bias ' l ; the equilibrium will remain a MI one. Thus since @e MI @ > 0; the net e¤ect of an increase in in a MI equilibrium is an increase in e MI : NowsupposethatweareinaSSequilibrium. Thene SS = 1 2 ( 1 2 ' l ) 1 ; where ' l 2 (~ ' l ; ' l ) is the leftist media outlet s idiosyncratic preference para- meter. Thusitisimmediatetoverifythat @e SS @ > 0:Moreover,theequilibrium 133 probability that the media outlet will slant its reports in a SS equilibrium is q = 1 2y 1 2 p c ( 1 2 ' l ) ; thus @q @ < 0: Thus the net e¤ect of an increase in in a SS equilibrium is a higher lobbiese¤orts and a lower probability of news- slantingbythemediaoutlet. NowsupposeweareinaPI equilibrium. Then e PI = 1 2 2 q (12y) 2 c 1 and ~ ' l = 1 2 p c (12y) : Thus an increase in leads to a lower ~ ' l : Now there are two possible cases. Either ' l is still lower than the new ~ ' l ; in which case the equilibrium will still be a PI one and thus the nete¤ectofanincreasein wouldbejustanincreaseinlobbiese¤orts(since @e PI @ > 0). On the other hand, if the ' l is now higher than ~ ' l ; the equilibrium becomes a SS one. Nevertheless, from the above reasoning we know that in a SS equilibrium @e SS @ > 0 and @q @ < 0: Thus in this second case we have that the net e¤ect of an increase in is to increase lobbiese¤orts and a decrease the probability of news-slantingby the media outlet. Q.E.D. Proof of Proposition 7 Suppose we are in a MI equilibrium. Then e MI = 1 2 2 p c 1 and ' l = 1 2 p c . An increase in c leads to a lower ' l ; thus for any initial level of the media outlet s bias ' l ; the equilibrium will remain a MI one. Thus since @e MI @c < 0; the net e¤ect of an increase in in a MI equilibrium is a decrease in e MI : NowsupposethatweareinaSSequilibrium. Thene SS = 1 2 ( 1 2 ' l ) 1 ; where ' l 2 (~ ' l ; ' l ) is the leftist media outlet s idiosyncratic preference pa- rameter. Then obviously @e SS @c = 0: On the other hand, the equilibrium probability that the media outlet will slant its reports in a SS equilibrium is q = 1 2y 1 2 p c ( 1 2 ' l ) ;thus @q @c < 0: Thus the net e¤ect of an increase in c in a SS equilibrium is a lower probability of news-slantingby the media outlet. Now suppose we are in a PI equilibrium. Then e PI = 1 2 2 q (12y) 2 c 1 and ~ ' l = 1 2 p c (12y) : Thus an increase in c leads to a lower ~ ' l : Now there are 134 two possible cases. Either ' l is still lower than the new ~ ' l ; in which case the equilibrium will still be a PI one and thus the net e¤ect of an increase in would be just a decrease in lobbiese¤orts (since @e PI @c < 0). On the other hand, ifthe' l isnowhigherthan ~ ' l ;theequilibriumbecomesaSS one. Nev- ertheless,fromtheabovereasoningweknowthatinaSS equilibrium @e SS @c = 0 and @q @c < 0: Thus inthis secondcasewe have thatthenet e¤ectof anincrease in is to decrease lobbiese¤orts (up to the bound where e PI = e SS ) and a decrease the probability of news-slantingby the media outlet. The same reasoning applies to the comparative statics for y: Q.E.D. APPENDIXA2 Informative Equilibria of the CheapTalkgame 1) Partially Informative equilibrium Leftist media outlet pools on m a ; Rightist media outlet pools on m b . In such equilibrium the probability of receiving message m a and m b respec- tively, conditional on the state of the world being A are the following: 80 Pr(m a js =A;^ e PI a ;^ e PI b ) = Pr(' l )1+Pr(' 0 )Pr(z a js =A;^ e PI a ;^ e PI b )+Pr(' r )0 (A1) Pr(m b js =A;^ e PI a ;^ e PI b ) = Pr(' l )0+Pr(' 0 )Pr(z b js =A;^ e PI a ;^ e PI b )+Pr(' r )1 (A2) Therefore, votersposterior beliefs will be given by: PI (s = Ajm a ) = (A3) y +(12y)h a (^ e PI a ;^ e PI b ;) (y +(12y)h a (^ e PI a ;^ e PI b ;))+(y +(12y)(1h b (^ e PI a ;^ e PI b ;)))(1) 80 A similar derivation applies to Pr(m a js =B) and Pr(m b js =B): 135 PI (s = Ajm b ) = (A4) y +(12y)(1h a (^ e PI a ;^ e PI b ;)) (y +(12y)(1h a (^ e PI a ;^ e PI b ;)))+(y +(12y)h b (^ e PI a ;^ e PI b ;))(1) WherethesuperscriptPI standsforpartiallyinformative. Giventhestrategies that media outlet will adopt in this partially informative equilibrium, the following lemma holds: Lemma 5 In a partially informative equilibrium where PI (' l jz i ) =m a ;8i = a;b and PI (' r jz i ) = m b ; 8i = a;b; the posterior beliefs of voters will satisfy the following condition: PI (s =Ajm a )> PI (s =Ajm b ) Proof. Suppose not. That is PI (s =Ajm a )< PI (s =Ajm b ); which implies: (1)(y +h b (12y))+(1)(y +(1h b )(12y))< 0 That is (1)[(y +Pr(z b js =B)(12y))+(y +(1Pr(z b js =B))(12y))]< 0 which is clearly impossible Q.E.D. Thus, we should just understand under which conditions the biased media outlet types will have no incentive to deviate and adopt a separating strategy. Given the symmetry of our setting we can focus on the leftist media outlet. By Lemma 1 the no-deviation condition for the leftist media outlet is simply reducedtotheconditionunderwhichuponreceivingsignalz b theleftistmedia outlet does not have incentive to deviate from its pooling strategy by sending messagem b :Whenreceivingsignalz b ,theleftistmediaoutletoptimalpolicyis P PI ' l (z b ) =' l + 12Pr(s =Ajz b ;^ e PI a ;^ e PI b ) ;thustheno-deviationcondition is: P PI m (m a )P ' l (z b ) PI (s = Ajm b ) ) P PI m (m b ) > P PI m (m a ): We can have 3 possible cases: 1)P PI m (m a ) PI (s =Ajm b ): 2) P PI m (m b )>P PI m (m a )>P PI ' l (z b ); this can be true only if: ' l <x m 2 PI (s =Ajm a )Pr(s =Ajz b ;^ e PI a ;^ e PI b ) = ' l Thus if this condition hold, by monotonicity the no-deviation condition be- comes P PI m (m b )>P PI m (m a ) which is always true. 3)P PI m (m a )x m 2 PI (s =Ajm a )Pr(s =Ajz b ;^ e PI a ;^ e PI b ) = ' l Thenbymonotonicitytheno-deviationconditionwillbeequivalentto2P PI ' l (z b ) P PI m (m a )P PI m (m b )< 0; that is ' l <x m PI (s =Ajm a )+ PI (s =Ajm b )2Pr(s =Ajz b ;^ e PI a ;^ e PI b ) =~ ' l (A5) Moreover we can easily see that ~ ' l > ' l : Suppose not, then it must be the case that PI (s = Ajm b ) > PI (s = Ajm a ) which contradicts lemma 5. Thus puttingcase1)andcase3)togetherwecanseethattheno-deviationcondition for a leftist media outlet in a partially informative equilibriumis simply (A5). 2) Semi-separating equilibrium 137 Leftist and Rightist media outlet randomize between pooling and separating strategies In the semi-separating equilibrium the probability of receiving message m a and m b respectively, conditional on the state of the world, are the following: 81 Pr(m a js =A;^ e SS a ;^ e SS b ) = Pr(z a js =A;^ e SS a ;^ e SS b )(12qy)+qy (A6) Similarly: Pr(m b js =B;^ e SS a ;^ e SS b ) = Pr(z b js =B;^ e SS a ;^ e SS b )(12qy)+qy (A7) Therefore, the votersposterior beliefs in this semi-separating equilibrium are given by: SS (s = Ajm a ) = (A8) h a (^ e SS a ;^ e SS b ;)(12qy)+qy (h a (^ e SS a ;^ e SS b ;)(12qy)+qy)+((1h b (^ e SS a ;^ e SS b ;))(12qy)+qy)(1) SS (s = Ajm b ) = (A9) (1h a (^ e SS a ;^ e SS b ;))(12qy)+qy ((1h a (^ e SS a ;^ e SS b ;))(12qy)+qy)+(h b (^ e SS a ;^ e SS b ;)(12qy)+qy)(1) Where the superscript SS stands for semi-separating. We have the following Lemma: Lemma 6 Inasemi-separatingequilibriumwheretheleftistandrightistmedia outlet play the following strategies: SS (' l jz a ) =m a ; SS (' l jz b ) =fqm a ;(1q)m b g; SS (' r jz b ) =m b ; SS (' r jz a ) =f(1q)m a ;qm b g the posterior beliefs of voters are such that: SS (s =Ajm a )> SS (s =Ajm b ) 81 A similar derivation applies to Pr(m a js =B) and Pr(m b js =A): 138 Proof. By contradiction. Suppose not. That is SS (s = Ajm a ) < SS (s = Ajm b ); which implies: (h a +h b 1)(1)(12qy)< 0 which is clearly impossible since (12y) > 0 and h a +h b > 1; by Condition 1. Q.E.D. For such semi-separating equilibrium to hold a leftist media outlet must be indi¤erent between sending message m a and m b upon receiving signal z b (a similar condition applies for the rightist media outlet type). Assume that the leftistmediaoutletreceivessignalz b ; thenitsidealpolicywouldbeP SS ' l (z b ) = ' l + 12Pr(s =Ajz b ;^ e SS a ;^ e SS b ) ;thus' l willbeindi¤erentbetweensending message m a and m b if and only if: P SS m (m b )P SS ' l (z b ) = P SS m (m a )P SS ' l (z b ) We know from the Lemma 6 that SS (s = Ajm a ) > SS (s = Ajm b ) =) P SS m (m b )>P SS m (m a ): We can thus have 3 possible cases: 1)P SS m (m a ) SS (s =Ajm b ): 2) P SS m (m b )> P SS m (m a )> P SS ' l (z b ); which by monotonicity implies that the no-deviation condition becomes: P SS m (m b ) =P SS m (m a ) which can never be the case since SS (s =Ajm a )> SS (s =Ajm b ): 3)P SS m (m a ) < P SS ' l (z b ) < P SS m (m b ) thus by monotonicity the no-deviation 139 condition becomes P SS m (m b )+P SS m (m a )2P SS ' l (z b ) = 0; that is ' l =x m SS (s =Ajm a )+ SS (s =Ajm b )2Pr(s =Ajz b ;^ e SS a ;^ e SS b ) = ' l (A10) Thustheno-deviationconditioninasemi-separating equilibriumissimply (A10). 3) Maximally informative equilibrium Rightist media outlet and Leftist media outlet adopt a sepa- rating strategy. In a maximally informative equilibrium votersposterior beliefs are: MI (s =Ajm a ) = h a (^ e MI a ;^ e MI b ;) (h a (^ e MI a ;^ e MI b ;))+(1h b (^ e MI a ;^ e MI b ;))(1) (A11) MI (s =Ajm b ) = 1h a (^ e MI a ;^ e MI b ;) (1h a (^ e MI a ;^ e MI b ;))+h b (^ e MI a ;^ e MI b ;)(1) (A12) Where the superscript MI stands for maximally informative. It is straight- forward to notice that given Condition 1; MI (s = Ajm a ) > MI (s = Ajm b ). Thus we check under what conditions the leftist media outlet will not have incentive to deviate upon receiving signal z b by sending message m a :The ideal policy of the leftist media outlet when it received signal z b is given by P MI ' l (z b ) =' l + 12Pr(s =Ajz b ;^ e MI a ;^ e MI b ) ; thus the no-deviation condi- tion will be: P MI m (m b )P MI ' l (z b ) MI (s = Ajm b ) =) P MI m (m b ) > P MI m (m a ); thus we can have two cases (since P MI m (m b )>P MI ' l (z b ) always in a maximally informative equilibrium): 140 1) P MI m (m a )>P MI ' l (z b ); which implies that the no-deviation condition is P MI m (m b ) MI (s =Ajm b ). 2) P MI m (m a ) x m MI (s =Ajm a )+ MI (s =Ajm b )2Pr(s =Ajz b ;^ e MI a ;^ e MI b ) Hence: ' l >x m Pr(s =Ajz a ;^ e MI a ;^ e MI b )Pr(s =Ajz b ;^ e MI a ;^ e MI b ) = ' l (A13) 141 AppendixB APPENDIX B1 Small-Hsiao Tests of IIA Assumptions in Multinomial Logit Model TableA1.1reportstheresultsoftheSmall-HsiaotestsoftheIIAassumption over the fully specied Multinomial Logit model for the two stage electoral choice model. 82 Ho: Odds(OutcomeJ vs OutcomeK) are independent of other alternatives Omitted lnL(full) lnL(omit) chi2 df P>chi2 Abstention 3068,03 2857,361 421,337 53 0.000 against Ho Communicative voting 3328,598 3137,55 382,095 53 0.000 against Ho Note. Regression includes age, gender, occupation, marital status, size of urban area, media market and institutional characteristics dummies Table A1.1. SmallHsiao test for the IIA assumption Multinomial logit Whole sample evidence Tables A1.2 and A1.3 report the results of the Small-Hsiao tests of the IIA assumptionoverthefullyspeciedMultinomialLogitmodelforthethreestage electoralchoicemodel, relativetothesubsamplesof CSLP andCLWP voters, respectively. 82 The Small-Hsiao test avoids both the asymptotic bias of the likelihood ratio test orig- inally suggested by McFadden, Train and Tye, and the matrix manipulation and inversion required for the Hausman-type test recently suggested by Hausman and McFadden(Small and Hsiao (1985); pg. 625). 142 Ho: Odds(OutcomeJ vs OutcomeK) are independent of other alternatives Omitted lnL(full) lnL(omit) chi2 df P>chi2 Abstention 1309,75 1284,024 51,451 52 0,495 for Ho Strategic voting 1326,92 1269,235 115,235 52 0.000 against Ho Table A1.2. SmallHsiao test for the IIA assumption Multinomial logit Subsample of CSLP voters Note. Regression includes age, gender, occupation, marital status, size of urban area, media market and institutional characteristics dummies evidence Ho: Odds(OutcomeJ vs OutcomeK) are independent of other alternatives Omitted lnL(full) lnL(omit) chi2 df P>chi2 Abstention 1657,86 1544,29 227,137 52 0.000 against Ho Strategic voting 2021,96 1918,92 206,079 52 0.000 against Ho Table A1.3 SmallHsiao test for the IIA assumption Multinomial logit Subsample of CLWP voters Note. Regression includes age, gender, occupation, marital status, size of urban area, media market and institutional characteristics dummies evidence APPENDIX B2 The Data ThemaindatasourceusedinourempiricalinvestigationistheWorldValue Survey(1999-2002). Thisdatacollectionrepresentsthefourthandmostrecent wave carried out by the World Values Survey and European Values Survey groups. Thesurveyscovers60countriesandarerepresentativeof theuniverse of all adults aged 18 or above. This data set has been designed to enable a cross-national,cross-culturalcomparisonofvaluesandnormsonawidevariety of topics. It contains information regarding the socioeconomic status, a broad range of social values and the political preferences of each respondent. Each 143 individual has two corresponding weight attached. The rst one is a national level post-stratication weight. In other words, it is the weight attached to the individual to correct the sample to reect the national distribution of individuals. 83 The second one is a post-stratication weight to correct for the fact that some countries have much bigger samples than others, and their sizes are not related to the relative size of their population. In other words, this second weight allows analyzing the behavior of individuals belonging to nationaldi¤erentsurveys. Sinceourdatasetcontainsindividualsof14di¤erent European countries, we use this cross-national weight in our empirical study. The 14 European countries under investigation in our study are the fol- lowing: Austria, Denmark, Belgium, Netherlands, Sweden, Finland, Portugal, Spain,Greece,Germany,Italy,France,UnitedKingdomandIreland. Thesec- onddatasourcethatweemployinouranalysisisdrawnfromKooleandKatz (2000). Morespecically,wehaveanalyzedtheinformationcontainedinthere to classify each party in each of the 14 countries as a "sure loser" or a "likely winner". The third data set we use is the Mark and Steenberg (1999) expert survey on the position of parties on the left-right scale in the 14 countries underanalysis. Tocapturethefunctioningofthemediamarketinthecountry wheretheindividualiseligibletovotewehaveusedtheinformationcontained in the "Press freedom 1994-2001" released by The Freedom House and the HerndahlIndexofmediaconcentrationcontainedSanchez-Tabernero(2004). Finally,weusedtheDatabaseofPoliticalInstitutions(DPI2004)oftheWorld Bank to construct the variables regarding the institutional characteristics of each country. 83 For example, if the sample contains twice as many university-educated respondents as there are in the adult population as a whole, members of this group are given a weight of 0.5. 144 Table A2.1. Description of variables Variable Name Description Sources Dependent variables Abstain Dummy variable taking value 1 if the individual does not vote or cast a blank vote and 0 if votes World Values Survey (2000) Communicative Voting Dummy variable taking value 1 if the individual votes for a looser party and 0 if votes for a winner. World Values Survey (2000) and Koole and Katz (2000) SocioEconomic Characteristics Age 1829 Dummy variable taking value 1 if individual has an age between 18 and 29, 0 otherwise. World Values Survey (2000) Age 3049 Dummy variable taking value 1 if individual has an age between 30 and 49, 0 otherwise. World Values Survey (2000) Age 5069 Dummy variable taking value 1 if individual has an age between 50 and 69, 0 otherwise. World Values Survey (2000) Dummy variable taking value 1 if the individual highest education attainment is high school, 0 otherwise World Values Survey (2000) Dummy variable taking value 1 if the individual has attended a universitylevel course, 0 otherwise World Values Survey (2000) Dummy variable taking value 1 if household has an income level between 4 and 6 in a 10 point scale (10 being the highest), 0 otherwise. World Values Survey (2000) Dummy variable taking value 1 if household has an income level between 7 and 8 in a 10 point scale (10 being the highest), 0 otherwise. World Values Survey (2000) Dummy variable taking value 1 if household has an income level higher or equal to 9 in a 10 point scale (10 being the highest), 0 otherwise. World Values Survey (2000) Women Dummy variable taking value 1 if the individual is a woman and 0 otherwise World Values Survey (2000) High level of income Middle level of education High level of education Lowmiddle level of income Middlehigh level of income 145 Table A2.1. Description of variables (2) Variable Name Description Sources Private Benefits and Expressive Motivations Dummy variable taking value 1 if the individual belongs to a political party, 0 otherwise World Values Survey (2000) Dummy variable taking value 1 if the individual belongs to a special interest group, 0 otherwise World Values Survey (2000) Dummy variable taking value 1 if individual rates the political system of his country above 5 in a 10 point scale (10 being the highest), 0 otherwise. World Values Survey (2000) Dummy variable taking value 1 if the individual consider politics to be very important or rather important in her life, 0 otherwise. World Values Survey (2000) Dummy variable if the individual discuss politics frequently or occasionally World Values Survey (2000) Level of Information and Political Preferences Dummy variable taking value 1 if the individual follows politics in the news less than once a week, 0 otherwise World Values Survey (2000) Dummy variable taking value 1 if the individual is moderate (individual's political position is 5 or 6 in a 10 point scale) or does not have a policy position on the left right spectrum (independent), 0 otherwise World Values Survey (2000) Interaction term taking value 1 if individual is at the same time uninformed about politics AND moderate or independent, 0 otherwise World Values Survey (2000) Leftist extremist Dummy variable taking value 1 if individual political position is below 3 in a 10 point scale (1 being extreme left, 10 being extreme right) World Values Survey (2000) Rightists Extremist Dummy variable taking value 1 if individual political position is above 8 in a 10 point scale (1 being extreme left, 10 being extreme right) World Values Survey (2000) Choice Set Closer to a "sure loser" party Dummy variable taking value 1 if the ideologically closest party to the individual political position is a "sure loser" and 0 if it is a "likely winner" party. World Values Survey (2000); Koole and Katz (2000) and Marks and Steenbergen Moderate/Independent x Uninformed Believe politics is important Discuss politics frequently or occasionally Uninformed about politics Moderate or independent Belong to a Political Party Belong to a Special Interest Group Good opinion about the political system of the country 146 Table A2.1. Description of variables (3) Variable Name Description Sources Media Characteristics in the Country where the Individual Votes Institutional Characteristics of Political System of the Country where the Individual Votes In “ plurality” systems, legislators are elected using a winnertakeall / first past the post rule. “ 1” if this system is used, 0 if it isn’ t. The sum of the squared seat shares of all parties in the opposition. The weighted average of the number of representatives elected by each constituency size. Records the minimum vote share that a party must obtain in order to take at least one seat in PR systems. DPI 2004, World Bank (2004) DPI 2004, World Bank (2004) DPI 2004, World Bank (2004) DPI 2004, World Bank (2004) Inverse Index of Media Freedom HH Index of Media Concentration The Freedom House (2004) SanchezTabernero (2004) HirschmanHerfindal Index of Concentration of the Media Industry Index of Media Freedom of the country: higher index corresponds to a lower level of media freedom Plurality System Mean District Magnitude Threshold for representation Herfindal Index Opposition Parties 147 Table A2.2. Summary Statistics Variable Obs Mean Std. Dev. Min Max Abstenionists 17072 0.206 0.405 0 1 Votes for "sure loser" parties 13548 0.187 0.390 0 1 Middle level of education 17072 0.360 0.480 0 1 High level of education 17072 0.214 0.410 0 1 Middlehigh level of income 17072 0.151 0.358 0 1 High level of income 17072 0.088 0.283 0 1 Women 17072 0.535 0.499 0 1 Belong to a political Party 17072 0.057 0.231 0 1 Belong to a Special Interest Group 17072 0.562 0.496 0 1 Good opinion about the political system of the country 17072 0.467 0.499 0 1 Believe politics is important 17072 0.364 0.481 0 1 Discuss politics frequently or occasionally 17072 0.699 0.459 0 1 Uninformed about politics 17072 0.190 0.393 0 1 Moderate or indipendent 17072 0.506 0.500 0 1 Indipendent * Uninformed 17072 0.128 0.334 0 1 Left wing extremist 17072 0.072 0.259 0 1 Right wing extremist 17072 0.154 0.361 0 1 Closer to a "sure loser" party 17072 0.391 0.488 0 1 Inverse Index of Media Freedom 17072 17.640 6.943 9 30 HH Index of Media Concentration 17072 2.847 0.733 1.677 4.143 Plurality System 17072 0.500 0.500 0 1 Threshold for representation 17072 2.387 2.013 0 5 Herfindal Index Opposition Parties 17072 0.492 0.137 0.271 0.712 Mean District Magnitude 17072 16.291 33.661 1 150 APPENDIX B3 Robustness Checks Tables A3.1 and A3.2 report the results of the di¤erent specications of the Sequential Logit model and Nested Logit models for electoral participation in the two stage electoral choice model. 84 This constitutes a further robustness check of our results. As we can see the main results are indeed robust to di¤erent empirical specications. 84 The results of robustness checks on electoral participation and communicative voting for the three-stage electoral choice model are available upon request to the authors. 148 (1) (2) 0.061 0.028 ( 0.061 ) ( 0.064 ) 0.028 0.050 ( 0.076 ) ( 0.082 ) 0.258 *** 0.183 ** ( 0.085 ) ( 0.087 ) 0.337 *** 0.223 ** ( 0.109 ) ( 0.112 ) 0.887 *** ( 0.159 ) 0.228 *** ( 0.054 ) 0.445 *** ( 0.053 ) 0.487 *** ( 0.061 ) 0.206 ** ( 0.058 ) 0.682 *** 0.438 *** ( 0.113 ) ( 0.121 ) 1.086 *** 1.044 *** ( 0.059 ) ( 0.061 ) 0.020 0.077 ( 0.130 ) ( 0.132 ) 0.293 *** 0.183 *** ( 0.049 ) ( 0.054 ) 0.030 *** ( 0.005 ) 0.029 ( 0.032 ) Plurality System 0.071 ( 0.088 ) Threshold for representation 0.076 *** ( 0.016 ) Herfindal Index Opposition Parties 0.122 ( 0.218 ) 0.006 *** ( 0.001 ) Countries Dummies NO YES Pseudo R2 0.12 0.15 Number of Observations 17072 17072 Percentage of Correct Predictions 79.94% 80.64% *Significant at 0.10 level **Significant at 0.05 level ***Significant at 0.01 level Note. Dependent variable is whether the individual would not vote in a general election. All regression include age, gender, occupation, marital status and sizeof urbanarea dummies.Robust standard errors are in parenthesis HH Index of Media Concentration Moderate or indipendent Closer to a "sure loser" party Inverse Index of Media Freedom Uninformed about politics Mean District Magnitude Middle level of education High level of education Good opinion about the political system of the country Moderate/Indipendent x Uninformed Table A3.1. Estimates of Electoral Participation Robustness Checks : (1) Regression without "expressive" dummies (2) Regression with country fixed effects Two stage model Belong to a Special Interest Group Discuss politics frequently or occasionally Sequential Logit Middlehigh level of income Believe politics is important High level of income Belong to a political Party 149 (1) (2) (3) (1) 0.049 0.030 0.024 0.236 ( 0.060 ) ( 0.061 ) ( 0.062 ) ( 0.244 ) 0.224 ** 0.180 ** 0.217 ** 0.502 ( 0.073 ) ( 0.077 ) ( 0.078 ) ( 0.333 ) 0.317 ** 0.301 ** 0.212 ** 0.318 ** ( 0.081 ) ( 0.085 ) ( 0.086 ) ( 0.149 ) 0.398 ** 0.385 ** 0.314 ** 0.534 ** ( 0.107 ) ( 0.110 ) ( 0.110 ) ( 0.240 ) 0.865 ** 0.859 ** 0.844 ** 1.005 ** ( 0.159 ) ( 0.158 ) ( 0.159 ) ( 0.251 ) 0.366 ** 0.360 ** 0.370 ** 0.418 ** ( 0.050 ) ( 0.050 ) ( 0.052 ) ( 0.129 ) 0.536 ** 0.533 ** 0.522 ** 0.897 ** ( 0.050 ) ( 0.050 ) ( 0.050 ) ( 0.375 ) 0.525 ** 0.526 ** 0.516 ** 0.490 ** ( 0.060 ) ( 0.060 ) ( 0.060 ) ( 0.101 ) 0.175 ** 0.167 ** 0.216 ** 0.212 ( 0.056 ) ( 0.056 ) ( 0.057 ) ( 0.136 ) 0.326 ** 0.321 ** 0.378 ** 0.479 ** ( 0.120 ) ( 0.119 ) ( 0.119 ) ( 0.231 ) 0.968 ** 0.973 ** 1.004 ** 0.937 ** ( 0.058 ) ( 0.059 ) ( 0.059 ) ( 0.062 ) 0.043 0.035 0.065 0.020 ( 0.131 ) ( 0.130 ) ( 0.131 ) ( 0.138 ) Closer to a "sure loser" party 0.261 ** 0.265 ** 0.227 ** 0.682 ( 0.048 ) ( 0.049 ) ( 0.050 ) ( 0.457 ) Occupation dummies NO YES YES YES Marital status dummies NO YES YES YES Electoral systems dummies NO NO YES NO Pseudo R2 0.12 0.12 0.13 Number of Observations 17072 17072 Percentage of Correct Predictions *Significant at 0.10 level Middle level of education Sequential Logit Uninformed about politics High level of education Middlehigh level of income High level of income Coefficients Note. Dependent variable is whether the individual would not vote in a general election. All regression include age, gender and size of urban area dummies. Robust standard errors are in parenthesis ** Significant at the 0.05 level Chi2(1)=8248.18 LR test of homoskedasticity (IV for the nested logit = 1) Belong to a political Party Belong to a Special Interest Group Good opinion about the political system Moderate/Indipendent x Uninformed Believe politics is important Moderate or indipendent Discuss politics frequently or occasionally Prob>chi2=0.00 17072 17072 80.25% 80.08% 79.97% Nested Logit Coefficients Table A3.2. Estimates of Electoral Participation Robustness Checks No media and institutional dummies Two stage model Table A3.3 reports the results of the robustness checks on the test on the swingvoter s curse fordi¤erent specications of swingervoters (onlyindepen- 150 dents, nomoderates)anddi¤erentspecicationof informativeness. As wecan see the results of these robustness checks are not supporting the theoretical prediction. Indeed, being independent and uninformed seems actually to be positively correlated with the probability of turnout. 0.538 *** 0.679 *** ( 0.070 ) ( 0.231 ) 1.409 *** 1.447 *** ( 0.087 ) ( 0.320 ) 0.503 *** 0.512 *** ( 0.138 ) ( 0.145 ) 0.289 *** 0.469 ** ( 0.099 ) ( 0.206 ) 1.017 *** 0.980 *** ( 0.064 ) ( 0.066 ) 0.006 0.053 ( 0.113 ) ( 0.121 ) Pseudo R2 Number of Observations Percentage of Correct Predictions *Significant at 0.10 level **Significant at 0.05 level Sequential Logit Nested Logit Table A3.3. Estimates of Electoral Participation Robustness checks on the test on the swing voter's curse: alternative definitions of swinger and informative voters Two stage model 17072 Nested Logit 0.14 17072 Uninformed about politics (less than several times a week) Sequential Logit Moderate or Indipendent Moderate/Indipendent x Uninformed 0.13 17072 80.73% Indipendent x Uninformed Uninformed about politics (less than once a week) Indipendent ***Significant at 0.01 level 80.32% 17072 Note. Dependent variable is whether the individual would not vote in a general election. All regression include age, gender, occupation, marital status, size of urban area, educational level, income level, "expressive motivations", media market and institutional characteristics dummies. Robust standard errors are in parenthesis Similarly in order to test the robustness of our results on communicative voting, Table A3.4 and A3.5 report the results of alternative specications of the Sequential Logit model and Nested Logit models. 151 0.139 ** ( 0.073 ) 0.241 *** ( 0.085 ) 0.011 ( 0.094 ) 0.186 ( 0.113 ) 0.283 ** ( 0.114 ) 0.073 ( 0.063 ) 0.498 *** ( 0.057 ) 0.024 ( 0.060 ) 0.042 ( 0.069 ) 0.219 *** ( 0.083 ) 0.212 ** ( 0.086 ) 0.296 *** ( 0.091 ) 0.530 *** ( 0.060 ) Pseudo R2 0.09 Number of Observations 13548 Percentage of Correct Predictions 64.76% *Significant at 0.10 level **Significant at 0.05 level ***Significant at 0.01 level Sequential Logit Table A3.4. Estimates of Communicative Voting Robustness check Regression with country fixed effects Two stage model Closer to a "sure loser" party High level of education Middlehigh level of income Discuss politics frequently or occasionally Uninformed about politics Middle level of education High level of income Note. Dependent variable is whether the individual would vote for a "sure loser" party. Regressionincludesage,gender,occupation,maritalstatus,size ofurban area and countryof residence dummies. Robusts standard errors are in parenthesis Good opinion about the political system of the country Believe politics is important Belong to a political Party Left wing extremist Belong to a Special Interest Group Right wing extremist 152 (1) (2) (3) (1) Middle level of education 0.354 0.309 0.299 0.298 ( 0.067 ) ( 0.069 ) ( 0.070 ) ( 0.103 ) High level of education 0.568 0.487 0.486 0.428 ( 0.075 ) ( 0.080 ) ( 0.080 ) ( 0.140 ) Middlehigh level of income 0.010 0.035 0.039 0.018 ( 0.088 ) ( 0.092 ) ( 0.093 ) ( 0.126 ) High level of income 0.237 0.198 * 0.156 0.221 ( 0.106 ) ( 0.111 ) ( 0.111 ) ( 0.142 ) Belong to a political Party 0.247 0.249 ** 0.233 0.229 * ( 0.109 ) ( 0.110 ) ( 0.110 ) ( 0.124 ) Belong to a Special Interest Group 0.040 0.057 * 0.011 0.093 ( 0.057 ) ( 0.057 ) ( 0.060 ) ( 0.083 ) 0.629 0.624 0.615 0.570 ( 0.054 ) ( 0.054 ) ( 0.054 ) ( 0.117 ) 0.068 0.060 0.037 0.051 ( 0.058 ) ( 0.059 ) ( 0.059 ) ( 0.077 ) 0.037 0.040 0.013 0.093 ( 0.066 ) ( 0.066 ) ( 0.067 ) ( 0.102 ) Uninformed about politics 0.200 0.204 0.184 0.200 ( 0.077 ) ( 0.078 ) ( 0.080 ) ( 0.119 ) Left wing extremist 0.178 0.157 0.165 * 0.065 ( 0.084 ) ( 0.086 ) ( 0.086 ) ( 0.113 ) Right wing extremist 0.280 0.282 ** 0.260 0.424 ( 0.084 ) ( 0.084 ) ( 0.086 ) ( 0.146 ) 0.651 0.662 ** 0.621 0.670 ** ( 0.053 ) ( 0.054 ) ( 0.055 ) ( 0.097 ) Occupation dummies NO YES YES YES Status dummies NO YES YES YES Electoral Systems dummies NO NO YES NO Pseudo R2 0.0384 0.055 0.0612 Number of Observations 13548 13548 13548 13548 Percentage of Correct Predictions 65% 65% 65% *Significant at 0.10 level ** Significant at the 0.05 level ** ** * ** ** Note. Dependent variable is whether the individual would vote for a "sure loser" party. All regression include age, gender and size of urban area dummies. Robust standard errors are in parenthesis Closer to a "sure loser" party ** Prob>chi2=0.00 LR test of homoskedasticity (IV for the nested logit = 1) Chi2(1)=8248.18 Good opinion about the political system of the country Sequential Logit Coefficients ** ** ** ** Table A3.5. Estimates of Communicative Voting Robustness checks No media and Institutional dummies Two stage model Believe politics is important Discuss politics frequently or occasionally * ** ** ** ** ** ** Nested Logit Coefficents ** ** ** ** ** ** ** ** * 153 APPENDIX B4 Robustness Checks on di¤erent countries subsamples In this appendix we perform some robustness checks on electoral partici- pation and communicative voting on di¤erent countries subsamples. First we exclude from our sample all the countries where the di¤erence between the average turnout in the two closest elections and the sample turnout is higher than 10% (i.e., Finland, France, Ireland, Netherlands and Portugal). Table A4.1. report the regression results on electoral participation and communica- tive voting for the fully specied nested logit model on this subsample. 0.058 0.286 *** ( 0.199 ) ( 0.098 ) 0.208 0.423 *** ( 0.313 ) ( 0.117 ) 0.128 0.077 ( 0.139 ) ( 0.129 ) 0.445 *** 0.104 ( 0.169 ) ( 0.142 ) 1.040 *** 0.444 *** ( 0.320 ) ( 0.139 ) 0.253 *** 0.009 ( 0.087 ) ( 0.091 ) 0.514 ** 0.375 *** ( 0.206 ) ( 0.094 ) 0.495 *** 0.034 ( 0.087 ) ( 0.083 ) 0.141 0.101 ( 0.117 ) ( 0.100 ) 0.382 * 0.225 * ( 0.211 ) ( 0.117 ) 0.983 *** ( 0.072 ) 0.145 ( 0.148 ) 0.105 ( 0.124 ) 0.494 *** ( 0.103 ) 0.388 0.615 *** ( 0.293 ) ( 0.118 ) 0.085 ** 0.065 *** ( 0.042 ) ( 0.016 ) 0.419 ** 0.208 *** ( 0.170 ) ( 0.073 ) Plurality System 0.264 0.320 ( 0.267 ) ( 0.207 ) Threshold for representation 0.203 *** 0.010 ( 0.047 ) ( 0.042 ) Herfindal Index Opposition Parties 3.053 * 2.900 *** ( 1.777 ) ( 0.683 ) 0.015 0.015 ( 0.020 ) ( 0.020 ) Number of Observations LR test of homoskedasticity (IV for the nested logit = 1) ***Significant at 0.01 level 9442 12144 Note. Nested logit model. Regression includes age, gender, occupation, marital status and size of urban area dummies. Robust standard errors are in parenthesis chi2(1)= 7174.43; Prob > chi2 = 0.000 Abstention Communicative Voting Left wing extremist Right wing extremist Table A4.1 Estimates of Electoral Participation and Communicative Voting. Subsample of countries with low dicrepancy between actual turnout and sample turnout Two stage model Middle level of education Mean District Magnitude Closer to a "sure loser" party High level of education Belong to a Special Interest Group Good opinion about the political system of the country Inverse Index of Media Freedom HH Index of Media Concentration *Significant at 0.10 level **Significant at 0.05 level Middlehigh level of income High level of income Belong to a political Party Moderate/Indipendent x Uninformed Believe politics is important Discuss politics frequently or occasionally Uninformed about politics Moderate or indipendent 154 As a second robustness check of our results we exclude from our sample all the countries where there are no extreme loser parties (either on the left or on the right of the political spectrum) (i.e., Austria, Ireland, Finland, Spain, Sweden, Belgium). Table A4.2. report the regression results on electoral participation and communicative voting for the fully specied nested logit model on this subsample. 0.214 0.284 *** ( 0.216 ) ( 0.097 ) 0.427 0.379 *** ( 0.298 ) ( 0.114 ) 0.200 0.001 ( 0.146 ) ( 0.128 ) 0.357 ** 0.151 ( 0.186 ) ( 0.144 ) 1.000 *** 0.195 ( 0.227 ) ( 0.126 ) 0.210 ** 0.016 ( 0.100 ) ( 0.087 ) 0.720 *** 0.449 *** ( 0.273 ) ( 0.095 ) 0.483 *** 0.035 ( 0.101 ) ( 0.077 ) 0.202 0.073 ( 0.129 ) ( 0.104 ) 0.580 ** 0.222 ** ( 0.234 ) ( 0.114 ) 0.963 *** ( 0.064 ) 0.022 ( 0.136 ) 0.073 ( 0.084 ) 0.473 *** ( 0.148 ) 0.623 * 0.665 *** ( 0.335 ) ( 0.148 ) 0.048 *** 0.037 ** ( 0.019 ) ( 0.017 ) 0.064 0.037 ( 0.069 ) ( 0.061 ) Plurality System 0.113 0.242 ( 0.310 ) ( 0.241 ) Threshold for representation 0.070 * 0.037 ( 0.040 ) ( 0.028 ) Herfindal Index Opposition Parties 1.962 3.203 *** ( 1.937 ) ( 0.438 ) 0.007 *** 0.004 *** ( 0.003 ) ( 0.001 ) Number of Observations LR test of homoskedasticity (IV for the nested logit = 1) ***Significant at 0.01 level 7238 9351 Note. Nested Logit model. Regression includes age, gender, occupation, marital status and size of urban area dummies. Robust standard errors are in parenthesis chi2(1)= 8075.28; Prob > chi2 = 0.000 Abstention Communicative Voting Left wing extremist Right wing extremist Table A4.2. Estimates of Electoral Participation and Communicative Voting. Subsample of countries with extreme right and left loser parties Two stage model Middle level of education Mean District Magnitude Closer to a "sure loser" party High level of education Belong to a Special Interest Group Good opinion about the political system of the country Inverse Index of Media Freedom HH Index of Media Concentration *Significant at 0.10 level **Significant at 0.05 level Middlehigh level of income High level of income Belong to a political Party Moderate/Indipendent x Uninformed Believe politics is important Discuss politics frequently or occasionally Uninformed about politics Moderate or indipendent 155 AppendixC Proof of Proposition 8 After m draws, given that a current di¤erence in signals in favor of r equal to n; the value function of voter i will be: V i (n) = 8 > > > > > > < > > > > > > : max 8 < : (12(n))x i ; v(n)V i (n+1)+(1v(n))V i (n1)c 9 = ; if (n)< ^ i max 8 < : (2(n)1)(1x i ); v(n)V i (n+1)+(1v(n))V i (n1)c 9 = ; if (n) ^ i (41) Theprobleminvolvesanalyzingastochasticprocesswithtwoabsorbingstate. More specicallywe want todetermine the equations characterizingthese two absorbing states (i.e., n ¯ i and n i ): First, suppose that the state of the world s = r: Then at a given point in time, givenadi¤erenceinsignalsinfavorofr equalton;thevaluefunctionof anindividualwithidiosyncraticpreferencesx i willsatisfythefollowingsecond order di¤erence equation: V r i (n) =V r i (n+1)+(1)V r i (n1)c where the associated homogenous equation is: y 2 y +(1) = 0 whose solutions are: y 1 = 1;y 2 = 1 Moreover,sincethedi¤erenceequationisnon-homogenousithasalsoaspecic solution of the form V r i (n) =Kn; thus we should also nd a solution of: [K(n+1)K(n)+(1)K(n1)] =c 156 Thus K = c 21 (42) Thus, the generic solution to this second order equation is: V r i (n) =a+b n +Kn where = 1 : In order to nd the values of a and b we should consider the two terminal conditions given stopping rule n i and n ¯ i : V r i ( n i ) = (2( n i )1)(1x i ) (43) V r i (n ¯ i ) = (12(n ¯ i ))x i (44) that is (43) represents the utility of individual i when reaching n i signals in favor of state r (where she chooses alternative R): Similarly (44) represents the utility of individual i when reachingjn ¯ i j signals in favor of state l (where she chooses alternative L): Thus, given these two terminal conditions we have that: a+b n i +K n i = 1 n i 1+ n i (1x i ) a+b n ¯ i +Kn i = n ¯ i 1 1+ n ¯ i x i where (n) = 1 1+ n : Thus a = 1 n i 1+ n i (1x i )b n i K n i Thus V r i (n) = 1 n i 1+ n i (1x i )+b( n n i )K( n i n) where b = 2 n ¯ i n i 1 (1+ n ¯ i ) 1+ n i ( n ¯ i n i ) ! + K( n i n ¯ i )+12x i ( n ¯ i n i ) 157 V r i (n; n i ;n ¯ i ) = 1 n i 1+ n i (1x i )+ ( n n i ) ( n ¯ i n i ) " 2 n ¯ i n i 1 (1+ n ¯ i ) 1+ n i ! +K( n i n ¯ i )+12x i # K( n i n) Now, suppose that the state of the worlds =l: Then at a given point in time, given a di¤erence in signals in favor of r equal to n; the value function of an individual with idiosyncratic preferences x i will satisfy the following second order di¤erence equation: V l i (n) = (1)V l i (n+1)+V l i (n1)c The general solution of this di¤erence equation is: V l i (n) =a+b 1 n Kn Using as before the terminal conditions to determine the value of a and b : a+b 1 n i K n i = 1 n i 1+ n i (1x i ) a+b 1 n ¯ i Kn ¯ i = n ¯ i 1 1+ n ¯ i x i Thus a = 1 n i 1+ n i (1x i )b 1 n i +K n i hence: V l i (n) = 1 n i 1+ n i (1x i )b 1 n i 1 n +K( n i n) b = n i n ¯ i n ¯ i n i " 2 1 n i n ¯ i 1+ n i (1+ n ¯ i ) +K( n i n ¯ i )1+2x i # 158 Thus V l i (n; n i ;n ¯ i ) = 1 n i 1+ n i (1x i )+ n ¯ i n i n n n ¯ i n i " 2 1 n i n ¯ i 1+ n i (1+ n ¯ i ) +K( n i n ¯ i )1+2x i # +K( n i n) Thus the expected value of individual i givena di¤erence of signals in favor of r equal to n is: V i (n; n i ;n ¯ i ) = 1 1+ n V r i (n; n i ;n ¯ i )+ n 1+ n V l i (n; n i ;n ¯ i ) Thus: V i (n; n i ;n ¯ i )= 1 1+ n 8 > > > > > > > > < > > > > > > > > : 0 B @ 1 n i 1+ n i (1x i )+ ( n n i ) ( n ¯ i n i ) 2 ( n ¯ i n i 1) (1+ n ¯ i )(1+ n i ) +K( n i n ¯ i )+12x i K( n i n) 1 C A + n 0 B @ 1 n i 1+ n i (1x i )+ n ¯ i ( n n i ) n ( n ¯ i n i ) 2 ( n i n ¯ i 1) (1+ n i )(1+ n ¯ i ) K( n i n ¯ i )+12x i +K( n i n) 1 C A 9 > > > > > > > > = > > > > > > > > ; (45) Therefore, the optimal rightiststopping rule n i will be the value such that @V i @ n i j n i = 0; that is: @V i @ n i j n i = 1 1+ n @V r i @ n i j n i + n 1+ n @V l i @ n i j n i = 0 similarly, the optimal leftiststopping rule n ¯ i will be the value such that @V i @n ¯ i j n ¯ i = 0; that is: @V i @n ¯ i j n=n ¯ i = 1 1+ n @V r i @n ¯ i j n ¯ i + n 1+ n @V l i @n ¯ i j n ¯ i = 0 Where it must be always the case that n ¯ i < 0 and n i > 0. 85 Hence n i is 85 Suppose not. That is n ¯ i > 0: Thus (n ¯ i ) > (n = 0) = p: If x i > 1 2 ; this would imply that (n ¯ i )> ^ i and thus i (n ¯ i ) =R which contradicts the denition of n ¯ i : If x i < 1 2 ; then since n = 0 < n ¯ i ; this implies that i (n = 0) = L and thus the voter would never start sampling. A similar proof applies to show that n i > 0: 159 dened implicitly by the following equation: (ln) n i n ¯ i n i (2x1)(1+ n ¯ i )( n ¯ i 1)[2 K( n i n ¯ i )] =K 1 n i (46) similarly n ¯ i is dened implicitly by the following equation: (ln) n ¯ i n ¯ i n i (2x1) n i +1 + 1 n i [2 K( n i n ¯ i )] =K n ¯ i 1 (47) Notice that the optimal stopping rule n i and n ¯ i do not depend on n: That is the optimal stopping rule do not change depending on the realization of the signals. Moreover, sinceV(n; n i ;n ¯ i ) isdenedontheset = [0;1][0;1]; in order to ensure that unique critical point characterized by ( n i ;n ¯ i ) is a global maximum, it must be the case that i) The Hessian Matrix at ( n i ;n ¯ i ) is negative semidenite; ii) The expected utility at ( n i ;n ¯ i ) is higher that the expected utility at the boundaries. That is a) V(0; n i ;n ¯ i ) > V(0;0;0) = max(U i (Ljq);U i (Rjq)); 86 b) V(n; n i ;n ¯ i ) > V(n; n i ;1) and V(n; n i ;n ¯ i ) > V(n;1;n ¯ i ): Therst conditionis satisedsincetheHessianmatrixat ( n i ;n ¯ i ) is: Hj n i ;n ¯ i = (ln) n ¯ i n n i +1 ( n +1) n ¯ i n i K 0 0 (ln)( n n i )(1+ n ¯ i ) ( n +1) n ¯ i n i K which is clearly negative semidenite. 87 Moreover: V(0; n i ;n ¯ i )V(0;0;0) = 8 > > > > > < > > > > > : n ¯ i 1 n i +1 (2x1)+ 1 n i (2 K( n i n ¯ i )) 2 n ¯ i n i for x i 1 2 1 n i h n ¯ i +1 (12x)+ n ¯ i1 (2 K( n i n ¯ i )) i 2 n ¯ i n i for x i > 1 2 Therefore since by the rst order conditions (46) and (47) it must always be 86 Noticethatobviouslystrategiessuchas( n i = 0;n ¯ i < 0)or( n i > 0;n ¯ i = 0);cannotexist. 87 A detailed formal derivation of this Hessian Matrix is available upon request to the author. 160 the case that: 2 ( n ¯ i 1)(2x1)(1+ n ¯ i )> 0 (48) 2 1 n i +(2x1) n i +1 > 0 (49) Then V(0; n i ;n ¯ i ) > V(0;0;0) 8x i : Finally V(n; n i ;1) = V(n;1;n ¯ i ) = 1;8c> 0. Hence ( n i ;n ¯ i ) is a global maximum of V i (n; n i ;n ¯ i ). Let s now analyze the comparative statics: @ n i @x i / @ 2 V i @ n i @x i n i ;n ¯ i @ 2 V i @ n i @x i n i ;n ¯ i = 2(ln) n i n ¯ i +1 n ¯ i n i 1 n i < 0 (50) Since n ¯ i n i > 0 and ln< 0: Similarly: @n ¯ i @x i / @ 2 V i @n ¯ i @x i n i ;n ¯ i @ 2 V i @n ¯ i @x i n i ;n ¯ i = 2(ln) n ¯ i n ¯ i 1 n i +1 n ¯ i n i < 0 (51) Therefore @ n i @x i > @n ¯ i @x i if and only if: 2(ln) n i n ¯ i +1 n ¯ i n i 1 n i >2(ln) n ¯ i n ¯ i 1 n i +1 n ¯ i n i that is if and only if: 2(ln) n ¯ i n i ( n ¯ i n i 1)( n i + n ¯ i ) n ¯ i 1 1 n i ! > 0 Therefore since: ( n ¯ i n i 1) 8 > > > < > > > : < 0 for x i < 1 2 = 0 for x i = 1 2 > 0 for x i > 1 2 161 Thus @ n i @x i 8 > > > < > > > : < @n ¯ i @x i for x i < 1 2 = @n ¯ i @x i for x i = 1 2 > @n ¯ i @x i for x i > 1 2 (52) since for x i < 1 2 ; n i > jn ¯ i j and thus in our notation n i > jn ¯ i j and hence n ¯ i n i < 1; instead for x i = 1 2 ; n i =jn ¯ i j and thus in our notation n i =jn ¯ i j and hence n ¯ i n i = 1: Similarly for x i > 1 2 ; n i <jn ¯ i j and thus in our notation n i < jn ¯ i j and hence n ¯ i n i > 1: Let s now analyze the comparative statics w.r.t. @ n i @ / @ 2 V i @ n i @ n i ;n ¯ i =2(ln) n i n ¯ i 1 n ¯ i n i 1 n i > 0 (53) Similarly: @n ¯ i @ / @ 2 V i @n ¯ i @ n i ;n ¯ i =2(ln) n ¯ i 1 n i ( n ¯ i n i )(1 n ¯ i ) < 0 (54) That is the higher is ; the more voters care about knowing the true state of the world and the more they will sample in both directions. Therefore: @ 2 V i @ n i @ n i ;n ¯ i > @ 2 V i @n ¯ i @ n i ;n ¯ i if and only if 2(ln) n i n ¯ i 1 n ¯ i n i 1 n i > 2(ln) n ¯ i 1 n i ( n ¯ i n i )(1 n ¯ i ) That is i¤: 2 ln n ¯ i 1 1 n i n ¯ i n i 1 > 0 162 Thus since ( n ¯ i n i 1) 8 > > > < > > > : < 0 for x i < 1 2 = 0 for x i = 1 2 > 0 for x i > 1 2 then: @ n i @ 8 > > > < > > > : < @n ¯ i @ for x i < 1 2 = @n ¯ i @ for x i = 1 2 > @n ¯ i @ for x i > 1 2 (55) Let s now analyze the comparative statics w.r.t. c: That is, @ n i @c / @ 2 V i @ n i @c n i ;n ¯ i : @ 2 V i @ n i @c n i ;n ¯ i = 1 21 " (ln) n i ( n i n ¯ i ) n ¯ i 1 n ¯ i n i 1 n i 1 # < 0 (56) Similarly @n ¯ i @c / @ 2 V i @n ¯ i @c n i ;n ¯ i @ 2 V i @n ¯ i @c n i ;n ¯ i = 1 21 (1+(ln) n ¯ i n i n ¯ i n ¯ i 1 n i 1 n ¯ i n i )> 0 (57) Therefore @ 2 V i @n ¯ i @c n i ;n ¯ i > @ 2 V i @ n i @c n i ;n ¯ i if and only if: n ¯ i n i n ¯ i n ¯ i 1 n i 1 n ¯ i n i + n i ( n i n ¯ i ) n ¯ i 1 n ¯ i n i 1 n i < 0 hence if and only if: ( n ¯ i n i 1) n ¯ i n i n ¯ i 1 1 n i < 0 Hence: @ n i @c 8 > > > < > > > : < @n ¯ i @c for x i < 1 2 = @n ¯ i @c for x i = 1 2 > @n ¯ i @c for x i > 1 2 (58) Q.E.D. 163 Proof of Corollary 2 @Pr( i =Ljs=r) @c > 0, @Pr( i =Rjs=l) @c > 0, @Pr( i =Ljs=r) @x i < 0, @Pr( i =Rjs=l) @x i > 0, @Pr( i =Ljs=r) @ < 0 and @Pr( i =Rjs=l) @ < 0; simply follows from the comparative statics results of Proposition 8. We want instead to show that more moderate votershavealowerprobabilityofmakingerrors. FromLemma1 inBrocasand Carrillo(2007a)wecanderivetheprobabilityofchoosingthewrongalternative for a given state of the world, that is: Pr( i =Ljs =r) = Pr(hitting n ¯ i jr) = 2( n i )1 ( n i )(n ¯ i ) (n ¯ i ) Pr( i =Rjs =l) = Pr(hitting n i jl) = 12(n ¯ i ) ( n i )(n ¯ i ) [1( n i )] Thus the ex-ante probability of making an error is: Pr(error) = Pr(s =r)Pr( i =Ljs =r)+Pr(s =l)Pr( i =Rjs =l) that is: Pr(error) = 1( n i )(1(n ¯ i ))3(n ¯ i )(1( n i )) 2(( n i )(n ¯ i )) which we can rewrite as: Pr(error) = n i ( n ¯ i 1)+(1 n i ) 2 n ¯ i n i Hence: dPr(error) dx i = @Pr(error) @ n i @ n i @x i + @Pr(error) @n ¯ i @n ¯ i @x i where @Pr(error) @ n i = 1 2 (ln) n i n ¯ i 1 2 n ¯ i n i 2 < 0 @Pr(error) @n ¯ i = 1 2 (ln) n ¯ i 1 n i 2 n ¯ i n i 2 > 0 164 hence given (50) and (51): @Pr(error) @x i = (ln) 2 n ¯ i n i 3 " 2 n i n ¯ i 1 2 n ¯ i +1 1 n i 2n ¯ i n ¯ i 1 n i +1 1 n i 2 # which could be simplied as: @Pr(error) @x i = (ln) 2 n ¯ i n i 3 ( n ¯ i n i 1) n ¯ i 1 1 n i n i 2n ¯ i n i ( n ¯ i 1)+ n ¯ i n ¯ i 2 n i (1 n i ) Thus since ( n ¯ i n i 1) 8 > > > < > > > : < 0 for x i < 1 2 = 0 for x i = 1 2 > 0 for x i > 1 2 ; then: @Pr(error) @x i 8 > > > < > > > : < 0 for x i < 1 2 = 0 for x i = 1 2 > 0 for x i > 1 2 Q.E.D. Proof of Corollary 3 WenowwanttoanalyzeU i (Lj(n ¯ i )),U i (Rj( n i ))andcomparethem. Where: U i (Lj(n ¯ i )) = ( n ¯ i 1) 1+ n ¯ i x i U i (Rj( n i )) = (1 n i ) 1+ n i (1x i ) Therefore: U i (Lj(n ¯ i ))>U i (Rj( n i )) if and only if: 2 n ¯ i +1 n i +1 n ¯ i n i 1 > 2x i 1 (59) 165 thus given (63): (2x1) = ( n ¯ i n i 1) ( n ¯ i n i +1) [2 K( n i n ¯ i )] thus the above inequality becomes: 2 n ¯ i n i 1 n ¯ i + n i n ¯ i +1 n i +1 ( n ¯ i n i +1) ! K( n i n ¯ i ) ( n ¯ i n i 1) ( n ¯ i n i +1) Let s now focus on rightist voters. That is individuals with x i > 1=2: For x i > 1=2; n ¯ i n i 1 > 0: Thus the above inequality can be simplied as: 2 n ¯ i + n i n ¯ i +1 n i +1 ! K( n i n ¯ i ) Hence: 2 n ¯ i + n i n ¯ i +1 n i +1 ! K( n i n ¯ i ) which is equivalent to: c 2 (21) ( n i n ¯ i ) n ¯ i + n i n ¯ i +1 n i +1 ! (60) Moreover from (46): (ln) = K 1 n i n ¯ i n i n i (2x1)(1+ n ¯ i )2 ( n ¯ i 1)+K( n i n ¯ i )( n ¯ i 1) (61) Similarly from (47): (ln) = K n ¯ i 1 n ¯ i n i n ¯ i (2x1) n i +1 +2 1 n i K( n i n ¯ i ) 1 n i (62) Therefore combining (61) and (62) it must be the case that: K( n i n ¯ i ) = 2 (1+ n ¯ i n i ) ( n ¯ i n i 1) (2x1) (63) Thus, itmustbethecasethat 2 K( n i n ¯ i )> 0: Henceitisalwaysthecase 166 that c< 2 (21) ( n i n ¯ i ) : Hence denoting: ~ c = n ¯ i + n i n ¯ i +1 n i +1 ! thus from (60) it must be the case that for x i > 1=2 : U i (Lj(n ¯ i )) 8 > > > > < > > > > : >U i (Rj( n i )) i¤ 2 (21) ( n i n ¯ i ) ~ c<c< 2 (21) ( n i n ¯ i ) =U i (Rj( n i )) i¤ c = 2 (21) ( n i n ¯ i ) ~ c 0 then: U i (Lj(n ¯ i )) 2 (21) ( n i n ¯ i ) n ¯ i + n i n ¯ i +1 n i +1 ! (64) Therefore, for x i < 1=2 U i (Lj(n ¯ i )) 8 > > > > < > > > > : >U i (Rj( n i )) i¤c< 2 (21) ( n i n ¯ i ) ~ c =U i (Rj( n i )) i¤c = 2 (21) ( n i n ¯ i ) ~ c <U i (Rj( n i )) i¤ 2 (21) ( n i n ¯ i ) ~ c<c< 2 (21) ( n i n ¯ i ) Notice that: d~ c dc = @~ c @n ¯ i @n ¯ i @c + @~ c @ n i @ n i @c Where: @~ c @n ¯ i = (ln) n ¯ i n i +1 1 n i n ¯ i +1 2 167 @~ c @ n i = (ln) n i n ¯ i +1 1 n ¯ i n i +1 2 moreoverby(56)and(57)weknowthat @n ¯ i @c > 0and @ n i @c < 0:Hence @~ c @n ¯ i @n ¯ i @c < 0 and @~ c @ n i @ n i @c < 0: Therefore: d~ c dc < 0 That is as c increases, the set ~ C = 2 (21) ( n i n ¯ i ) ~ c; 2 (21) ( n i n ¯ i ) becomes larger. It is also immediate to verify that for x j = 1x i < 1 2 : U i (Lj(n ¯ i )) 8 > > > < > > > : >U i (Rj( n i )) i¤ U j (Lj(n j )U j (Rj(n j )) Q.E.D. Proof of Corollary 4 Let s start analyzing the derivative of the expected utility at n ¯ i : dU i (Lj(n ¯ i )) dx i = @U i (Lj(n ¯ i )) @x i + @U i (Lj(n ¯ i )) @n ¯ i @n ¯ i @x i Where @U i (Lj(n ¯ i )) @x i =1 and: @U i (Lj(n ¯ i )) @n ¯ i = @ @n ¯ i ( n ¯ i 1) 1+ n ¯ i x i = 2 (ln) n ¯ i n ¯ i +1 2 then given (51): dU i (Lj(n ¯ i )) dx i = 4 (ln) 2 2n ¯ i n ¯ i +1 2 n i +1 n ¯ i 1 n ¯ i n i 1 hence since by (47): ln = K n ¯ i n i (1+ n ¯ i n i ) 2 n i n ¯ i (2 K( n i n ¯ i )) 168 then: dU i (Lj(n ¯ i )) dx i = K 2 n ¯ i n i (1+ n ¯ i n i ) 2 2 n i (2 K( n i n ¯ i )) 2 ! 1 n ¯ i +1 2 n i +1 n ¯ i 1 1 thus dU i (Lj(n ¯ i )) dx i < 0 if and only if: K 2 < n ¯ i 1 n ¯ i +1 2 2 n i (2 K( n i n ¯ i )) 2 n ¯ i n i (1+ n ¯ i n i ) 2 n i +1 hence c< 2 (21) ( n i n ¯ i ) 1 0 @ r n ¯ i n i n i +1 (1+ n ¯ i n i ) r n ¯ i1 n ¯ i +1 n i ( n i n ¯ i ) +1 1 A = 2 (21) ( n i n ¯ i ) c L Thus dU i (Lj(n ¯ i )) dx i 8 > < > : < 0 for c< 2 (21) ( n i n ¯ i ) c L > 0 for 2 (21) ( n i n ¯ i ) c L <c< 2 (21) ( n i n ¯ i ) Similarly: dU i (Rj( n i )) dx i = 1 K 2 n ¯ i n i n ¯ i n i 1 2 n ¯ i +1 2n ¯ i (2x1) 2 n i +1 2 1 n i that is dU i (Rj( n i )) dx i > 0 if and only if: c< 2 (21) ( n i n ¯ i ) 1 0 @ (1+ n ¯ i n i ) r n ¯ i +1 n ¯ i n i n ¯ i n i +1 r 1 n i ( n i n ¯ i ) +1 1 A = 2 (21) ( n i n ¯ i ) c R that is dU i (Rj(n ¯ i )) dx i 8 > < > : > 0 for c< 2 (21) ( n i n ¯ i ) c R < 0 for 2 (21) ( n i n ¯ i ) c R <c< 2 (21) ( n i n ¯ i ) 169 Notice also that by symmetry for x i = 1x j > 1 2 : dU i (Rj( n i )) dx i = dU j (Lj(n j )) dx j Q.E.D. Proof of Proposition 9 We can decompose the expected utility of individual i given stopping rule n i ;n ¯ i ; as the di¤erence between her expected utility (gross of the cost) given suchstoppingruleminustheexpectedcostofsampling. ThatisgivenGU i (n; n i ;n ¯ i ) andC i (n; n i ;n ¯ i )being,respectively,theexpectedgrossutilityandtheexpected cost of sampling of individual i given stopping rule n i and n ¯ i and a current di¤erence of signals in favor of R equal to n; the expected utility of individual i; V i (n; n i ;n ¯ i ); is equal to: V i (n; n i ;n ¯ i ) =GU i (n; n i ;n ¯ i )C i (n; n i ;n ¯ i ) Let s start deriving expected gross utility of individual i. The expected gross utility of sampling given a current di¤erence in signals in favor of r equal to n; will be: GU i (n) =v(n)GU i (n+1)+(1v(n))GU i (n1) (65) That is the gross expected utility of individual i follows a second order di¤er- ence equation, whose terminal conditions are: GU i ( n i ) = (2( n i )1)(1x i ) (66) GU i (n ¯ i ) = (12(n ¯ i ))x i (67) thatis(66)representsthegrossutilityofindividualiwhenreaching n i signals in favor of state r (where she chooses alternative R): Similarly (67) represents the gross utility of individual i when reaching jn ¯ i j signals in favor of state l 170 (where she chooses alternative L): First, suppose that the state of the world s = r: Then at a given point in time, givenadi¤erenceinsignalsinfavorofr equalton;thevaluefunctionof thisgrossutility,foranindividualwithidiosyncraticpreferencesx i willsatisfy the following second order di¤erence equation: GU r i (n) =V r i (n+1)+(1)V r i (n1) where the associated homogenous equation is: y 2 y +(1) = 0 whose solutions are: y 1 = 1;y 2 = 1 Thus, the generic solution to this second order equation is: GU r i (n) =a+b n where = 1 : Thus, giventhetwoterminalconditions(66)and(67)wehave that: a+b n i = 1 n i 1+ n i (1x i ) a+b n ¯ i = n ¯ i 1 1+ n ¯ i x i Thus a = 1 n i 1+ n i (1x i )b n i Thus GU r i (n; n i ;n ¯ i ) = 1 n i 1+ n i (1x i )+b( n n i ) where b = 2 n ¯ i n i 1 (1+ n ¯ i ) 1+ n i ( n ¯ i n i ) ! + 12x i ( n ¯ i n i ) 171 GU r i (n; n i ;n ¯ i ) = 1 n i 1+ n i (1x i )+ ( n n i ) ( n ¯ i n i ) " 2 n ¯ i n i 1 (1+ n ¯ i ) 1+ n i ! +12x i # Now, suppose that the state of the worlds =l: Then at a given point in time, given a di¤erence in signals in favor of r equal to n; the value function of the expected gross utility for an individual with idiosyncratic preferences x i will satisfy the following second order di¤erence equation: GU l i (n) = (1)GU l i (n+1)+GU l i (n1) The general solution of this di¤erence equation is: GU l i (n) =a+b 1 n Using as before the terminal conditions (66) and (67) to determine the value of a and b : a+b 1 n i = 1 n i 1+ n i (1x i ) a+b 1 n ¯ i = n ¯ i 1 1+ n ¯ i x i Thus a = 1 n i 1+ n i (1x i )b 1 n i hence: GU l i (n; n i ;n ¯ i ) = 1 n i 1+ n i (1x i )b 1 n i 1 n b = n i n ¯ i n ¯ i n i " 2 1 n i n ¯ i 1+ n i (1+ n ¯ i ) 1+2x i # 172 Thus GU l i (n; n i ;n ¯ i ) = 1 n i 1+ n i (1x i )+ n ¯ i n i n n n ¯ i n i " 2 1 n i n ¯ i 1+ n i (1+ n ¯ i ) 1+2x i # Thus the expected gross utility of individual i given a di¤erence of signals in favor of r equal to n is: GU i (n; n i ;n ¯ i ) = 1 1+ n GU r i (n; n i ;n ¯ i )+ n 1+ n GU l i (n; n i ;n ¯ i ) Thus the expected gross utility of individual i given stopping rule ( n i ;n ¯ i ) will be: GU i (n; n i ;n ¯ i ) = 1 1+ n 0 B @ 1 n i 1+ n i (1x i )+ ( n n i ) ( n ¯ i n i ) 2 n ¯ i n i 1 (1+ n ¯ i )(1+ n i ) +12x i 1 C A + n 1+ n 0 B @ 1 n i 1+ n i (1x i )+ n ¯ i ( n n i ) n ( n ¯ i n i ) 2 n i n ¯ i 1 (1+ n i )(1+ n ¯ i ) +12x i 1 C A hence: GU i (0; n i ;n ¯ i ) = 1 2 2 1 n i n ¯ i 1 n ¯ i n i + n ¯ i n i 1 n ¯ i n i (2x i 1)1 ! (68) representsrepresentsthegrossutilitythatindividualiisexpectingtogetwhen shestartssamplinggiventheoptimalstoppingrule( n i ;n ¯ i ). Therefore,theex- ante benetofsamplingforindividuali,isgivenbythedi¤erencebetweenthe expected gross utility of starting to sample and the utility she gets when not sampling. That is, the benet of sampling for individual i; given the optimal stopping rule ( n i ;n ¯ i ); is given by: B i (0; n i ;n ¯ i ) =GU i (0; n i ;n ¯ i )max(U i (Ljq);U i (Rjq)) 173 that is, for q = 1 2 : B i (0; n i ;n ¯ i ) = 8 < : GU i (0; n i ;n ¯ i )+x i for x i 1 2 GU i (0; n i ;n ¯ i )+1x i for x i > 1 2 hence B i (0; n i ;n ¯ i ) = 8 < : 1 2 n ¯ i1 n ¯ i n i 2 1 n i + n i +1 (2x1) for x i 1 2 1 2 1 n i n ¯ i n i [2 ( n ¯ i 1)( n ¯ i +1)(2x1)] for x i > 1 2 (69) Thus given (48) and (49), the expected net benet of start sampling is always positive8x i : We want now to analyze the expected cost of sampling. The expected disu- tility of sampling given a current di¤erence in signals in favor of r equal to n; is given by: D i (n) =v(n)D i (n+1)+(1v(n))D i (n1)c (70) That is the expected disutility of sampling follows a second order di¤erence equation whose terminal conditions are: D r i ( n i ) = 0 (71) D r i (n ¯ i ) = 0 (72) that is (71) represents the expected disutility of individual i when reaching n i signals in favor of state r (where she chooses alternative R): Similarly (72) represents the expected disutility of sampling of individual i when reaching jn ¯ i j signals in favor of state l (where she chooses alternative L): They are both equal to zero since it is obviously the case that when individual i stops sampling, her disutility fromsampling is zero. First, suppose that the state of the world s = r: Then at a given point in time, given a di¤erence in signals 174 in favor of r equal to n; the value function of the disutility from sampling of anindividualwithidiosyncraticpreferencesx i willsatisfythefollowingsecond order di¤erence equation: D r i (n) =D r i (n+1)+(1)D r i (n1)c where the associated homogenous equation is: y 2 y +(1) = 0 whose solutions are: y 1 = 1;y 2 = 1 Moreover,sincethedi¤erenceequationisnon-homogenousithasalsoaspecic solution of the form V r i (n) =Kn; thus we should also nd a solution of: [K(n+1)K(n)+(1)K(n1)] =c Thus K = c 21 Thus, the generic solution to this second order equation is: D r i (n) =a+b n +Kn where = 1 : In order to nd the values of a and b we use the two terminal conditions (71) and (72). Hence: a+b n i +K n i = 0 a+b n ¯ i +Kn ¯ i = 0 Thus a =b n i K n i 175 b = K( n i n ¯ i ) ( n ¯ i n i ) Thus D r i (n; n i ;n ¯ i ) =b( n n i )K( n i n) Thus D r i (n; n i ;n ¯ i ) = K( n i n ¯ i ) ( n ¯ i n i ) ( n n i )K( n i n) Now, suppose that the state of the worlds =l: Then at a given point in time, given a di¤erence in signals in favor of r equal to n; the value function of the disutility from sampling of an individual with idiosyncratic preferences x i will satisfy the following second order di¤erence equation: D l i (n) = (1)V l i (n+1)+V l i (n1)c The general solution of this di¤erence equation is: D l i (n) =a+b 1 n Kn Using as before the terminal conditions (71) and (72) to determine the value of a and b: a+b 1 n i K n i = 0 a+b 1 n ¯ i Kn ¯ i = 0 Thus a =b 1 n i +K n i b 1 n i 1 n ¯ i =K( n i n ¯ i ) b = n i n ¯ i n ¯ i n i [K( n i n ¯ i )] hence: D l i (n; n i ;n ¯ i ) =b 1 n i 1 n +K( n i n) 176 b = n i n ¯ i n ¯ i n i [K( n i n ¯ i )] Thus D l i (n; n i ;n ¯ i ) = n ¯ i ( n i n ¯ i ) n n i n n ¯ i n i K +K( n i n) Thus the expected disutility of sampling of individual i given a di¤erence of signals in favor of r equal to n is: D i (n; n i ;n ¯ i ) = 1 1+ n D r i (n; n i ;n ¯ i )+ n 1+ n D l i (n; n i ;n ¯ i ) Thus the expect disutility of sampling given stopping threshold n i and n ¯ i is: D i (n; n i ;n ¯ i ) = 1 1+ n ( n i n ¯ i )( n n i ) ( n ¯ i n i ) KK( n i n) + n 1+ n n ¯ i ( n i n ¯ i ) n n i n n ¯ i n i K +K( n i n) ! Therefore simplifying the above expression: D i (n; n i ;n ¯ i ) = 1 1+ n ( n i n ¯ i )( n n i ) ( n ¯ i n i ) K(1 n ¯ i )K( n i n)(1 n ) (73) which is clearly negative since ( n i n ¯ i )( n n i )(1 n ¯ i ) < ( n i n)( n ¯ i n i )(1 n ) because: ( n i n ¯ i )( n n i )(1 n ¯ i )>( n i n)( n ¯ i n i )(1 n ) since ( n i n ¯ i )> ( n i n) and: ( n n i )(1 n ¯ i )+( n ¯ i n i )(1 n ) = ( n n ¯ i ) n i 1 > 0 Thereforetheexpectedcostofsamplinggiventheoptimalstoppingrule( n i ;n ¯ i ) 177 is given by: C i (n; n i ;n ¯ i ) = jD i (n; n i ;n ¯ i )j = (74) K 1+ n (n ¯ i n i )( n n i ) 1 n ¯ i ( n ¯ i n i ) ( n i n)(1 n ) ! > 0 which represents how much individual i is expecting to spend in sampling costs. Moreover, the expected disutility of start sampling is given by: D i (0; n i ;n ¯ i ) = ( n i n ¯ i )(1 n i ) 2( n ¯ i n i ) K 1 n ¯ i (75) Therefore the expected cost of start sampling is given by: C i (0; n i ;n ¯ i ) =jD i (0; n i ;n ¯ i )j = ( n i n ¯ i )(1 n i ) 2( n ¯ i n i ) K n ¯ i 1 (76) Hence the net expected benet of start sampling is given by: B NET i (0; n i ;n ¯ i ) = 8 > > < > > : n ¯ i1 h n i +1 (2x1)+ 1 n i (2 K( n i n ¯ i )) i 2 n ¯ i n i for x i 1 2 1 n i h n ¯ i +1 (12x)+ n ¯ i1 (2 K( n i n ¯ i )) i 2 n ¯ i n i for x i > 1 2 Thusgiven(48)and(49),theexpectednetbenetofstartsamplingispositive 8x i : Moreover,wecanexpresstheexpectedutilityofindividualiasthedi¤erence between the expected gross utility of individual i and her expected cost of sampling: V i (n; n i ;n ¯ i ) =GU i (n; n i ;n ¯ i )C i (n; n i ;n ¯ i ) 178 hence: V i (n; n i ;n ¯ i )= 1 1+ n 8 > > > > > > > > < > > > > > > > > : 0 B @ 1 n i 1+ n i (1x i )+ ( n n i ) ( n ¯ i n i ) 2 ( n ¯ i n i 1) (1+ n ¯ i )(1+ n i ) +K( n i n ¯ i )+12x i K( n i n) 1 C A + n 0 B @ 1 n i 1+ n i (1x i )+ n ¯ i ( n n i ) n ( n ¯ i n i ) 2 ( n i n ¯ i 1) (1+ n i )(1+ n ¯ i ) K( n i n ¯ i )+12x i +K( n i n) 1 C A 9 > > > > > > > > = > > > > > > > > ; (77) Noticethatexpectedutilitycontainedin(77)isequivalenttotheoneexpressed in(45),whichweobtainedwithoutdecomposingtheexpectedgrossutilityand the expected cost of sampling. We now analyze the comparative statics on the expected benet and ex- pected cost of sampling at the optimum. Let s start focusing on x i 1 2 and let s analyze how this benet of sampling varies as x i changes: dB i (0; n i ;n ¯ i ) dx i = @B i (0; n i ;n ¯ i ) @x i + @B i (0; n i ;n ¯ i ) @ n i @ n i @x i + @B i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @x i where @B i (0; n i ;n ¯ i ) @x i = n ¯ i 1 n ¯ i n i n i +1 > 0 @B i (0; n i ;n ¯ i ) @ n i = (ln) n i n ¯ i 1 2 n ¯ i n i 2 (2x1) n ¯ i +1 2 n ¯ i 1 (78) where by (48) it is always the case that @B i (0; n i ;n ¯ i ) @ n i > 0: At the same time: @B i (0; n i ;n ¯ i ) @n ¯ i = (ln) n ¯ i 1 n i 2 n ¯ i n i 2 2 1 n i (2x1) 1+ n i (79) where by (49) it is always the case that @B i (0; n i ;n ¯ i ) @n ¯ i < 0: Therefore given (50) 179 and (51): dB i (0; n i ;n ¯ i ) dx i = n ¯ i 1 n ¯ i n i n i +1 + (ln) 2 1 n ¯ i n i n ¯ i 1 1 n i n ¯ i n i 3 2 4 (12x) 1+ n ¯ i n i ( 2n ¯ i 2 n i )+ 2 n ¯ i n ¯ i 2 n i 1 n i + n i 2n ¯ i n i n ¯ i 1 3 5 hence since (1 n ¯ i n i ) 8 > > > < > > > : > 0 for x i < 1 2 = 0 for x i = 1 2 < 0 for x i > 1 2 , then dB i (0; n i ;n ¯ i ) dx i > 0 for x i < 1 2 : Moreover: dB i (0; n i ;n ¯ i ) d = @B i (0; n i ;n ¯ i ) @ + @B i (0; n i ;n ¯ i ) @ n i @ n i @ + @B i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @ where @B i (0; n i ;n ¯ i ) @ = n ¯ i 1 n ¯ i n i 1 n i > 0 then given (53) and (78) @B i (0; n i ;n ¯ i ) @ n i @ n i @ > 0 and given (54) and (79) @B i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @ > 0 Therefore: dB i (0; n i ;n ¯ i ) d > 0 Similarly: dB i (0; n i ;n ¯ i ) dc = @B i (0; n i ;n ¯ i ) @ n i @ n i @c + @B i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @c 180 then given (56) and (78): @B i (0; n i ;n ¯ i ) @ n i @ n i @c < 0 and given (57) and (79): @B i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @c < 0 hence dB i (0; n i ;n ¯ i ) dc < 0 Let s now focus on x i > 1=2 and perform the same comparative statics as before: @B i (0; n i ;n ¯ i ) @x i = 1 n i n ¯ i n i n ¯ i +1 < 0 @B i (0; n i ;n ¯ i ) @ n i = 1 2 (ln) n i n ¯ i n i 2 n ¯ i 1 (2x1) n ¯ i +1 2 n ¯ i 1 where by (48) it is always the case that @B i (0; n i ;n ¯ i ) @ n i > 0: At the same time: @B i (0; n i ;n ¯ i ) @n ¯ i = (ln) n ¯ i 1 n i 2 n ¯ i n i 2 2 1 n i +(2x1) 1+ n i < 0 where by (49) it is always the case that @B i (0; n i ;n ¯ i ) @n ¯ i < 0. Therefore given (50) and (51): dB i (0; n i ;n ¯ i ) dx i = 1 n i n ¯ i n i n ¯ i +1 + (ln) 2 n ¯ i n i 3 (80) 2 6 4 1 n ¯ i1 2x1 1 n i h 2n ¯ i 1 2 n i 2 + 2 n i 2n ¯ i 1 2 i 2 2 n i n ¯ i +1 1 n i n ¯ i 1 2 +2 2n ¯ i n i +1 n ¯ i1 1 n i 2 3 7 5 181 Therefore given (63) and substituting (51) in (80): dB i (0; n i ;n ¯ i ) dx i = 1 n i n ¯ i n i n ¯ i +1 + (ln) 2 n ¯ i n i 3 2 6 6 6 4 (2 K( n i n ¯ i )) ( n ¯ i n i1) 2n ¯ i 1 2 n i 2 + 2 n i 2n ¯ i1 2 n ¯ i1 1 n i ( n ¯ i n i +1) +2 (1 n ¯ i n i ) h n ¯ i n ¯ i 2 n i (1 n i )+ n i 2n ¯ i n i ( n ¯ i1) i n ¯ i1 1 n i 3 7 7 7 5 Thus, simplifying the above expression and given that ( n ¯ i n i 1) > 0 for x i > 1 2 : dB i (0; n i ;n ¯ i ) dx i = 1 n i n ¯ i n i n ¯ i +1 + (ln) 2 ( n ¯ i n i 1) n ¯ i n i 3 1 n i n ¯ i 1 ( n ¯ i n i +1) 2 4 4 n ¯ i n i n ¯ i 1 (1 n i ) n i + n ¯ i K( n i n ¯ i ) h 2n ¯ i 1 2 n i 2 + 2 n i 2n ¯ i 1 2 i 3 5 < 0 Therefore, for x i > 1 2 ; given given that ( n ¯ i n i 1) > 0; it must be the case that dB i (0; n i ;n ¯ i ) dx i < 0: Itisalsoimmediatetoverifythatforx i > 1 2 ; itisalsothe case that dB i (0; n i ;n ¯ i ) d > 0 and dB i (0; n i ;n ¯ i ) dc < 0: Let s perform the comparative statics on the expected cost of sampling: dC i (0; n i ;n ¯ i ) dx i = @C i (0; n i ;n ¯ i ) @ n i @ n i @x i + @C i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @x i Hence @C i (0; n i ;n ¯ i ) @ n i = @ @ n i ( n i n ¯ i )(1 n i ) ( n ¯ i n i ) K n ¯ i 1 = K n ¯ i 1 2 n ¯ i n i 1 n i (ln) n i ( n i n ¯ i ) n ¯ i 1 n ¯ i n i ! > 0 182 @C i (0; n i ;n ¯ i ) @n ¯ i = @ @n ¯ i ( n i n ¯ i )(1 n i ) ( n ¯ i n i ) K n ¯ i 1 = K 1 n i 2 n ¯ i n i 1 n ¯ i +(ln) n ¯ i ( n i n ¯ i ) 1 n i n ¯ i n i ! < 0 since obviously as n i increase, the expected cost of sampling increases and as n ¯ i increases (i.e.,jn ¯ i j decreases), the expect cost of sampling decreases. Thus given (50) and (51): dC i (0; n i ;n ¯ i ) dx i = (ln)K 1 n ¯ i n i 2 0 B B @ 2n ¯ i1 n i 1 n i 1 n i (ln) n i ( n i n ¯ i ) n ¯ i1 n ¯ i n i + n ¯ i 1 2 n i n ¯ i1 1 n ¯ i +(ln) n ¯ i ( n i n ¯ i ) 1 n i n ¯ i n i 1 C C A which simplies to: dC i (0; n i ;n ¯ i ) dx i = (ln)K n ¯ i n i 1 n ¯ i n i 2 0 B @ ( n i + n ¯ i )(ln)( n i n ¯ i ) n i 2n ¯ i n i ( n ¯ i1)+ n ¯ i n ¯ i 2 n i (1 n i ) n ¯ i n i n ¯ i1 1 n i 1 C A thus dC i (0; n i ;n ¯ i ) dx i > 0 if and only if n ¯ i n i 1 < 0: Hence, since ( n ¯ i n i 1) 8 > > > < > > > : < 0 for x i < 1 2 = 0 for x i = 1 2 > 0 for x i > 1 2 ; then: dC i (0; n i ;n ¯ i ) dx i 8 > > > < > > > : > 0 for x i < 1 2 = 0 for x i = 1 2 < 0 for x i > 1 2 (81) Therefore, the more moderate voters are, the higher their expected cost of sampling. It is also immediate to verify that: dC i (0; n i ;n ¯ i ) d = @C i (0; n i ;n ¯ i ) @ n i @ n i @ + @C i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @ > 0 (82) 183 since @ n i @ > 0 and @n ¯ i @ < 0: Moreover, it is obviously the case that: @C i (0; n i ;n ¯ i ) @c > 0 (83) Let s now analyze the comparative statics on the net benet of sampling. dB NET i (0; n i ;n ¯ i ) dx i = @B NET i (0; n i ;n ¯ i ) @x i + @B NET i (0; n i ;n ¯ i ) @ n i @ n i @x i + @B NET i (0; n i ;n ¯ i ) @n ¯ i @n ¯ i @x i Where @B NET i (0; n i ;n ¯ i ) @ n i = 0, @B NET i (0; n i ;n ¯ i ) @n ¯ i = 0;sinceattheoptimumthemarginal costofonemoredrawisexactlyequaltothemarginalbenetofonemoredraw. Hence: dB NET i (0; n i ;n ¯ i ) dx i = @B NET i (0; n i ;n ¯ i ) @x i = 8 < : n ¯ i1 n ¯ i n i n i +1 > 0 for x i < 1 2 1 n i n ¯ i n i n ¯ i +1 < 0 for x i > 1 2 Moreover: dB NET i (0; n i ;n ¯ i ) d = @B NET i (0; n i ;n ¯ i ) @ = n ¯ i 1 n ¯ i n i 1 n i > 0 and: dB NET i (0; n i ;n ¯ i ) dc = @B NET i (0; n i ;n ¯ i ) @c = n ¯ i 1 n ¯ i n i ( n i n ¯ i ) 1 n i < 0 Q.E.D.

Abstract (if available)

Abstract Three essays compose the dissertation. The first essay entitled "Indirect Lobbying and Media Bias " analyzes amodel where voters have state-contingent preferences over policies and lobbies engage in in fluence activities to affect the information that a media outlet collects on the state of the world. The media outlet acts as a " filter" between lobbies and voters. It has to decide what to communicate to voters given the information it collects and its idiosyncratic bias. We show that, by targeting voters, lobbies are able to indirectly in fluence the political outcome and thus create a distortion in the political process. When the media outlet has a small idiosyncratic bias the (unique) equilibrium is characterized by a large level of lobbies ' in fluence activities and no "news-slanting " by the media outlet. When the media outlet 's idiosyncratic bias is large, the (unique) equilibrium involves a low level of lobbies' in luence activities and a high probability of "news-slanting" by the media outlet. Moreover, we show that a higher idiosyncratic bias of the media outlet may be associated with a lower policy distortion and a higher voters' welfare. On the other hand, public policy measures aimed at increasing the cost of lobbies' influence activities would decrease the distortion in the policy outcome and increase voters welfare. Finally, asymmetries in lobbies' influence activities lead to different probabilities of "news-slanting" by different media outlet 's types.

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Asset Metadata

Creator Sobbrio, Francesco (author)

Core Title Essays in political economics

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 07/14/2010

Defense Date 03/30/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag indirect lobbying,information acquisition,media bias,OAI-PMH Harvest,voting

Language English

Advisor Carrillo, Juan D. (committee chair), Mattozzi, Andrea (committee member), Tan, Guofu (committee member), Wilburn, Kenneth (committee member), Wilkie, Simon J. (committee member)

Creator Email sobbrio@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1345

Unique identifier UC1437786

Identifier etd-Sobbrio-20080714 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-88107 (legacy record id),usctheses-m1345 (legacy record id)

Legacy Identifier etd-Sobbrio-20080714.pdf

Dmrecord 88107

Document Type Dissertation

Rights Sobbrio, Francesco

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu