University of Southern California Dissertations and Theses

Neuroeconomic mechanisms for valuing complex options

(USC Thesis Other)

Neuroeconomic mechanisms for valuing complex options

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content NeuroEconomic Mechanisms for Valuing Complex Options by T. Dalton Combs A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (NEUROSCIENCE) August 2016 Copyright 2016 T. Dalton Combs Acknowledgments I would like to thank the members of my committee, my friends, and my family for shepherdingmethroughthisprocess. Withouttheirsupporttheworkinthisdocument, everything that is coming after it, and so much that came before it would have been impossible. IamgratefultomembersoftheLosAngelesBehavioralEconomicsLaboratory(LA- BEL) for their insights and comments in the various phases of the project. I would also thank participants at the 2013, 2014, and 2015 Social Neuroscience retreats (Catalina island, USC). All remaining errors are mine. These studies were conducted under the University of Southern California IRB approval UP-12-00528. This work was funded in part by the National Science Foundation grant SES-1425062. Contributions IsabelleBrocas, JuanCarrillo, TDaltonCombs, NireeKodaverdian, andJohnMon- terosso all contributed to this work. To make their individual contributions clear, con- tributions to each chapter are broken down into 6 elements: Experimental Design - Determining how to answer the motivating questions. An- swering: what stimuli would need to be presented to whom and when? What data should be collected and how? ii Implementation - Programming the software for stimuli presentation or data collec- tion. Collection - Interacting with subjects and recording data. Analysis - Computing statistics, running models, or exploring the collected data. Story - Outlining the narrative arch of the text. Text - Contributing text to this document. Figures - Made the figures in this document. The authors names are in alphabetical order. The level of an authors contribution should not be inferred from the ordering. Chapter 1 and Appendix A The experiments described in this chapter were designed by Isabelle Brocas, Juan Carrillo, T Dalton Combs, and Niree Kodaverdian; and implemented by T Dalton Combs and Niree Kodaverdian. T Dalton Combs and Niree Kodaverdian ran the data collection. IsabelleBrocas, JuanCarrillo, TDaltonCombs, andNireeKodaverdianana- lyzed the data. Isabelle Brocas, Juan Carrillo, T Dalton Combs, and Niree Kodaverdian shaped the story, contributed to the text, and made the figures. Chapter 2 and Appendix B The experiments described in this chapter were designed by Isabelle Brocas, Juan Carrillo, T Dalton Combs, and Niree Kodaverdian; and implemented by Niree Kodav- erdian. Isabelle Brocas, Juan Carrillo, T Dalton Combs, and Niree Kodaverdian all assisted in the data collection. Isabelle Brocas, Juan Carrillo, T Dalton Combs, and Niree Kodaverdian analyzed the data. Isabelle Brocas, Juan Carrillo, and T Dalton iii Combs, shaped the story. Isabelle Brocas, Juan Carrillo, T Dalton Combs, and Niree Kodaverdian contributed to the text. T Dalton Combs made the figures. Chapter 3 The experiments described in this chapter were designed by Isabelle Brocas, Juan Carrillo, T Dalton Combs, Niree Kodaverdian, and John Monterosso; and implemented by T Dalton Combs and Niree Kodaverdian. T Dalton Combs and Niree Kodaverdian ran the data collection. Isabelle Brocas, T Dalton Combs, and Niree Kodaverdian analyzed the data. Isabelle Brocas, T Dalton Combs, and John Monterosso shaped the story. T Dalton Combs and Isabelle Brocas contributed to the text. T Dalton Combs made the figures. iv Table of Contents Acknowledgments ii List of Figures vii List of Tables xi Chapter 1: Consistency in Simple vs. Complex Choices Over the Life Cycle 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Bundles with identical goods . . . . . . . . . . . . . . . . . . . . 8 1.2.2 Bundles with di↵ erent goods . . . . . . . . . . . . . . . . . . . . 11 1.3 Experimental design and procedures . . . . . . . . . . . . . . . . . . . . 12 1.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.4.1 Frequency of violations . . . . . . . . . . . . . . . . . . . . . . . 19 1.4.2 Severity of violations . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.3 Trivial trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5 Understanding violations . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Chapter 2: Value-Based Decision-Making: A New Developmental Paradigm 38 2.0.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.0.2 Specific scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.0.3 Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.0.4 Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.0.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Chapter 3: Bundling Options in Value-Based Decision-Making: Attention, Calcu- lation, and Working Memory 50 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.2 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 v 3.2.3 MRI data acquisition. . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2.4 MRI data preprocessing . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.5 Behavioral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.6 Analysis of reaction times . . . . . . . . . . . . . . . . . . . . . . 59 3.2.7 MRI data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2.8 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3.1 Behavioral results . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3.2 Reaction times . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.3.3 Regions correlating with subjective value . . . . . . . . . . . . . 65 3.3.4 Regionsinvolvedincomplexconditions(SCALINGandBUNDLING) 69 3.3.5 Regionsinvolvedincomplexcalculations(BUNDLINGvs. SCAL- ING) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.6 Connectivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.7 Other analyses of interest . . . . . . . . . . . . . . . . . . . . . . 72 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Bibliography 76 Appendix A 93 Appendix B 106 vi List of Figures 1.1 Trials a 12 vs. a 0 12 and b 12 vs. b 0 12 ...................... 9 1.2 The 35 trials in treatment S......................... 15 1.3 Screenshot of one trial in treatment C ................... 17 1.4 Number of violations in treatments S (left) and C (right) . . . . . . . . 20 1.5 Direct (left) and Indirect (right) violations in treatment C ....... 22 1.6 Severity of violations in treatments S (left) and C (right) . . . . . . . . 24 1.7 Choices to remove for consistency in treatments S (left) and C (right) . 26 1.8 Number of violations in treatment A (trivial trials) . . . . . . . . . . . 27 1.9 Choice violations by subjects with at most two treatment A violations 28 2.1 Decision-making tasks. (A) In each trial of the Choice tasks, par- ticipants were shown one option on the left (Opt.1) and one option on the right (Opt. 2). They touched one of three buttons displayed at the top of their screen to select an option or to express indi↵ erence (middle button). (B) In Ranking tasks, participants ranked options from most preferred(greenface)toleastpreferred(yellowface). Bothtypesoftasks were conducted in the (C) Goods domain involving objects, in the (D) Social domain involving sharing rules for self (hand pointing out) and other (hand pointing right), and in the (E) Risk domain involving lot- teries consistingof quantities (number of tokens) and probabilities(green share of the pie). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 vii 2.2 PerformanceimproveswithageintheGoods-andSocial-Choice tasks but not in the Risk-Choice task. Y-axis reports the average number of transitivity violations in the Choice tasks for each age group (x-axis)brokendownbydomain(Goods,Social,andRisk). Theshadings are the 95% confidence intervals. . . . . . . . . . . . . . . . . . . . . . . 42 2.3 Transitivityviolationsdecreasewithagedi↵ erentlyacrosschoices. Each cell represents the color-coded average number of transitive viola- tions involving a higher ranked option (x-axis) and a lower ranked option (y-axis), as revealed by explicit rankings obtained in the Goods-Ranking task. Lightercolorsreflectmoreviolations. Allagegroupsaremorelikely to make transitivity violations when options have similar ranks. There is convergence to a state where participants almost never commit transitiv- ity violations when choices involve their best (dark color in left column) or their worst (dark color in bottom row) options. The vectors in the top right corner of each heat map show the average gradient in the heatmap. Subjects become more consistent if the rank of the higher-ranked option goes up, or if the rank of the lower-ranked option goes down. . . . . . . 43 2.4 Leftpanel: Socialvs. Goodsafterremovingheuristicusers.The developmental signature of consistency is comparable in the Goods and Social domains among children who do not use heuristics. Right panel: Riskvs. Goodsafterremovingheuristicusers. Thedevelopmental signatureofconsistencyisdi↵ erentintheGoodsandRiskdomainsamong children who do not use heuristics. All children are similarly inconsistent and improvements occur later in life. . . . . . . . . . . . . . . . . . . . . 45 2.5 Transitive violations across choices among non heuristic users: (A) In the Social domain, there is convergence to a state where partic- ipants almost never commit transitivity violations when choices involve their highest-ranked options (“they know what they want”). (B) In the Risk domain, there is convergence to a state where participants almost never commit transitivity violations when choices involve their lowest- ranked options (“they know what they do not want”). . . . . . . . . . . 46 3.1 Three types of trial. The first is a single item, the second is two portions of the same item, the third is one portion each of two items. . . 56 3.2 Experimental Design.Inthe fMRI task, each participant had to choose between an o↵ -screen reference (REF) option and an on-screen option. In the post-fMRI task, each participant had to choose between two on-screen options. All trials were self-paced. . . . . . . . . . . . . . 57 viii 3.3 Value tracking regions. A) Regions tracking value in the fMRI task (Model (1)). B) Regions tracking value in CONTROL (Model (2)). C) Regions tracking value in BUNDLING (Model 2). See table 3.1 for all active regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.4 Attentiveness is required in complex conditions. Compared to CONTROL, both SCALING and BUNDLING trials have significantly less activity in the posterior nodes of the Default Mode Network. A canonical map of default more network (A) from Smith et al. (2009) appear similar to corrected contrasts of CONTROL>SCALING (B) and CONTROL>BUNDLING (C). There are no regions are significant for the contrasts SCALING>CONTROL or BUNDLING>CONTROL. . . . 70 3.5 Thecontrastbetweenthesingle-item-trialregressorandthere- gressors for scaled-option-trials and bundled-option-trials cor- relates the the canonical default mode network Smith et al. (2009). A voxelwise correlation between the correlation coe cient of 0.29 was calculated using fslcc. The p-value on a persons correlation is <10 308 . However,aPearsoncorrelationtestassumesindependentobser- vations, which is never true in neuroimaging, especially after smoothing. addito salis grano, that’s still a good correlation and tiny p-value. . . . . 71 3.6 Relative to SCALING, BUNDLING recruits regions associated with calculation. IPS activation in a neurosynth meta analysis for ‘cal- culation’(A)baresastrikingresemblancetotheBUNDLING>SCALING contrast(B). A contrast of meta analyses for ‘calculation’ and ‘saccades’ (C)alsosupportstheclaimthattheIPSactivityintheBUNDLING>SCALING contrast is caused by calculation-like cogitation. In (C) red regions are more associated with calculation and blue regions are more associated with saccades. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.7 ThevmPFCismoreconnectedtothedlPFCduringBUNDLING trials than during CONTROL trials from gPPI. Both the right dlPFC (peak p-value = 0.029 corrected) and left dlPFC (peak p-value = 0.093corrected)aresignificantlygreaterinthecontrastoftheBUNDLING connectivity regressor than in the CONTROL connectivity regressor. . . 74 A.1 Trials (a 12 vs. a 0 12 ), (b 12 vs. b 0 12 ), (c 12 vs. c 0 12 )............... 93 A.2 Clusterrepresentation. Misclassifiedtrials(left)andnumberofviolations (right) in treatments S and C........................ 100 B.1 Options used in the Goods-Choice and Goods-Ranking tasks. 109 ix B.2 Options used in the Social-choice and Social-ranking tasks. Par- ticipants were presented with choices involving sharing rules between them and other. For elementary school each token represented a toy, which was personalized for each participants to ensure they liked it. For undergraduate students, each token represented $2. . . . . . . . . . . . . 110 B.3 Options used in the Risk-choice and Risk-ranking tasks. Par- ticipants were presented with choices involving lotteries. For elementary school each token represented a toy, which was personalized for each par- ticipants to ensure they liked it. For undergraduate students, each token represented $2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 B.4 Transitive Reasoning Task. The animal wearing the hat is the oldest ineachvignetteontheleft. Theparticipanthastoanswerinthevignette on the bottom right by choosing the animal he thinks is the oldest given the information on the left, or by reporting it cannot be known (?). . . . 112 B.5 Sensitivity analysis ............................ 117 B.6 Choice reversals across domains and age. .............. 122 B.7 Choice removals across domains and age. .............. 123 B.8 Classification errors (all subjects). .................. 124 B.9 Discrepancies between explicit and implicit rankings (all sub- jects)...................................... 125 B.10Inconsistencies with respect to explicit ranking (all subjects) . 126 B.11Evolution of Prosocial behavior..................... 131 B.12Performance in the reasoning task. .................. 135 x List of Tables 1.1 Summary of treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2 Pearson correlations of memory, intelligence and GARP violations. . . . 31 1.3 Pearson correlations for the OA population . . . . . . . . . . . . . . . . 32 1.4 OrdinaryLeastSquares(OLS)regressionofnumberofviolationsintreat- ment C (all subjects) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.5 OLS Regression of number of violations in treatment C (subjects with 2 or less violations in treatment A). . . . . . . . . . . . . . . . . . . . . . 35 3.1 Local minima in corrected p-value parametric value regressor. Thresholded for p 0.005 corrected. Minima in occipital cortex or white matter excluded. Where cluster spanned multiple functional regions, a regional mask was used to locate the peak voxel within a region. mOFC; medial OrbitoFrontal Cortex, vmPFC; ventroMedial PreFrontal Cortex, SFG; Superior Frontal Gyrus, dlPFC; DorsoLateral PreFrontal Cortex . 66 3.2 Local minima in corrected p-value parametric value regressor for CONTROL trials. Thresholded for p 0.005 corrected. Minima in occipital cortex or white matter excluded. Where cluster spanned multiple functional regions, a regional mask was used to locate the peak voxel within a region. vmPFC ;ventroMedial PreFrontal Cortex, MTG; MidTemporal Gyrus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3 Local minima in corrected p-value parametric value regressor for Bundling trials Part1......................... 67 xi 3.4 Local minima in corrected p-value parametric value regressor for Bundling trials Part2. These tables contain many more minima because a lower threshold was needed to report the mOFC activation. dlPFC; DorsoLateral PreFrontal Cortex, SFG; Superior Frontal Gyrus, IPS;IntraParietal Sulcus, CS; Central Sulcus, ACC; antirior cingulate cortex, V.str.: Ventral Striatum, mOFC;medial OrbitoFrontal Cortex, vmPFC;ventroMedial PreFrontal.Cortex . . . . . . . . . . . . . . . . . . 68 3.5 Localminimaincorrectedp-valueforBUNLDING>SCALING. Thresholded for p 0.01. . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.6 Localminimaincorrectedp-valueforBUNDLING CONNECTIVITY >CONTROL CONNECTIVTY. Thresholded for p 0.1 corrected. 72 A.1 Summary statistics by cluster. . . . . . . . . . . . . . . . . . . . . . . . 99 A.2 Types of preferences by subjects in clusters 1 and 2 . . . . . . . . . . . . 103 B.1 Sample description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 B.2 Indi↵ erences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 B.3 Revealed preferred options in the Social domain (from implicit rankings) 130 B.4 Revealed preferred options in the Risk domain (from implicit rankings) 132 B.5 Complex transitive reasoning determinants (all subjects) . . . . . . . . . 135 B.6 Transitivity violations in the Goods domain . . . . . . . . . . . . . . . . 137 B.7 Transitivity violations in the Social domain . . . . . . . . . . . . . . . . 137 B.8 Transitivity violations in the Risk domain . . . . . . . . . . . . . . . . . 138 xii Chapter 1 Consistency in Simple vs. Complex Choices Over the Life Cycle Employing a variant of GARP, we study consistency in aging by comparing the choices of younger adults (YA) and older adults (OA) in a ‘simple’, two-good and a ‘complex’ three-good condition. We find that OA perform worse than YA in the complex condition but similar to YA in the simple condition, both in terms of the number and severity of GARP violations. Working memory and IQ scores correlate significantly with consistency levels, but only in the complex treatment. Our findings suggest that the age-related deterioration of neural faculties responsible for working memory and fluid intelligence is an obstacle for consistent decision-making. 1 1 AversionofthischapteriscurrentlyunderreviewbyGamesandEconomicBehavior. Mycoauthors on that article (Niree Kodaverdian, Isabelle Brocas and Juan Carrillo) made considerable contributions to the text in this chapter. 1 1.1 Introduction As most day-to-day decisions involve comparing options and making trade-o↵ sbetween them, understanding how people attribute value to options is crucial in understanding how people make decisions. Economics builds theories under the assumption that indi- viduals have unambiguous values for options and maintain stable preferences. These in turn imply consistency of choice, which can be tested empirically. Experimental studies have shown that choice consistency is prevalent, at least for younger adults (Andreoni and Harbaugh (2009), Andreoni and Miller (2002), Choi et al. (2014)). By contrast, our knowledge about choice consistency in older adults is still incomplete. Understanding the e↵ ect of age on consistency can provide a foundation for refined economic models. Recent field and experimental evidence has shown that older adults (OA) make di↵ erent choices as compared to younger adults (YA) in a variety of domains. 2 Such di↵ erences can potentially be due to two very di↵ erent mechanisms: either preferences change with age or preferences remain stable but the ability to act consistently on them changes with age. There is indirect evidence for both possibilities. In line with the first prong, aging brings dramatic changes in our motivations, which in turn a↵ ect the decisions we make (Carstensen and Mikels (2005), Mather and Carstensen (2005)). At the same time, the aging process a↵ ects many brain structures and brain mechanisms, hindering the ability to evaluate alternatives and select among options (Mather and Nielsen(2011),Mohretal.(2010)),especiallywhentheybecomecomplex(Besedeˇ setal. (2012a,b), Brand and Markowitsch (2010)) Disentangling between preference changes 2 Seee.g.AlbertandDu↵ y(2012),Ameriksetal.(2007),Bellemareetal.(2008),Castleetal.(2012), Engel (2011), Fehr et al. (2003). However, there is also evidence that OA and YA make similar choices in some of the same domains (Charness and Villeval (2009), Dror et al. (1998), Kovalchik et al. (2005), Sutter and Kocher (2007)). Yet others find curvilinear age e↵ ects (Harrison et al. (2002), Read and Read (2004)). Some studies o↵ er to resolve these mixed findings, by arguing that results are highly sensitivetodi↵ erencesinthelearningrequirements(Mataetal.(2011)),thecompletenessofinformation (Zamarian et al. (2008)), the number of options to choose between (Brand and Markowitsch (2010)) and the contents of choice sets (Mather (2012)). 2 and mistakes is essential for policy-making purposes (Bernheim and Rangel (2009)) as well as for purposes of cost avoidance on the part of the decision maker (Lichtenstein and Slovic (1973)). We aim to resolve this problem by controlling for di↵ erences in preferences and testing consistency. In this paper, we propose to use the Generalized Axiom of Revealed Preference (GARP) to test the internal consistency of the preferences of YA and OA by o↵ ering repeated choices between bundles of goods. Additionally, we vary the complexity of the task by changing the number of unique goods that are present in a choice. Our goal is to understand the e↵ ect of aging on consistency as a function of the complexity of the situation. More specifically, we use a controlled laboratory experiment with a 2⇥ 2 design, where YA and OA make choices in two di↵ erent domains: simple and complex. In the simple domain, subjects decide between two bundles each composed of di↵ erent quantities of the same two goods (e.g., w pistachios plus x cheese vs. y pistachios plus z cheese). In the complex domain, subjects choose between two bundles, each also composed of di↵ erent quantities of two goods, but now with exactly one common good (e.g., w pistachios plus x cheese vs. y pistachios plus z crackers). BesidesthecontributionofcomparingYAandOAinasimpleandacomplexdomain, ourdesignhasthreenewelementsrelativetotheexistingliterature(reviewedbelow). As opposed to previous studies, we ask subjects to choose between two bundles presented pictorially. This simplifies the choice problem relative to presenting a large number of bundles (as in Harbaugh et al. (2001)) or relative to presenting a budget set on a coordinate plane (as in Choi et al. (2007, 2014), Fisman et al. (2007)). Moreover, we include trivial trials to our task, where subjects choose between a smaller and a larger quantity of one desirable good. Subjects who fail these trials are likely to violate one or more assumptions of the model; they are inattentive, they do not monotonically value 3 the good over the tested range, and/or they misunderstand the task. This allows us to conduct the consistency analysis both with the full sample and with the subsample of subjects for whom we are most confident the model is appropriate. In addition, our subjects perform a working memory and an IQ test. This allows us to study the determinants of consistency. Before reviewing the main results of the paper, we want to stress one potential problem with our analysis, namely that of sample selection. Despite our best e↵ orts to match samples, di↵ erences found across age groups may be due to cohort-specific factors and unrelated to age, as in any panel study. Furthermore, subjects that select themselvesintoourexperimentmaynotberepresentativeoftheirpopulationagegroup. Anydi↵ erenceswefindacrosstheagesamplesmaybedrivenbydi↵ erencesinsociability, emotionality,experienceoropportunitycostoftime,allofwhichmayinfluencedecision- making quality. It should also be noted that the mean household income of our YA sampleisgreaterthanthatofourOAsample, andthatmostofourYAsubjectsidentify as White or Asian, while most of our OA subjects identify as White or Black. With this caveat in mind, we next summarize the two main findings of our study. First, both OA and YA are reasonably (and roughly equally) consistent in the sim- ple treatment whereas OA are significantly more inconsistent than YA in the complex treatment. This di↵ erence across populations applies generally: to the number of total violations, to the number of violations by type (direct and indirect) and to the severity of violations (using two di↵ erent criteria). Surprisingly, a significant fraction of sub- jects (12% of YA and 33% of OA) fails the trivial trials. This calls into question the reliability and interpretability of the consistency results for those individuals. We then conductthesameanalysiswiththesubsampleofsubjectswhopassthetrivialtrials. Not surprisingly, the total number of violations is substantially smaller in this subsample. 4 Importantly, however, the treatment e↵ ect is identical: marginal di↵ erences between OA and YA in the simple domain and significant di↵ erences in the complex domain. Second,wefindthatdi↵ erencesinviolationsinthecomplextreatmentareassociated withdi↵ erencesinperformanceintheworkingmemorytest. SinceYAscoresignificantly higher in that test compared to OA, most of the di↵ erence in performance across ages is captured through the working memory e↵ ect. Our findings thus indicate that the workingmemorysystemismoreheavilyrecruitedinthecomplextaskthaninthesimple one. The result echoes the studies reviewed below, which show this precise relationship betweencomplexityandworkingmemorydemands. Interestingly,theresultalsoextends to IQ (although less strongly) but it should be noted that working memory and IQ are highly correlated. Finally, we also conduct an individual and cluster analysis (see ). One group of sub- jects is very inconsistent in both the simple and complex treatments. A second group, mostly composed of OA, are individuals who commit almost no violations in the simple treatment. Interestingly, thesesubjectshaveapreferencethatcanbeimplementedwith a simple rule: maximize the quantity of the favorite good in the bundle. Their behavior becomes significantly more inconsistent in the complex domain, possibly because that simple rule is less intuitive to implement in that context. The last group, mostly com- posed of YA, are subjects who do not exhibit preferences that can be implemented with simple rules. They are slightly less consistent than the previous group in the simple treatment but significantly more consistent in the complex one. The study builds on three strands of the literature. First, laboratory experiments have used GARP to assess the degree of consistency of subjects in di↵ erent domains, such as goods (bundles with positive quantities of two or more desirable items), risk (bundles of quantities and probabilities) and social (bundles of money for oneself and 5 money for another party). Studies find that YA are generally consistent with revealed preference. 3 Second, experiments have concurred in the finding that consistency increases be- tween 8 and 12 years old children (Bradbury and Nelson (1974)) and thereafter stabi- lizes (Harbaugh et al. (2001)). By contrast, the full trajectory across the lifetime has not been established. Indeed, some laboratory (Kim and Hasher (2005), Tentori et al. (2001)) and field (Dean and Martin (2014)) experiments find that OA are more consis- tent than YA while other laboratory (Finucane et al. (2002, 2005)) and field (Echenique et al. (2011)) experiments find the opposite. These disparate findings may be partly due to two methodological choices. First and contrary to standard practices in experi- mental economics, decisions in those YA vs. OA studies are not incentivized. Second, they use di↵ erent domains (health, extra credit, grocery coupons, nutrition, finance). This introduces confounding factors since di↵ erent age groups have varying degrees of domain-specific expertise. Additional support for an inverse relationship between age and consistency can be found in the recent work by Choi et al. (2014). In this online study, Choi et al. (2014) show that GARP consistency in the risk domain decreases with age and increases with household wealth. The paper combines benefits of field (large, representative sample size) and laboratory (controlled, incentivized) experiments. Moreover, the findings are not likely driven by self-selection, as the subjects are drawn from a sample designed 3 Seee.g.AndreoniandHarbaugh (2009),Choietal.(2014),Mattei(2000),Sippel(1997)forstudies in the good domain, Andreoni and Harbaugh (2009), Choi et al. (2007, 2014) for studies in the risk domain and Andreoni and Miller (2002), Fisman et al. (2007) for studies in the social domain. Studies also report GARP consistent behavior in the context of criminal behavior (Visser et al. (2006)) and by inebriated (Burghart et al. (2013) or sleepy (Castillo et al. (2014) subjects. In a cross cultural study, Tanzanian YA are found to commit more GARP violations as compared to YA from the United States (Cappelen et al. (2014) Finally, in a multi-domain study (bundles of consumption goods, labor hours, and token money) with female mental hospital patients, Battalio, R. C., Kagel, J. H., Winkler, R. C., Fisher, E. B., Basmann, R. L., Krasner (1973) find some inconsistencies but when a subsequent work (Cox (1997)) studies the same data taking into account severity of violations, all but one of the subjects is deemed consistent. 6 to be representative of the Dutch population. Their study, however, does not address the two questions we are interested in, namely (i) how choice inconsistencies depend on the combination of age and task complexity and (ii) whether they can be traced to compromised working memory and fluid intelligence. Third,studieshavedemonstratedthattaskcomplexityimposesdemandsonworking memory. Working memory is the short-term mental maintenance (Cohen et al. (1997), Curtis and D’Esposito (2003)) and manipulation of information (Pochon et al. (2001)), andthisprocessislesse cientinOA.Varyinglevelsoftaskcomplexitymayaccountfor di↵ erencesinchoiceconsistencybetweenOAandYA.Indeed,neuroimagingstudieshave shown that the working memory regions of the brain are recruited during more di cult tasks, suchasthoserequiringtask-switching(Macdonaldetal.(2000)), integral-solving (Krueger et al. (2008)), and attention-shifting (Kondo et al. (2004)). Crucially, the circuitry is di↵ erentially recruited as tasks become more complex (Baker et al. (1996), Braver et al. (1997), Carlson et al. (1998), Cohen et al. (1997), Demb, J. B., Desmond, J. E., Wagner, A. D., Vaidya, C. J., Glover, G. H., and Gabrieli (1995), Greene et al. (2004)). 4 Interestingly,ithasbeenshownthatolderadultsperformworseonsuchtasks (Brand and Markowitsch (2010), Grady et al. (2006), Henninger et al. (2010), Zamarian et al. (2008)) and the age-related atrophy of regions involved in working memory (Raz etal.(2005))couldbeamaincauseofthatdecline: theseregionsareactivatedlessinOA ascomparedtoYAinworkingmemorytasks(RypmaandD’Esposito(2000)),especially when the number of items to be maintained (Cappell et al. (2010)) or manipulated (Wright (1981)) in memory is high. Thearticleisorganizedasfollows. Thetheoreticalframeworkispresentedinsection 1.2. The experimental setting is described in section 1.3. The analysis is reported in 4 This relationship extends to tasks requiring the explicit representation and manipulation of knowl- edge, when the ability to reason relationally is essential (Kroger et al. (2002)), when the number of dimensions to be considered simultaneously is increased (Christo↵ et al. (2001)), or when the number of objects to remember is increased (Gould et al. (2003)). 7 sections 1.4 and 1.5. Concluding remarks are gathered in section 1.6. The individual analysis can be found in the Appendix. 1.2 Theoretical background Consider a subject making choices between pairs of bundles, each with two goods that are assumed to be desirable, in the sense that more of each good is strictly preferred to less. A choice between a pair of bundles is called a “trial.” Denote a xy :=(q a x ,q a y )the bundle a xy that has positive quantities q a x and q a y of goods x and y,respectively. 1.2.1 Bundles with identical goods Suppose first that bundles are composed of the same two goods (x,y 2 {1,2} with x 6= y) and consider trials with bundles a 12 and a 0 12 so that each bundle has strictly more quantity of one good and strictly less of the other (q a x >q a 0 x , q a y <q a 0 y ). In the experimental section, this is called treatment S (for simple). When a trial is considered in isolation, the question of consistency is moot, and any choice between pairs of bundles with the aforementioned properties is consistent with the maximization of monotonic and transitive preferences. However, when we jointly consider a pair of trials, some combinations of choices may constitute a violation of revealed preferences (which we call D S , for direct violation in the simple treatment). 5 Here is why. Consider the example in Figure 1.1 and suppose that a 12 is chosen over a 0 12 and b 12 is chosen over b 0 12 .Since q a 0 x >q b x for all x,wehave a 12 a 0 12 b 12 .Since q b 0 x >q a x for all x,we have b 12 b 0 12 a 12 . This forms a contradiction to the maximization of monotonic and transitive preferences. Definition 1 sets conditions for a direct violation in a pair of trials of treatment S. 5 The seminal work on revealed preference theory is due to Samuelson (1938) . It was subsequently extended by Afriat (1967), Houthakker (1950), Varian (1982) among others. 8 - 6 t a 12 t b 0 12 t b 12 t a 0 12 q 2 q 1 0 Figure 1.1: Trials a 12 vs. a 0 12 and b 12 vs. b 0 12 Definition 1 Direct violation in a pair of trials of the simple treatment (D S ). (i) Trials a 12 vs. a 0 12 and b 12 vs. b 0 12 may involve aD S -violation if and only if q a 0 x q b x for all x (with at least one strict inequality) and q b 0 x q a x for all x (with at least one strict inequality). (ii) A D S -violation occurs when a 12 is chosen over a 0 12 and b 12 is chosen over b 0 12 . The logic of the argument is very similar to the standard revealed preferences argu- ment made in earlier GARP studies (Choi et al. (2007), Harbaugh et al. (2001), Sippel (1997)). The only di↵ erence is that, in our case, the set of options per choice is dra- matically reduced. Therefore, a choice in one trial only reveals that the selected option, or “bundle,” is preferred to the only other bundle proposed rather than to any bundle on the “budget line.” Notice that Definition 1 is made of two parts. Part (i) provides conditions such that choices in a pair of trials may result in a violation. Intuitively, the requirement is that for each trial one bundle dominates (i.e., has weakly more quantity of both goods and strictly more of at least one than) a bundle in another trial whereas the remaining bundle is dominated by (i.e., has weakly less quantity of both goods and strictlylessofatleastonethan)theremainingbundleintheothertrial. Naturally,some pairs of trials will fail to satisfy this condition, in which case a D S -violation will not be 9 possible. Given a pair of trials such that a D S -violation is possible, part (ii) provides conditions such that the violation indeed occurs. Again intuitively, the requirement is that in each trial the subject selects the bundle that is dominated by a bundle in the other trial. In our example, the dominated bundles are a 12 and b 12 . Hence, only one out of the four possible choice combinations will result in a D S -violation. Given n trials, there are n(n1)/2 pairs of trials. By considering all pairs of trials and checking whether the condition in Definition 1(i) is satisfied, we can identify all possible violations between pairs of trial. Then, actual violations are determined simply by checking whether a subject’s selected bundles (in those pairs of trials in which a violation is possible) satisfy the condition in Definition 1(ii). Two important remarks are in order. First, it is unfortunately not possible to deter- mine the maximum number of violations that a subject can e↵ ectively incur. Indeed, when a subject makes a choice that induces a violation it may preclude violations be- tween other pairs of trials. 6 Second, by the discrete nature of our choice problem, it is possible that a direct violation occurs between a triplet of trials (or more) even though the condition in Definition 1(i) is not satisfied by any pair of trials in that triplet (and therefore no direct violation occurs between pairs of trials in the triplet). In Appendix A1, we construct an example of such case. Given our choice of bundles, conditions such that direct violations can occur between triplets of trials – but not between pairs of trials in that triplet – are very rare but still possible. We will not consider them in the analysis, which means that our experimental study identifies a lower bound in the number of GARP violations incurred by our subjects. 6 To see this, consider the example in Figure 1.1 and suppose there is a third trial between bundles c12 and c 0 12 such that q c x <q a x and q c 0 x >q a 0 x for all x.Bychoosing a12 over a 0 12 and b12 over b 0 12 the subject incurs a violation. However, by choosing a12 over a 0 12 the subject precludes any possible violation between the pair of trials a12 vs. a 0 12 and c12 vs. c 0 12 (even though a violation would have occurred had the subject chosen a 0 12 over a12 and c12 over c 0 12 ). 10 1.2.2 Bundles with di↵ erent goods Assume now that there are three possible goods (x,y,z2 {3,4,5} with x6= y6= z) and as before, bundles are composed of two goods. Consider trials between pairs of bundles that have exactly one good in common, that is, between bundle a xy and bundle a 0 xz . In the experimental section, this is called treatment C (for complex). As the choice problem involves more goods, the decision is arguably more complicated. Since a trial still has two bundles and each bundle still has positive quantities of exactly two goods, the two treatments remain comparable. By definition, each bundle now has strictly more quantity of at least one good (only a xy has a positive quantity of good y and only a 0 xz has a positive quantity of good z). Again, when a trial is considered in isolation, any choice between pairs of bundles is consistent with the maximization of monotonic and transitive preferences. Definition 2 identifies conditions for a direct violation in a pairoftrialsoftreatmentCtooccur. Theseareverysimilartotheconditionsdescribed in Definition 1. Definition 2 Direct violation in a pair of trials of the complex treatment (D C ). (i) Trials a xy vs. a 0 xz and b xz vs. b 0 xy may involve aD C -violation if and only if q a 0 x q b x and q a 0 z q b z (with at least one strict inequality) and q b 0 x q a x and q b 0 y q a y (with at least one strict inequality). (ii) A D C -violation occurs when a xy is chosen over a 0 xz and b xz is chosen over b 0 xy . Just like in the example of Figure 1.1, when the conditions of Definition 2(i) and (ii) are satisfied, we get a xy a 0 xz b xz and b xz b 0 xy a xy which is a contradiction to the maximization of monotonic and transitive preferences. Interestingly, in treatment C there is also the possibility of incurring an indirect violation (I C ). An I C -violation involves choices in three trials, each with a di↵ erent common good. Definition 3 describes an indirect violation. 11 Definition 3 Indirect violation in a triplet of trials of the complex treatment (I C ). (i) Trials a xy vs. a 0 xz , b xz vs. b 0 yz and c yz vs. c 0 xy may involve an I C -violation if and only if q a 0 x q b x and q a 0 z q b z (with at least one strict inequality), q b 0 y q c y and q b 0 z q c z (with at least one strict inequality), and q c 0 x q a x and q c 0 y q a y (with at least one strict inequality). (ii) An I C -violation occurs when a xy is chosen over a 0 xz , b xz over b 0 yz and c yz over c 0 xy . Although the argument is slightly more sophisticated, the idea behind indirect vio- lations is similar to that behind direct violations. An I C -violation may occur if in each trial, one bundle dominates the bundle composed of the same goods in another trial and the remaining bundle is dominated by the bundle composed of the same goods in the other trial. In Definition 3(i) and given that more quantity is always desirable, we have a 0 b, b 0 c, and c 0 a. Whenthisconditionissatisfied, anindirectviolationoccursif the subject chooses bundles a, b, and c. Indeed, these choices imply a a 0 b b 0 c on one hand, and c c 0 a on the other, which forms a contradiction. Forthesamereasonsasinthesecondremarkofthesimpletreatment,inthecomplex treatmentitmaybethecasethatadirectviolationinvolvingthreeormoretrialsoccurs but no violation occurs between any subset of two trials. Similarly, it may be the case that an indirect violation involving four or more trials occurs but no violation occurs between any subset of three trials. For simplicity, we will again ignore those violations. 1.3 Experimental design and procedures Tostudychoiceconsistencyofyoungeradults(YA)andolderadults(OA)withdi↵ erent levels of complexity, we conduct an experiment based on the setup described in the the- ory section using the MatLab extension Psychtoolbox (Brainard (1997), Pelli (1997)). 12 We ran 10 sessions with OA and 7 sessions with YA. Each session had between 5 and 8 subjects and lasted between 1.5 and 2 hours. OA sessions were conducted at two OA- SIS senior centers in Los Angeles, OASIS Baldwin Hills and OASIS West Los Angeles. A total of 51 OA (age 59-89) were recruited through the OASIS activities catalogue. 7 Six subjects were omitted from analysis: four subjects experienced software malfunc- tioning; one spontaneously reported miscomprehension of the task halfway through the experiment; the only male subject in the pool was excluded to make the sample more demographically homogeneous. We therefore retained 45 female OA for the analysis. 8 OA in our sample are highly educated. 9 Given their education level, we deemed it appropriate to recruit college students for our YA sample. 10 YA subjects were recruited from the Los Angeles Behavioral Economics Laboratory (LABEL) pool, which consists of over 2,500 USC students, and sessions were conducted at LABEL, in the department of Economics at the University of Southern California. In order to match gender, we recruited 50 YA female USC students, age 18-34. 11 All subjects were compensated with a fixed amount of $20 plus an incentive payment (described below). 7 OASIS is a non-profit organization active in 25 states. Its mission is to promote successful aging by disseminating knowledge and o↵ ering classes and volunteering opportunities to its members. Re- cruitment is mostly word-of-mouth, with existing members referring new members. More information can be found at http://www.oasisnet.org. 8 The overwhelming majority of OASIS members are female (88%), which explains the extreme gender selection in our sample but also raises some concerns about self-selection. Besedeˇ s et al. (2012b). also report a larger fraction of female participation (75%), although the di↵ erence is not as extreme as ours. 9 The distribution of their highest educational attainment is: PhD (4%), MA (22%), Professional degree (2%), BA (29%), AA (11%), some college credit (26%), and trade/technical/vocational school (4%). This is representative of the OASIS members and substantially above national averages. It is not surprising that an organization dedicated to the sharing of knowledge and promotion of research-based programs attracts individuals with above average levels of education and intellectual curiosity. 10 All the YA in our sample are USC students. Based on national average statistics (reported by U.S News in 2009), we expect that 26% of undergraduates will pursue a graduate degree. Therefore, education of our OA is comparable to the final education that can be expected for our YA. 11 For more information about the laboratory, see http://dornsife.usc.edu/label.Wehad45 undergraduate and 5 master students in our YA sample from all 4 disciplines: Arts and Humanities (10%), Natural Sciences (30%), Social Sciences (50%), and Technical Sciences (10%). 13 As discussed in the introduction, due to the selection problem, any experimental evidence we find regarding di↵ erences in behavior between our YA and OA does not prove a causal e↵ ect of age. In section 1.5 we briefly review di↵ erent channels through which our findings could be explained (such as di↵ erences in experience, opportunity cost of time, emotionality, sensitivity to fatigue or hunger, etc.). However, if such mech- anismswerecrucial, wewouldnotexpectthemtodiscriminateacrosstaskcomplexity. 12 Instead, as developed below, we find a clear di↵ erential e↵ ect across task complexity. GARP task. Eachsubjectparticipatedin140coretrialswithfivegoods(1,2,3,4,5). In each core trial, subjects chose between two bundles each composed of two goods, and were not allowed to express indi↵ erence. There were 35 trials of the simple treatment S, where the same two goods (1,2) appeared in both bundles (a 12 vs. a 0 12 , b 12 vs. b 0 12 , etc.). There were also three sets of 35 trials of the complex treatment C, where each bundle had one common good and one unique good for a total of three goods (3,4,5) in each trial. These three sets of 35 trials were identical up to a permutation of the identity of the common good: good 3 (a 34 vs. a 0 35 ), good 4 (a 34 vs. a 0 45 ) and good 5 (a 35 vs. a 0 45 ). Importantly, quantities in each bundle were chosen to maximize the chances to satisfy condition (i) in Definitions 1, 2 and 3: for each trial, we chose one bundle that dominated a bundle in as many other trials as possible and a second bundle that was dominated by a bundle in as many other trials as possible. There are two reasons for this choice. First, to give as many chances as possible to observe D S -, D C -, and I C - violations if subjects were inconsistent. Second, to minimize the chances of violations that are not identified in our analysis (e.g., direct violations between triplets of trials that are not captured with pairs of trials, as explained in the second remark of section 1.2.1 and Appendix A1). 12 For example, if the self-selected OA had a lower opportunity cost of time than the general OA population, and if opportunity cost of time a↵ ects decision consistency, then we would expect the e↵ ect to be present for both the simple and complex version of the GARP task. 14 Figure 1.2 depicts the 35 trials in treatment S. The x- and y-axis represent the quantities of the two goods. Each point represents a bundle of some quantity of good x and some quantity of good y. Each segment corresponds to one trial in which the two bundlesitconnectswereo↵ eredagainstoneanother. Forexample, theboldredsegment represents a trial in which a bundle of 1x and 5y were o↵ ered against a bundle of 2x and 2y. We used the same quantities for trials in treatmentC, in order to facilitate the comparison of violations across treatments. The only di↵ erence is that bundles have only one good in common. 13 Figure 1.2: The 35 trials in treatment S. Finally, we added 10 trivial trials to check for the attentiveness of subjects (treat- ment A). In these trials, subjects chose between di↵ erent quantities of the same good (q x vs. q 0 x ). Including trivial trials are typical in psychology experiments (under the misleading terminology of “catch trials”) but less common in economics, which assumes that incentive payments ensure attentiveness. For subjects who failed to choose the higher quantity option in treatment A, our design is not intended to (and therefore cannot) distinguish between inattention, satiation, disliking, or miscomprehension of the task, although our procedures were intended to minimize all four possibilities, as 13 If we were to depict it, we would use a three-dimensional graph. Each bundle would then have positive quantities of exactly two of three goods. 15 described below. Either way, such violations would call into question the reliability and interpretability of that subject’s choices in treatments S and C. All subjects faced the 150 trials, which were presented in a randomized and counterbalanced order. Table 1.1 summarizes this information. Treatment Goods # of trials S (1,2) vs. (1,2) 35 C (3,4) vs. (3,5) 35 C (3,4) vs. (4,5) 35 C (3,5) vs. (4,5) 35 A (1) vs. (1) 10 Total 150 Table 1.1: Summary of treatments A major concern in experiments on revealed preferences is the choice of goods. Following some of the recent literature on revealed preferences and value elicitation (Harbaugh et al. (2001), Hare et al. (2009), Rangel et al. (2013)), we opted for food items. We presented subjects with 21 popular salty and sweet snacks and asked them to pick five of them for consumption: two were then randomly used in treatment S and the other three in treatment C. Each portion was small (for example, one portion consisted of “two pistachios”) ensuring that the maximum quantity o↵ ered of each good was substantially below satiation level. 14 Subjects were instructed not to eat or drink anything except for water for a period of at least three hours prior to the experiment and all sessions were conducted between 10am and 2:30pm to ensure that subjects were hungry. 14 We made sure that all five selected items were desirable. To address the issue of complementarity or substitutability of goods, we also made sure that subjects understood they might have to consume a combination of two items at the end of the experiment. Appendix A2 presents the list of food items and quantities per portion. 16 Figure 1.3 presents a sample screenshot of a trial in treatment C. In this example, the subject had to choose between a bundle of 5 portions of chips plus 1 portion of peanutsandabundleof4portionsofchipsplus2portionsofpretzels. Attheendofthe experiment, onetrialwasrandomlyselectedforeachsubject, andthesubject’schoicein that trial was given to them to consume. Subjects were kept in the experimental room for 15 minutes following the end of the experiment. This was to ensure that all the foods would be fully consumed, that they would be consumed by the intended subject, and that they would not be consumed in combination with foods other than those in each subject’s bundle. One advantage of using food is that subjects cannot trade goods at the end of the experiment. Every subject complied with the procedure. Figure 1.3: Screenshot of one trial in treatment C Working memory and Raven’s IQ tests. After the GARP task, subjects performed a spatial working memory test and an IQ test. To measure working memory, we used the computerized Spatial Working Memory test (WM) developed by Lewandowsky et al. (2010). This test measures the capacity of individuals to store and retrieve information in short term memory. It runs as follows. The individual observes a 10⇥ 10 grid. A trial consists of a sequence of 2 to 6 dots that appear in di↵ erent cells of the grid for 0.9 seconds with 0.1 seconds between dots. After the final dot in a sequence disappears the 17 subject attempts tap the cells where the dots appeared in any order. Score decreases with the distance between the correct and the selected cells. The entire test consists of 32 such trials, including 2 practice trials. No feedback is given between trials or upon completion of the test. For IQ, we used the short version of Raven’s IQ test, namely Set I of Raven’s Advanced Progressive Matrices (APM) as developed by Raven, J., Raven, J.C., and Court (1998). This set consists of 12 non-verbal multiple choice questions that become progressively more di cult. For each question, there is a pattern with a missing element. From the eight choices below the pattern, the subject is to identify the piece that will complete the pattern. As Set I is typically used as a screening tool for Set II of the APM, the test provides a rough measure of IQ. Instructions for the test were read directly from the script provided with the test. The test was administered in the intended format (paper) and was not timed. Subjects were made familiar with the format of the test and method of thought required through two practice problems preceding the test. During this time, they were allowed to ask questions from the experimenters. The test started only after all subjects had a rmed their understanding of the instructions. Questionnaire. Following completion of the tests, subjects were asked to complete a questionnaire, adapted from one used by the Emotion and Cognition Lab at USC. It includes questions about their highest diploma, occupation, income, ethnicity, various stress rankings and health levels, as well as information relative to current medications. Summary. From a design viewpoint, there are two new elements relative to the existing experimental tests of revealed preferences. First, we study choice across ages and choices across task complexity but, most importantly, we study the interaction between the two. Second, we correlate choices with measures of memory and fluid intelligence, to better understand the source of di↵ erences in consistency over the life cycle. From a methodological viewpoint, there are also two novelties. First, we add 18 trivial tasks. This allows us to di↵ erentiate between subjects who violate consistency because they violate one of the premises of the model (such as inattention, satiation, disliking or miscomprehension) from those who violate consistency even though they are likely to satisfy all those premises. Second, each trial has only two possible choices. This is obviously less rich than the traditional setting, where a large number (or even a continuum) of options are presented. However, it allows us to focus on a simpler choice problem with an easy graphical depiction so that we can conduct a large number of trials in a relatively short period of time. 15 A sample copy of the instructions can be found in the Appendix. 1.4 Analysis 1.4.1 Frequency of violations Our first and central objective is to assess choice consistency across populations (YA vs. OA) and treatments (simple vs. complex). Comparisons across treatments are only possible for direct violations since the metric is radically di↵ erent between direct and indirect violations. To give an idea, for each set of 35 trials there are 35⇥ 34 2 = 595 pairs of trials, of which 170 can potentially result in direct violations. Therefore, there is a total of 170 possible D S -violations and 510 possible D C -violations. By contrast, of the 35 3 = 42,875 triplets of trials in treatment C, only 188 can result in an I C -violation. This means that at most 28.6% of choices can result in direct violations between pair of trials but only 0.4% can result in indirect violations between triplets of trials. 16 A more 15 Our design contrasts with some recent experimental literature in other domains (risk, time) where it is shown that convexifying the budget set helps obtaining accurate estimates Andreoni and Sprenger (2016,2012),Choietal.(2007). alsoperformmanytrialsthankstotheiringenioussoftwarepresentation. As explained in their paper, it is important to make sure that consistency is not accidental. This is ensured with a large number of decisions so that the test of Bronars (1987) is su ciently powerful. 16 Recall the second remark in section 1.2.1, stating that choices which induce some violations may preclude some others. As such, 170 and 188 are upper-limits on the number of e↵ ectively feasible direct violations of pairs (DS, DC) and indirect violations of triplets (IC), respectively. 19 informative measure to assess the extent of violations across treatments is to compare them with the number of violations incurred by a simulated subject choosing randomly between bundles. Figure 1.4 presents the cumulative distribution function (c.d.f.) of thenumberofrealizedD S -violationsineachpopulation(OA,YA)fortreatmentS(left) and the total number of realized D C - and I C -violations in each population (OA, YA) for treatment C (right). It also presents the c.d.f. of violations when the decisions in each set of 35 trials are simulated 100,000 times using a random choice rule. Figure 1.4: Number of violations in treatments S (left) and C (right) In treatmentS, a significant fraction of subjects have no violations (66% of YA and 42% of OA). This fraction shrinks substantially in treatmentC (34% of YA and 11% of OA). To quantify the extent of violations, we can use the random choice distribution. According to our simulation, there is a 10% chance that a subject choosing randomly willincurlessthan23violationsintreatmentSandlessthan105intreatmentC.Using these numbers as a benchmark, we get instead that 88% of our YA and 84% of our OA incur less than 23 violations in treatment S and 94% of our YA and 80% of our OA incur less than 105 violations in treatment C. Therefore, in line with previous studies (Battalio, R. C., Kagel, J. H., Winkler, R. C., Fisher, E. B., Basmann, R. L., Krasner 20 (1973), Cox (1997), Harbaugh et al. (2001), Sippel (1997)), the majority of our subjects incur relatively few violations. Perhaps more interestingly, we can compare violations across age groups. YA in our sample incur fewer violations than OA in our sample and di↵ erences are more pronounced in treatment C than in treatment S. More precisely, non-parametric Kolmogorov-Smirnov (KS) and Wilcoxon Rank Sum (WRS) tests of comparisons of c.d.f. establish marginal di↵ erences of distributions in treatment S (p-value = .110 and .043, respectively)andstrongdi↵ erencesofdistributionsintreatmentC(p-value=.001 and < .001, respectively). 17 As can be seen from the graph, the di↵ erence in treatment S is mostly driven by the higher fraction of subjects with 0 violations in the YA popu- lation. Figure 1.4 also highlights the usefulness of the random choice benchmark: even if in both treatments the empirical distributions of violations by YA and OA are signif- icantly smaller than if they were generated by a random choice process, the di↵ erence between empirical (YA or OA) and random distributions is more pronounced inS than in C for both populations. This is consistent with the hypothesis that treatment C is more di cult to comprehend and therefore likely to generate relatively more mistakes than treatmentS. In this respect, it is particularly interesting to notice the behavior in the tail of the distribution: the 16% of OA who commit the most mistakes in treatment C perform worse than the 16% of subjects who would commit the most mistakes if they all behaved randomly. As we will see later on, these are subjects who are likely to violate some assumption of the model. Overall, we find that treatment C is more di cult than treatment S and generates relatively more mistakes in both populations. Also, the results in this section are consistent with a strong age e↵ ect on the number of violations in the complex task and a weak or no age e↵ ect in the simple task. 17 As it is well-known, KS is sensitive to any di↵ erence in distributions (shape, spread, median, etc.) whereas WRS is mostly sensitive to changes in the median. In an attempt to remain agnostic about which test is more appropriate for our sample, we will report results for both tests in all of our comparisons of distributions. 21 Itisalsointerestingtodistinguishbetweendirectandindirectviolationsintreatment C, especially since D C -violations are of similar (though not identical) nature to the D S - violations presented in the left graph of Figure 1.4. Figure 1.5 separates violations in treatment C into direct (D C ) and indirect (I C ) for each population. As before, it also presents the results of a random choice rule. Figure 1.5: Direct (left) and Indirect (right) violations in treatment C AccordingtoKSandWRStests,di↵ erencesinthedistributionsbetweenYAandOA in treatment C are substantially more pronounced for direct violations (p-value < .001 forboth)thanforindirectviolations(p-value=.187and.022). Thedi↵ erenceismainly driven by the fact that a relatively high fraction of subjects in both populations (84% of YA and 64% of OA) do not incur any indirect violation. It also suggests that treatment C is cognitively more demanding even when we look only at direct violations. Hence, it is the di culty of having to compute and keep track of the value of a third good which makesthecomparisonoftwo-goodbundlesmorechallengingandnotsomuchtheadded possibility of a di↵ erent type of intransitivity through indirect violations. 22 1.4.2 Severity of violations So far, we have focused on the number of violations. However, not all violations are equally important. Indeed, as emphasized by Afriat (1967) e ciency index and further developed by Varian (1990) and more recently by Dean and Martin (2014), Echenique et al. (2011) among others, one should also take into account the severity of violations. Populations may di↵ er in frequency of violations but not in severity and vice-versa. There are several ways to study severity. One possibility is to consider an intuitive severity index which runs as follows. 18 Recall from Definitions 1, 2, and 3 that the condition for a GARP violation to occur between a pair (direct) or a triplet (indirect) of trials is that for both trials, the chosen bundle must have less quantity of both goods than the bundle not chosen in the other trial. This is independent of how much smaller these quantities are. However, it seems intuitive that if the di↵ erences in quantities between those bundles are small, the violation is less severe than if the di↵ erences are large. For example (and, as usual, assuming monotonic preferences) if my choices reveal apreferencefor(1,1)over(2,2),theviolationislessacutethaniftheyrevealapreference for(1,1)over(5,5). Thisisconsistentwiththetheorybehindstochasticchoices,whereby rational individuals are more likely to incur smaller mistakes than bigger ones. To formalize this idea of severity, we take each pair (triplet) of trials involved in a direct (indirect) violation, and measure the euclidean distance between the amounts in the chosen bundles and the amounts in the bundles that have weakly more quantity of both goods and were not chosen. We then take the minimum of these distances, which we call d. This value captures the minimum amount we should change one of the choices of the individual in order to remove the violation. It can also be interpreted 18 Contrary to the previously mentioned papers, our goal here is not to develop a new measure of severity in violations but, instead, to use a simple way to quantify their extent. 23 as the magnitude of the “mistake” incurred by not choosing the bundles with more quantities of both goods. To illustrate the concept, consider the case of a D S -violation described in Figure 1.1. If the individual commits a violation (that is, selects a 12 and b 12 ), the severity is given by d⌘ min d(a 12 ,b 0 12 ),d(b 12 ,a 0 12 ) .Intuitively,if a 12 is very close to b 0 12 ,it means that the error is small and reversing two very similar choices would remove the violation. For the case of D C and I C -violations in treatment C, the severity is given by d ⌘ min d(a xy ,b 0 xy ),d(b xz ,a 0 xz ) and by d ⌘ min d(a xy ,c 0 xy ),d(b xz ,a 0 xz ),d(c yz ,b 0 yz ) respectively. Notice that the euclidean distance is always taken between two bundles containing positive quantities of the same two goods. Includingallsubjectsintheanalysiswouldexacerbatedi↵ erencesinseveritybetween OA and YA since we know from section 1.4.1 that the fraction of perfectly consistent subjects (for whom d = 0) is larger in the younger population. To avoid this fictitious e↵ ect, we include in the analysis only subjects with a positive number of violations and count the average severity of the choices that are inconsistent for that subject (not of all choices). Figure 1.6 presents the c.d.f of this severity index by population and treatment. Figure 1.6: Severity of violations in treatments S (left) and C (right) 24 Given the bundles proposed in the experiment, the range of d is relatively small: between1.0and3.0intreatmentSandbetween1.0and2.0intreatmentC.Ifanything, this will bias the results against finding di↵ erences across treatments. With this in mind, we can see from the graph that some subjects commit only the minimal possible violations (d=1.0) whereas others incur more severe ones (d=1.5 on average). In treatmentS the distribution of severity of violations is not significantly di↵ erent across populations (p-value = .881 and .858 for KS and WRS tests). By contrast, in treatment C violations are significantly more severe for OA than for YA (p-value = .049 and .012 for KS and WRS tests). 19 An alternative measure of severity of violations consists of finding, for each indi- vidual, the minimum number of trials that need to be removed in order to suppress all violations for that individual. Subjects with more violations are likely to necessitate the elimination of more trials to achieve consistency. At the same time, if a subject makes one outlier choice, he may exhibit many inconsistencies that are “cleaned up” when that single trial is removed. 20 As before, we exclude the individuals with no violations to avoid artificially exacerbating di↵ erences between OA and YA. This means that the minimum number of trials to be removed is 1. Figure 1.7 presents the c.d.f. of the number of choices to be removed for perfect consistency by population and treatment. This severity measure yields similar results to the previous one. Indeed, the distri- bution of the number of choices that need to be removed to achieve consistency is not statistically di↵ erent for both populations in treatment S (p-value = .807 and .440 for 19 We performed the exact same analysis with the average amount (instead of the minimum amount) choices of an individual should be changed in order to remove the violation. So, for example, in Figure 1.1 that would be d 0 ⌘ d(a12,b 0 12 )+d(b12,a 0 12 ) /2. The results were very similar and the treatment e↵ ect sharper than before: still no significant di↵ erence between OA and YA in treatment S (p-value = .727 and .820 for KS and WRS tests) and significantly more severe violations for OA than YA in treatmentC (p-value = .023 and .004 for KS and WRS tests). The graphs are omitted for brevity. 20 This is similar to the Houtman-Maks index (Houtman, Martijn and Maks (1985)), a measure of severity often cited in the literature (e.g., in Choi et al. (2007) and Burghart et al. (2013), and which is defined as the largest subset of all observed choices that does not include any cycles. 25 Figure 1.7: Choices to remove for consistency in treatments S (left) and C (right) KS and WRS tests) but it is highly significant in treatmentC (p-value = .016 and .002 for KS and WRS tests). For example, in order to achieve consistency for two-thirds of the YA in treatment C, we only need to remove 3 trials whereas to achieve consistency for the same fraction of OA we need to remove 14 trials. Taken together, the results in this section lend further support to our previous finding: OA in our experiment are marginally more inconsistent than YA in the simple treatment but substantially more inconsistent than YA in the complex treatment, both in terms of the number and severity of violations. 1.4.3 Trivial trials We next analyze the behavior in treatment A to see if the premises of our analysis – that subjects are attentive, understand the task, like each good and always prefer more to less – are satisfied. Figure 1.8 presents the number of violations incurred by YA and OA in the 10 trivial trials. The results are highly surprising; we expected some mistakes but not quite as many asarerealized. Inbothpopulationsthereisasignificantfractionofsubjectswhoviolate at least one trivial trial (28% of YA and 62% of OA). There are even 3 subjects who 26 Figure 1.8: Number of violations in treatment A (trivial trials) violate all 10 trivial trials. Violations are much stronger in OA than in YA: both KS and WRS tests reject that samples are drawn from the same cumulative distribution functions (p-value = .002 and .001, respectively). This is a severe problem and suggests that at least some of our subjects do not satisfy the assumptions of the model. Subjects who fail 9 or 10 trivial trials are very likely expressing a preference for less rather than more food, even though our protocol imposed the strongest possible emphasis into hav- ing hungry subjects, desirable goods, and small portions. 21 For subjects who fail 4 or 5 trivial trials, it is more di cult to disentangle between inattentiveness, miscomprehen- sion, and interior optimal quantity. Either way, it calls into question the reliability and interpretability of the results on choice consistency. More generally, our results raise a red flag on choice consistency experiments and strongly suggest the importance of including trivial trials in studies of consistency to test whether the assumptions of the model are satisfied by the experimental subjects. 21 One subject with 101 violations inS and 536 violations inC explicitly stated during the debriefing that she tried to minimize the quantity to consume. 27 A natural step is to conduct the same study as in section 1.4.1 but only with the subset of the populations that we think satisfy the assumptions of our model. This sub- stantially reduces the sample size, and asymmetrically so for YA and OA. Furthermore, it creates its own selection problem since it is based on a variable (choices where less is preferred to more) which is linked to the dependent variable of the study. However, we still think it is a useful exercise and more satisfactory than ignoring the problem altogether. Below, we present the results when we restrict our attention to subjects who fail at most two trivial trials. We choose that number in order to exclude the subjects who unquestionably violate the premises of the model but, at the same time, to permit some mistakes and keep a reasonable sample size (44 YA and 30 OA). The choice of allowing two errors is admittedly ad-hoc. Figure 1.9 is the analogue Figure 1.4 for those individuals. Figure 1.9: Choice violations by subjects with at most two treatment A violations Asexpected, violationsarereducedwhenweconsideronlythesubjectswithatmost two errors in the trivial trials, most notably in treatment C. This suggests that a non- negligible fraction of violations may be attributed to factors outside the objective of the study. On the other hand, the basic results of the previous analysis remain unaltered. 28 As before, there are more violations by OA than by YA and the di↵ erence is more significant in the complex treatment than in the simple treatment. Formally, KS and WRS tests show marginal di↵ erences in distributions in treatment S (p-value = .072 and .016, respectively) and highly significant di↵ erences in treatmentC (p-value = .004 and .001, respectively). 22 1.5 Understanding violations An obvious reason why an individual might commit violations is that her preferences do notsatisfythemainGARPassumptions. GiventhebehaviorofsubjectsintreatmentA, there might be a non-negligible fraction of those individuals. Since the interpretation of theresultsisradicallydi↵ erentforthosesubjects,weinvestigatebelowthedeterminants of consistency using the entire population and also using the subsample of subjects for whom we are most confident that the model is appropriate (those who fail at most two trivial trials). A main hypothesis of our experiment is that OA will commit more violations than YA due in part to the cognitive di culty to store information regarding the attributes of the goods. Working memory is the ability for storing information for immediate processing (Baddeley (1992), Baddeley and Hitch (1974)). Subjects with low working memory and high working memory perform similarly in simple discrimination or detec- tion tasks, but in complex tasks, working memory predicts task performance (Cerella, John; Poon, Leonard W.; Williams (1980), Gick, Mary L; Morris, Robin G; Craik 22 Due to the ad-hoc nature of allowing two errors in treatment A, we also performed the same analysis with the most conservative possible measure, which is to include only subjects with no errors in trivial trials. Violations decrease substantially and the sample size is dramatically reduced to 17 OA and 36 YA so the statistical power is limited. However, the treatment e↵ ect is similar to that of the entire population: KS and WRS tests show no significant di↵ erences in distributions in treatment S (p-value = .534 and .305, respectively) and show significant di↵ erences in treatmentC (p-value = .060 and .022, respectively). Again, the graphs are omitted for brevity. 29 (1988)). If non-consistent choices are a result of the subject’s inability to simultane- ously maintain a representation of many values, then GARP violations are expected to be more pronounced in treatment C – where more item values must be held in-mind – than in treatment S. To investigate this hypothesis, we study scores in the spatial working memory test performed in the experiment. Performance in the working memory test is higher for YA (mean = 203, st. error = 3) than for OA (mean = 152, st. error = 1.73) and the di↵ erence is highly significant (p-value < .001). 23 This is consistent with many previous findings (see e.g., Salthouse and Babcock, 1991; Park et al., 2002). A regression between working memory scores andagroupdummyshowsthatthetwoarehighlycorrelatedbothwhenweconsiderthe full sample (p-value < .001, Adj. R 2 = 0.71) and when we restrict attention to subjects with at most two violations in treatment A (p-value < .001, Adj. R 2 = 0.69). Anothercandidatetoexplaindi↵ erencesinconsistencyacrossagegroupsisIQ.Gen- eralintelligencehastwomaincomponents: fluidintelligence, whichisourreasoningand problem solving ability, and crystallized intelligence, our ability to use skills, knowledge and experience. Intuitively, when a subject is asked to choose between two bundles, her objective is to accurately represent her true preferences and act accordingly. This task requires a certain level of reasoning about true values, which may rely on fluid intelligence. To test this hypothesis, we analyze Raven’s IQ answers that we collected from our subjects. Performance in Raven’s IQ test is again higher for YA than for OA both for the full sample (11.44 vs. 8.16) and for subjects with at most two violations in treatment A (11.39 vs. 8.77) and the di↵ erences are highly significant (p-value < .001 for both). This is not surprising. Indeed, the consensus is that fluid intelligence declines with age after early adulthood, while crystallized intelligence remains intact (Horn and Cattell, 23 Due to software malfunction, 2 OA did not complete the working memory test and are excluded from all following analyses which include the measure. 30 1967; Kaufman and Horn, 1996). Given that Raven’s test measures fluid intelligence, OA are expected to perform worse. Havingestablishedthatworkingmemory(WM)andfluidintelligence(IQ)arelower for older subjects, we now study the correlation between these two measures and the number of violations in treatment S (Viol-S) as well as the total number of direct and indirect violations in treatmentC (Viol-C). 24 The results are presented in Table 1.2 for the entire sample (left) and the subsample of subjects who fail at most two trivial trials (right). All subjects Viol-S Viol-C WM Viol-C 0.56 ⇤⇤⇤ WM -0.10 -0.23 ⇤ IQ -0.01 -0.22 ⇤ 0.68 ⇤⇤⇤ ⇤ , ⇤⇤ , ⇤⇤⇤ :significantat5%,1%,0.1%level Subjects with 2 or less violations in A Viol-S Viol-C WM Viol-C 0.12 WM -0.06 -0.26 ⇤ IQ -0.06 -0.29 ⇤ 0.65 ⇤⇤⇤ ⇤ , ⇤⇤ , ⇤⇤⇤ :significantat5%,1%,0.1%level Table 1.2: Pearson correlations of memory, intelligence and GARP violations. Exceptforthecorrelationbetweenviolationsinbothtreatments,theresultsarevery similar when we consider the entire sample or only the subjects who fail at most two trivial trials. We find no relationship between the number of violations in treatment S and performance in the working memory or IQ tests. By contrast, violations in treatment C are negatively correlated with both working memory and IQ scores. 24 We also conducted the analysis for direct and indirect violations separately and found qualitatively similar results. It is also worth noting that DC and IC are strongly correlated (Pearson correlation = 0.84). 31 The findings related to working memory are consistent with the hypothesis that subjects use a decision-making process that requires them to encode the value of items. They are not consistent with interpretations that subjects are attending to only the count of items or attending to only a single element of the options. The findings related to IQ suggest that fluid intelligence is heavily involved in choice processing only for the most complex tasks. It should be noted however that working memory and fluid intelligence are very strongly correlated. This is in line with previous studies (see e.g., Engleetal.(1999))andreflectsthefactthatbothworkingmemoryandfluidintelligence can be traced to the same brain systems (Geary (2005), Gray et al. (2003), Jaeggi et al. (2008), Kane and Engle (2002), Olesen et al. (2003), Prabhakaran et al. (1997)). Given the heterogeneity of age in our OA population (59 to 89 years old), a within- sampleanalysiscanlendsupportfortheagee↵ ectsobservedacrosssamples. Thematrix of correlations for the OA population is presented in Table 1.3. Older adults Viol-S Viol-C WM IQ Viol-C 0.50 ⇤⇤⇤ WM -0.17 -0.16 IQ 0.01 -0.18 0.31 ⇤ Age 0.07 0.00 -0.26 -0.09 ⇤ , ⇤⇤ , ⇤⇤⇤ :significantat5%,1%,0.1%level Table 1.3: Pearson correlations for the OA population The correlation between violations in treatment C and scores in working memory and IQ tests keep the same sign but lose significance when we consider only the OA population, in part due to the lower number of observations. Working memory scores and age are negatively correlated but the statistical significance of the e↵ ect is also low (p-value = 0.086), possibly for the same reasons. Finally, it is interesting to notice that age and violations in treatmentC are not correlated, which suggests that the age e↵ ect 32 on violations is channeled mostly through the deterioration in the ability to encode items (working memory) and solve problems (fluid intelligence). To further investigate the relationship between violations in the complex treatment and performance in working memory and IQ tests, we conduct a set of ordinary least squares (OLS) regressions where the dependent variable is the number of violations in C.Explanatoryvariablesincludethevariablespresentedabove(violationsinS,working memory scores, IQ scores) as well as a Younger Adult dummy (YA-d) and household income (Income). The results are presented in Table 1.4. 12 3 4 5 6 7 8 9 10 Const. 142 ⇤ 118 ⇤⇤ 50.5 ⇤⇤ 38.5 44.9 204 ⇤⇤ 148 ⇤⇤ 79.1 ⇤⇤⇤ 85.6 ⇤ 197 (57) (37) (14) (29) (123) (68) (44) (16) (35) (155) Viol-S 2.45 ⇤⇤⇤ 2.48 ⇤⇤⇤ 2.46 ⇤⇤⇤ 2.60 ⇤⇤⇤ 2.74 ⇤⇤⇤ (0.37) (0.37) (0.37) (0.43) (0.42) WM -0.66 ⇤ 0.43 -0.85 ⇤ -0.44 (0.31) (0.82) (0.38) (1.0) IQ -9.33 ⇤⇤ -9.72 -9.60 ⇤ -6.21 (3.5) (5.9) (4.3) (7.6) YA-d -46.2 ⇤ -43.3 -50.2 ⇤ -2.15 (18) (49) (22) (62) Income -3.05 5.91 -7.39 0.05 (7.5) (8.2) (9.2) (11) Adj. R 2 0.35 0.35 0.35 0.34 0.39 0.04 0.04 0.04 -0.01 -0.01 obs. 93 95 95 72 70 93 95 95 72 70 (standard errors in parentheses); ⇤ , ⇤⇤ , ⇤⇤⇤ =significantat5%,1%and0.1%level Table1.4: OrdinaryLeastSquares(OLS)regressionofnumberofviolationsintreatment C (all subjects) AftercontrollingforviolationsinS,workingmemory, IQ,andagegrouphavesignif- icant explanatory power to understand consistency in C (regressions 1-3), but income does not (regression 4). 25 The similarities in significance of the regressions are not 25 We should notice however a further selection problem since not all individuals reported the income of their household. Comparisons are also di cult since for most YA income refers to that of their parents whereas for OA it is theirs and their spouses. 33 surprising since we know from the previous analysis that WM and IQ are highly cor- related and age is a strong predictor of performance in those tests. 26 When violations in treatment C are regressed on all of the variables (regression 5), the coe cients on working memory scores, IQ scores, and the YA dummy lose significance as these are highly correlated xxxIB is this a good thing? referee 1 point 9 suggests so, but I am not surewhyxxxIBFinally, theresultsareverysimilarwhenthevariableViol-S isexcluded (regressions 6-10). However, the adjusted R 2 values are drastically lower, indicating a worse fit. For robustness, we then perform the same regressions with the subset of subjects who failed at most two trials in treatment A. The results are presented in Table 1.5. While violations in treatment S are no longer a significant predictor for violations in treatment C, working memory scores, IQ scores, and age group are still highly signifi- cant in their explanatory power (regressions 1-3) and income is still not (regression 4). Similar qualitative conclusions are obtained when we exclude violations in treatment S (regressions 6-10). Overall,theresultsareconsistentwithacognitivedeclinetheoryofbehavioraldi↵ er- ences between YA and OA. Our findings are suggestive of the following process: GARP consistency is mediated by the brain structures involved in working memory and fluid intelligence, both of which are a↵ ected by aging. When the environment is simple, the cognitive demands are limited so subjects with a low working memory and fluid intelli- gence (typically, but not exclusively, OA) can still perform the necessary reasoning. By contrast, when the environment is more complex, the capacity of a subject to store and retrieveinformationaswellastoperformlogicalreasoningisreflectedintheconsistency of her choices. 26 A principal component analysis on WM and IQ suggests that working memory data contains the largest fraction of the relevant information: the first component is mostly driven by working memory score and explains 70% of the data. 34 12 3 4 5 6 7 8 9 10 Const 56.6 ⇤⇤ 48.3 ⇤⇤⇤ 23.7 ⇤⇤⇤ 13.1 25.7 58.5 ⇤⇤ 49.9 ⇤⇤⇤ 24.7 ⇤⇤⇤ 15.5 33.2 (19) (14) (4.5) (9.5) (41) (19) (14) (4.3) (9.0) (40) Viol-S 0.18 0.17 0.17 0.20 0.26 (0.2) (0.2) (0.2) (0.3) (0.2) WM -0.23 ⇤ 0.12 -0.24 ⇤ 0.09 (0.1) (0.3) (0.1) (0.3) IQ -3.37 ⇤ -3.85 -3.45 ⇤ -3.83 (1.4) (1.9) (1.4) (1.9) YA-d -17.1 ⇤⇤ -21.4 -17.4 ⇤⇤ -19.4 (5.6) (14) (5.6) (14) Income 0.10 4.49 -0.32 3.87 (2.4) (2.4) (2.3) (2.3) Adj. R 2 0.05 0.07 0.10 -0.03 0.17 0.06 0.07 0.11 -0.02 0.17 obs. 74 74 74 53 53 74 74 74 53 53 (standard errors in parentheses); ⇤ , ⇤⇤ , ⇤⇤⇤ = significant at 5%, 1% and 0.1% level Table 1.5: OLS Regression of number of violations in treatment C (subjects with 2 or less violations in treatment A) Next,weexaminetheresponsesobtainedinourquestionnaire. WefindthatOAself- report a lower stress level compared to YA (p-value < .001) and that reported stress correlates with working memory scores (Pearson correlation = .29, p-value = .006). Interestingly, self-reported health rankings are similar across groups and uncorrelated to any relevant element of our analysis. Last, we check for di↵ erences across ethnic groups. We first note that our OA population is mostly composed of White and African American subjects while our YA population is composed of White and Asian subjects. Working memory scores, IQ scores, and violation counts across White OA and African American OA are not statistically di↵ erent. The same applies for the comparison be- tween White YA and Asian YA. Finally,thereareinevitablysomeunobservablefactorsthatmayhavedi↵ erente↵ ects on subjects of di↵ erent ages. One such factor is fatigue. The case could be made 35 that fatigue a↵ ects OA more severely than it a↵ ects YA, leading to disparate levels of consistency. Thereisastreamofpsychologicalresearchthatisrelevanttothequestionof whetherolderadultsaremoresusceptibletofatigue. Thisresearchisonthephenomenon of “ego-depletion” – the impairment of decision-making immediately following a task requiringthoughtfulnessorselfcontrol. Ifasubjectishighlysusceptibletoego-depletion then the quality of their decisions worsens as an experiment progresses. Research shows that older adults are less susceptible to ego-depletion than are younger adults (Dahm et al., 2011), so the main e↵ ect of ego-depletion in our experiment should oppose our findings. 27 Other possible factors include di↵ erences in the opportunity cost of time, sensitivity to hunger, cognitive skills or experience in individual decision making. Unfortunately, it is not feasible to rule out all these factors, given our design. While we agree that they raise caution as to the interpretation of our findings, we do not feel that any of them has a clear and unambiguous di↵ erential e↵ ect on our populations. 28 Perhaps more importantly, if either age group were to be more susceptible to any of these factors, it would be reasonable to believe that their performance would be a↵ ected in treatments S and C alike. 1.6 Conclusion In this paper we have studied choice consistency of younger and older adults in simple andcomplexdomains. Wehavehighlightedseveraldi↵ erencesinbehavioracrossourtwo 27 When violations per trial are regressed on their order of appearance, a Younger Adult dummy, and the interaction of these variables, order is a significant predictor of violations but the interaction of order and age dummy is not. This suggests that fatigue may a↵ ect consistency but not di↵ erently across age groups. 28 Forexample,OAarelikelytohavealoweropportunitycostoftime,butthismayverywellincrease consistency by inducing them to take more time, e↵ ort and care in their decision making. Cognitive skills help consistency but this is a↵ ected by education and our OA are at least as educated as our YA. Finally, YA in our sample are possibly more experienced with experimental tasks but it is unlikely that it eclipses the additional decades of decision-making experience held by the OA. 36 populations. Ourolderadultsarelessconsistentthanouryoungeradults, bothinterms of the number and severity of violations, especially when the choice task is complex. Also, we can trace the di↵ erences in consistency in the complex task to deficiencies of working memory, that is, in the ability to store and retrieve information regarding the value of the di↵ erent items in bundles. The individual analysis (see Appendix A) suggests that consistency across ages is similar in the simple task partly because the older adults in our sample have preferences consistentwithasimplerule(typically,tomaximizethequantityofthepreferreditemin the bundle) that can be easily implemented without errors. An important question for futurestudyiswhetherthesepreferencesareintrinsictosubjectsorifitisasecond-best strategy employed by individuals who are aware of their compromised working memory and fluid intelligence. Finally, the importance of working memory in ensuring choice consistency is a key result of the paper with fundamental medical and policy implications. Our experimen- tal design, characterized by two bundles presented in a screen, a left-right choice and the possibility of multiple repetitions (see Figure 1.3) is suitable to be implemented in the scanner. In future research, we plan to use fMRI techniques to study the neural correlates of choice consistency. We already know that simple choices between items involve the ventromedial prefrontal cortex (Hare et al. (2008, 2009)) that represents the value di↵ erence between options. Our objective is to study how the working memory system (which involves the dorsolateral prefrontal cortex) and the ventromedial pre- frontal cortex interact to produce consistent choices, and why this interaction di↵ ers across ages. 37 Chapter 2 Value-Based Decision-Making: A New Developmental Paradigm Adults have many abilities that children do not. Multiple paradigms exist to explain why these di↵ erences exist and change during development. Each of these paradigms describes an important aspect of development, but none of them alone can explain all of the diverse abilities that change as people grow. Here we present evidence that an important di↵ erence between children and adults cannotbeexplainedbyexistingparadigms; namely, thatadultsconsistentlyknow what they want, but young children do not. 1 2.0.1 Introduction Thisstudyinvestigatesthedevelopmentaltrajectoriesofvalue-baseddecision-makingin the Goods, Social, and Risk domains in children from Kindergarten to 5th grade. Con- sistency in choices develops gradually but di↵ erentially across domains and cannot fully be explained by the development of attentional control, logical reasoning, or integrative 1 A version of this chapter is being prepared for submission to Science. My coauthors on that article (Niree Kodaverdian, Isabelle Brocas and Juan Carrillo) made considerable contributions to the text in this chapter. 38 thinking. In both the Social and Risk domains, the early developmental trajectory is hidden by the centration e↵ ect, or the tendency to use heuristics. We measure the consistency of preferences by testing for transitive choices; if a subject chooses option A over option B, option B over option C, and A over C, then her choices are transitive and that implies that her preferences are consistent. A handful of studies have shown that children are less consistent than adults when choosing foods or toys(Bruyneeletal.(2012),Harbaughetal.(2001),ListandMillimet(2008),Smedslund (1960)), while age is less of a predictor of consistency in the Social (Harbaugh and Krause (2000)) and Risk (Harbaugh et al. (2002)) contexts. We explore the pattern of children’s inconsistencies as a function of their preferences. In the Goods domain, children become more consistent as they learn to know what they like most and least. In the Social domain, children learn what they like most but not what they like least, while in the Risk domain, they learn what they like least and not what they like most. These results taken together suggest that self knowledge of preferences is what solidifies during our window of observation and it does so asymmetrically in the Social and Risk domains. It is intuitive however that di↵ erences in transitivity across ages and domains may reflectotherknownaspectsofdevelopment. Eventhoughchildrenknowthattheyprefer A to B, B to C, and A to C, their choices may not conform to this ranking. This could occurbecauseattentionalcontrol,whichhaspreviouslybeenassociatedwithintransitive behavior in adults for complex choices (Brocas et al. (2016)) is still underdeveloped in children (Astle and Scerif (2008), Davidson et al. (2006)). Alternatively, it may be because the ability to reason transitively is not yet in place (Bouwmeester and Sijtsma (2006), Bryant and Trabasso (1971), Piaget (1942, 1948), Rabinowitz et al. (1994)) which may be necessary to support transitive decision-making. Last, it may result from children’s inability to focus on more than one attribute of an item at a time, a 39 phenomenon referred to as centration (Crain (2015), Donaldson (1982), Piaget et al. (1967)). 2.0.2 Specific scope The objective of this research is to assess the common and domain-specific developmen- tal trajectories of transitive decision-making in the Goods, Social, and Risk domains and to determine if the dominant developmental paradigms (attentional control, logical reasoning, and centration) are enough to explain age- and domain-related di↵ erences in transitive decision-making. Our study is most closely related to the literature on choice consistency. Earlier studies however have relied on the Generalized Axiom of Revealed Preferences (GARP), an indirect test of transitivity which focuses on choices between bundles of options given a budget constraint, a system of prices, and non satiation as- sumptions (Samuelson (1938), Varian (1982)). By contrast, our design abstracts from assumptions on preferences and delivers results directly comparable across domains. We recruited 134 children from Kindergarten to 5th grade and 51 Undergraduate students to participate in three Choice tasks and three Ranking tasks (Figure 2.1). In each Ranking task, we asked participants to provide explicit rankings of seven items. In each Choice task, we asked them to choose between all 21 pairwise combinations of those items. The Goods-Choice and Goods-Ranking tasks involved goods, the Social- Choice and Social-Ranking tasks involved sharing rules between self and other, and the Risk-Choice and Risk-Ranking tasks involved lotteries. We determined whether the pairwise choices in the Choice tasks were transitive and how intransitive choices were distributed over rankings elicited in the Ranking tasks. We included catch trials to assess attentional control, and a reasoning task to measure transitive reasoning. To as- sess centration, we determined whether actual choices were consistent with attending to 40 A) Choice Task B) Ranking Task C) Goods D) Social E) Risk Opt. 1 Opt. 2 Figure2.1: Decision-makingtasks. (A)IneachtrialoftheChoicetasks,participants were shown one option on the left (Opt.1) and one option on the right (Opt. 2). They touched one of three buttons displayed at the top of their screen to select an option or to express indi↵ erence (middle button). (B) In Ranking tasks, participants ranked options from most preferred (green face) to least preferred (yellow face). Both types of tasks were conducted in the (C) Goods domain involving objects, in the (D) Social domain involving sharing rules for self (hand pointing out) and other (hand pointing right), and in the (E) Risk domain involving lotteries consisting of quantities (number of tokens) and probabilities (green share of the pie). single attributes. For analysis, we grouped children into the age groupsK-1st (Kinder- garten and 1st grade), 2nd-3rd (2nd and 3rd grades), 4th-5th (4th and 5th grades), and U (Undergraduates). The U age group was a control for adult level value-based decision-making. 2.0.3 Findings Transitive decision-making is domain-dependent (Figure 2.2). Violations of transitive reasoning decreased with age in both the Goods and Social domains, while no two age 41 groups di↵ ered significantly in the Risk domain. Within-age group di↵ erences existed as well: young children were significantly more consistent in the Social than in the Goods domain and U were less consistent in the Risk than in the other two domains. Theseresultsindicatefundamentaldi↵ erencesintheabilitytochooseconsistentlyacross domains. However, participants in theU age group were not making significantly more transitive choices compared to participants in the 4th-5th age group in any domain, initially suggesting that the development of transitivedecision-making stopsaround 4th grade in all domains. K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group Transitivity Violations per Subject Goods Social Risk Choice-Task Figure 2.2: Performance improves with age in the Goods- and Social-Choice tasks but not in the Risk-Choice task. Y-axis reports the average number of transitivity violations in the Choice tasks for each age group (x-axis) broken down by domain (Goods, Social, and Risk). The shadings are the 95% confidence intervals. 42 Transitivity in the Goods domain improves gradually with age. Althoughconsistency in the Goods-Choice task improved with age, that improvement was not uniform across all choices. In particular, trials featuring options ranked very di↵ erently in the Goods- Rankingtaskwereunlikelytobeinvolvedinatransitivityviolation. Bycontrast, choice trials featuring options ranked similarly were significantly more likely to be involved in transitivity violations (Figure 2.3). This general pattern was independent of age and suggested that closer choices were overall more di cult to make in a consistent way. We observed convergence to a state where participants almost never committed transitivityviolationswhenchoicesinvolvedtheirbestortheirworstoptions,suggesting that children “learn to know what they like most and least” gradually with age. 0.7 0.6 0.5 0.8 0.4 0.5 0.3 0.2 0.1 0.2 0.3 0.4 0.0 0.0 0.1 0.2 0.3 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 Rank of Higher Ranked Option Rank of Higher Ranked Option Rank of Higher Ranked Option Rank of Higher Ranked Option Rank of Lower Ranked Option Transitivity Violations in Goods-Choice-Task Plotted by Option Ranks in Goods-Ranking-Task for Each Age Group K and 1 st 2 nd and 3 rd 4 th and 5 th Undergraduate Figure2.3: Transitivityviolationsdecreasewithagedi↵ erentlyacrosschoices. Each cell represents the color-coded average number of transitive violations involving a higher ranked option (x-axis) and a lower ranked option (y-axis), as revealed by explicit rankings obtained in the Goods-Ranking task. Lighter colors reflect more violations. All age groups are more likely to make transitivity violations when options have similar ranks. There is convergence to a state where participants almost never commit tran- sitivity violations when choices involve their best (dark color in left column) or their worst (dark color in bottom row) options. The vectors in the top right corner of each heat map show the average gradient in the heatmap. Subjects become more consistent if therank of thehigher-ranked option goesup, or if therank of thelower-ranked option goes down. “Looking consistent” in the Social domain and the role of heuristics. We did not anticipatetofindthatsmallchildrenwouldbesignificantlymoreconsistentintheSocial- ChoicetaskcomparedtotheGoods-Choicetask. Onepossibleexplanationisthatgoods 43 are atomic and need to be evaluated as a whole, while social options can be decomposed into several simple attributes such as “objects for self,” “objects for other,” and “total number of objects,” that are easy to evaluate consistently. As such, a participant might focus on a single attribute at a time (centration) and use simple algorithms to choose. To test that hypothesis, we listed all such heuristics (for example, “pick the option that gives self more objects, and if both give the same, pick the option that gives other more objects”). The most popular heuristic was that of maximizing objects for self, then minimizing objects for other; the choices of 34.8% ofK-1st, 20% of2nd-3rd , 21.9% of 4th-5th and 4% of U were in-line with this heuristic. When we removed all heuristic users from our sample, the developmental signature matched that of the Goods domain (Figure 2.4, left panel). A systematic di↵ erence persisted however when we looked at how violations evolved between similarly- and di↵ erently-ranked options (Figure 2.5 (A)). We found that children learned to become consistent in choices involving their best options (“they learned to know what they liked most”) but they still committed violationsinchoicesinvolvingtheirworstoptions(“theydidnotlearntoknowwhatthey likedleast”),evenintheUagegroup. Last,anoticeabletrendwasthegradualevolution of behavior towards more integrative decision rules (such as maximizing e ciency), reflecting trade-o↵ s between the two attributes. This result suggests that as children age, they become better able to think in terms of prosociality and social e ciency confirming the results from related studies on other-regarding preferences (Fehr et al. (2008)). Limited development of consistency in the Risk domain. Given lotteries are multi- attributeoptions(ofprobabilitiesandoutcomes),wehypothesizedthatcentrationcould beplayingaroleintheRiskdomainaswell. Weagaindefinedallheuristicscharacterized bytheevaluationofoneattributeatatime,suchas“picktheoptionfeaturingthelarger number of goods, and if both have the same, choose the most likely option.” Again one 44 K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group Transitivity Violations per Subject Goods Social Risk Choice-Task Goods Social Social Choice-Task All Subjects w/o Heuristic Subjects K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group Goods Risk Risk Choice-Task All Subjects w/o Heuristic Subjects Figure 2.4: Left panel: Social vs. Goods after removing heuristic users.The developmental signature of consistency is comparable in the Goods and Social domains among children who do not use heuristics. Right panel: Risk vs. Goods after removing heuristic users. The developmental signature of consistency is di↵ erent in the Goods and Risk domains among children who do not use heuristics. All children are similarly inconsistent and improvements occur later in life. was used dominantly: 44.4% of K-1st, 34.5% of 2nd-3rd, 18.8% of 4th-5th and 7.8% of U chose the lottery o↵ ering the larger reward. When we removed all heuristic users, we found that the developmental signature did not match that of the Goods and Social domains (Figure 2.4, right panel). In particular, the number of violations was the same across all elementary school age groups and this was significantly di↵ erent from that of the U group, indicating that a potential milestone for Risk was outside our window of observation - somewhere in middle or high school. Also, children learned to become more consistent in choices involving their worst options (“they learned to know what they liked least”), but less so in choices involving their best options (“they did not learn to know what they liked most”), a trend opposite to the trend observed in the Social domain (Figure 2.5 (B)). Similar to the Social domain however, we found that 45 older participants were better able to make integrative decisions, in this case, trade-o↵ s between reward amounts and probabilities. 0.8 0.7 0.6 0.5 0.4 0.5 0.6 0.7 0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.3 0.4 0.5 0.7 0.6 0.5 0.4 0.1 0.2 0.3 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 Rank of Higher Ranked Option Rank of Higher Ranked Option Rank of Higher Ranked Option Rank of Higher Ranked Option Rank of Lower Ranked Option Rank of Lower Ranked Option 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 Transitivity Violations in Social-Choice-Task and Risk-Choice-Task Plotted by Option Ranks in the Respective Ranking-Task for Each Age-Group K and 1 st 2 nd and 3 rd 4 th and 5 th Undergraduates K and 1 st 2 nd and 3 rd 4 th and 5 th Undergraduates A) Social B) Risk Figure 2.5: Transitive violations across choices among non heuristic users: (A) In the Social domain, there is convergence to a state where participants almost never commit transitivity violations when choices involve their highest-ranked options (“they know what they want”). (B) In the Risk domain, there is convergence to a state where participants almost never commit transitivity violations when choices involve their lowest-ranked options (“they know what they do not want”). Who makes transitive choices? As noted earlier, centration took the form of heur- sistic usage and it was strongly associated with consistency. In addition, we found that among participants who did not use heuristics, intransitivity was strongly correlated across domains. Intransitivity was also strongly associated with mistakes in attention trials,indicatingthatattentionalcontrolwasplayingarole. Moreover,participantswho were better able to choose in the Choice tasks according to their explicit rankings in the Ranking tasks were also significantly more transitive. This e↵ ect is not reminiscent of any known paradigm. Last, performance in the transitive reasoning task was not a significant predictor when we controlled for age, centration, attentiveness, and the ability to act according to one’s own explicit preferences. 46 2.0.4 Interpretations Decision-making in the Goods domain: the developmental template. Foreachagegroup, the behavior observed in the Goods domain was consistent with the hypothesis that participants make choices by estimating and comparing noisy values. Under that hy- pothesis, decisions involving options close in value are confusing and prone to error, while decisions involving options valued di↵ erently are easy to make. The developmen- tal trajectory we observed suggests that the evaluation process becomes less and less noisy over time, reducing the number of confusing decisions, and hence the number of violations, especially among options ranked very di↵ erently (Figure 2.3). This pat- tern of improvement agrees with previous research on the development of consistent decision-making (Harbaugh et al. (2001)), yet it implies a more fundamental cause: that the ability to make the simplest decisions is what solidifies in this developmental window. Over time, children learn to know what they like most and least with more accuracy. In addition, the fact that inconsistency was not associated with the ability to reason transitively suggests that value-based reasoning requires the involvement of di↵ erent brain regions compared to logical reasoning (ventromedial prefrontal cortex in the first case (Levy and Glimcher (2012)) and parietal regions in the second (Hinton et al. (2010)). Furthermore, the association of inconsistency with age and attentiveness suggests that improvements in decision-making in the Goods domain are partly driven by known age-related changes in attentional control. Decision-making in the Social domain: the e↵ ect of centration. Reasoning over multipleattributesisknowntobeadi cultexerciseforchildren7yearsoldandyounger, and this ability develops during the concrete operational stage, somewhere between 2nd and 5th grade (Crain (2015), Piaget (1942)). The high utilization of heuristics we observed by the youngest children is therefore consistent with centration. Participants who have not yet overcome centration are more likely to pick a heuristic that makes 47 them “appear” consistent to the outside observer. Among children who do not use heuristics, we observe the same trajectory as in the Goods domain, suggesting that centration is concealing their underlying underdeveloped decision-making system. Decision-making in the Risk domain: too complex. As in the Social domain, making choices in the Risk domain requires the evaluation of multiple attributes. It is therefore naturaltoobserveasimilartendency, especiallyamongyoungchildren, toactaccording to heuristics and to “appear” consistent. However, integrative reasoning is largely more complex in the Risk domain and participants who do not use heuristics are not nearly as consistent as in the other two domains. All children were at the same level of performance suggesting that the ability to trade-o↵ probabilities and rewards was not yet developed, perhaps as a consequence of a still underdeveloped working memory system (Gathercole et al. (2004)). This result complements other studies reporting irrational decisions by children in the Risk domain (Harbaugh et al. (2002)). Adi↵ erent learning trajectory across domains. The results obtained for participants intheUagegroupagreewithmostfindingsontheliteratureonchoiceconsistency: that by adulthood, people have learned to know their preferences and are largely consistent in the Goods (Battalio, R. C., Kagel, J. H., Winkler, R. C., Fisher, E. B., Basmann, R. L., Krasner (1973), Cox (1997), Sippel (1997)) and Social domains (Andreoni and Miller(2002), Fismanetal. (2007), VisserandRoelofs(2011)). Ourfindingsin theRisk domain are less optimistic than previous ones (Andreoni and Harbaugh (2009), Choi et al. (2007, 2014), Fevrier and Visser (2004)), perhaps due to di↵ erences in design. However, our study identifies di↵ erent learning trajectories in these domains. In the Social domain, children learn to pick their most-preferred option. In the Risk domain, children learn to not pick their least-preferred option. In the Goods domain, they learn both. Theseasymmetriescannotbeexplainedbythedevelopmentofattentionalcontrol, 48 which should act similarly across domains, suggesting that self knowledge of preferences follows its own developmental trajectory. 2.0.5 Conclusion We have investigated the developmental trajectories of transitive decision-making in the Goods, Social, and Risk domains in children from Kindergarten to 5th grade and compared consistency levels with adult-level performance. We found that transitivity in choices develops gradually, but di↵ erentially across domains. In the Goods domain, children learn to know what they like most and least and they become more consistent over time. In both the Social and Risk domains, the early developmental trajectory is hidden by centration that manifests as a tendency to use heuristics that facilitate consistency. Children tend otherwise to learn what they like best but not what they like least in the Social domain, while they learn why they like least but not what they like best in the Risk domain. Even though the development of attentional control and the development of logical reasoning are candidates to explain the reduction of intransitivity over time, we find that only the former is predictive. However, attentional control only partly explains the development of transitive choice. The fact that children learn what they want and do not want di↵ erently across domains suggests the role of an ability acquired di↵ erentially across domains. The patterns we observe indicate that improved self-knowledge of preferences is that ability which supports the development of value-based decision-making. 49 Chapter 3 Bundling Options in Value-Based Decision-Making: Attention, Calculation, and Working Memory One of the core questions of Neuroeconomics is how humans value options. To date, most studies have focused on simple options and identified the ventrome- dial prefrontal cortex (vmPFC) as the primary value tracking region. In this study, we ask participants to make pairwise comparisons involving options of varying complexity: single items, bundles made of the same two single items, or bundles made of two di↵ erent single items. We found that novel patterns of ac- tivation were associated with choices involving bundles made of di↵ erent items. In those choices, we found that the Default Mode Network was deactivated, brain regions associated with calculation (Infraparietal Sulcus) were engaged, and there was increased connectivity between value tracking regions and the re- gion responsible for working memory (dorsolateral prefrontal cortex). Taken together, these results indicated that complex option valuation was supported by networks involved in attention, computation, and working memory. 1 1 A version of this chapter is being prepared for publication. My coauthors on that article (Niree Kodaverdian, Isabelle Brocas, John Monterosso, and Juan Carrillo) made considerable contributions to the text in this chapter. 50 3.1 Introduction Evidence from many lesion and fMRI studies converges in identifying the medial orbito- frontal cortex (mOFC), or sometimes more narrowly, the ventromedial prefrontal cortex (vmPFC) as a critical region in valuation when deciding between alternatives (Fellows (2011), Fellows and Farah (2007), Henri-Bhargava et al. (2012), Rangel et al. (2008)) or how much to pay for a good or item (Chib et al. (2009), Hare et al. (2008), Plassmann et al. (2007)). This finding has been consistently reported in studies involving food items, trinkets and money (see Clithero and Rangel (2013) for a meta-analysis). Most studies however have focused on choices involving single items, as opposed to complex bundles of multiple items. Among the few studies involving bundles, the vmPFC has been associated with the ability to make consistent choices between bundles (Camille et al. (2011)) and the mOFC has been shown to reflect the di↵ erence in subjective value between monetary options and bundled options (FitzGerald et al. (2009)). Other forms of complex options have been studied as well, in the form of multi-attribute options. Here again, activity in the vmPFC reflected the value of the combined items (Kahnt et al. (2011)). It seems intuitive that complex options are di cult to evaluate. Hence, the ability to make more complex value comparisons is likely to also involve the working mem- ory system, responsible for the short-term mental maintenance and manipulation of information. In the case of value-based decision-making, working memory has been reported to be associated with consistent choices involving complex bundles in older adults (Brocas et al. (2016)). It is already also known that during tasks that tax ex- ecutive function, activation is evoked in the dorsolateral prefrontal cortex (dlPFC) and the posterior parietal cortex (PCC), as demonstrated by many studies (Baker et al. (1996), Berman (1995), Goel et al. (1997), Goldberg et al. (1998), Nichelli et al. (1994), Osherson et al. (1998), Petrides (1994), Prabhakaran et al. (1997, 2000)). Activation 51 studies have shown that dorsal frontal regions are activated during tasks that are ex- perienced as di cult (Braver et al. (1997), Cohen et al. (1994, 1997), Luo et al. (2011), Monterosso et al. (2007)), during task switching (Dove et al. (2000)), and the dlPFC is di↵ erentially recruited as tasks become more complex (Baker et al. (1996), Braver et al. (1997), Carlson et al. (1998), Christo↵ et al. (2001), Cohen et al. (1997), Demb, J. B., Desmond, J.E., Wagner, A.D., Vaidya, C.J., Glover, G.H., andGabrieli(1995)). This relationship extends to tasks requiring the explicit representation and manipulation of knowledge, where the ability to reason relationally is essential (Kroger et al. (2002)). The role of dlPFC in value-based decision making has not been clearly established. It is sometimes reported to be activated and, if so, its involvement is interpreted in the context of the question of interest. For instance, the dlPFC has been found to encode the variability of multi-attribute objects (Kahnt et al. (2011)) and to be more activated when trade-o↵ s between attributes are required (McFadden et al. (2015)). In food choices, the dlPFC has been reported to modulate value (Camus et al. (2009), Hare et al. (2011), Sokol-Hessner et al. (2012)) and craving (Fregni et al. (2008)), and to be involved in self-regulation and self-control (Harris et al. (2013), Hutcherson et al. (2012)). The dlPFC has also been found to be functionally connected with the value coding regions in self-control paradigms (Hare et al. (2009)) and in multi-attribute paradigms (Rudorf and Hare (2014)). Last, the dlPFC was found significantly more activated in studies in which options involved a conflict to be resolved (Baumgartner et al. (2011), de Wit et al. (2009)). The dlPFC is however not usually reported to be active in studies involving single uni-attribute items. Taken together, these findings indicate that the potential role of dlPFC is to support value calculation (perhaps in various ways) when options are complex. Here we report the results of an fMRI study in which participants were asked to choose between real food options involving single item options and bundled options. 52 Bundles varied in complexity and were either composed of the same two single items or of two di↵ erent single items. Our design allows us to address the following questions: (1) Is there a common value tracking region when options are simple and complex? (2) Whataretheneuralmechanismsusedtocomputevalueasafunctionofcomplexity? (3) Does complexity involve brain networks implicated in attention and working memory? 3.2 Materials and methods 3.2.1 Subjects Twenty-sixhealthyadults(9male,17female,averageageof21.9years,allright-handed) were recruited from the Los Angeles Behavioral Economics Laboratory’s subject pool at the University of Southern California. Subjects could participate if they satisfied the standard eligibility criteria for fMRI studies. We also excluded subjects who reported to have food allergies, food restrictions or to be picky eaters. All participants received a $50 show-up fee for participating. They were also rewarded with one of their choices, selected randomly at the end of the session. One participant was excluded because of incomplete data collection. The Institutional Review Board of USC approved the study. 3.2.2 Procedures Participants were instructed to not eat for at least 4 hours before the experimental session. They were also instructed that they would have to stay after the session to consume what they had obtained and that they could not take any of the food items with them when they leave. This was implemented to make sure participants were hungry and thinking carefully about their choices during the session. The procedure wasexplainedbeforehandsothateachparticipantknewthatchoiceswerereal, andthey should make their best decision in every trial. 53 There were three tasks. In the pre-fMRI task, each participant was asked to rank 30 single item (CONTROL) options by order of preference. This ranking was used to create 40 bundles, 20 combinations of 2 same single items (SCALING options), and 20 combinationsof2di↵ erentsingleitems(BUNDLINGoptions). Theparticipantwasthen askedtoincludethoseoptionsintheirpreviousranking. Wethenselected11CONTROL options, 10 SCALING options and 10 BUNDLING options to include in the following tasks. These items were selected to so that each set of options (CONTROL, SCALING, and BUNDLING) has the same distribution of option value; there were some low-value, medium value, and high value options in each set. This enabled us to make each task regressor orthogonal to the value regressor. In the fMRI task, each participant made binary choices in the scanner. The median option of the 11 CONTROL options was a reference option, denoted hereafter by REF. Trials were divided into three conditions (Figure3.1): CONTROL,SCALINGandBUNDLING.IneachoftheCONTROLtrials, the participant had to choose between REF and one of the 10 remaining single item. In each of the SCALING trials, the participant had to choose between REF and one of the 10 combinations of 2 same single items. In each of the BUNDLING trials, the participant had to choose between REF and one of the 10 combinations of 2 di↵ erent single items. In all cases, REF was o↵ -screen, it was the same for each trial and was shown to the participant at the beginning of the experiment. The other option was on-screen and it was displayed at the beginning of each trial. Each individual trial was repeated 9 times for a total of 90 trials in each condition. The circles at the bottom of the screen told the participant what button selected which option, the solid circle always representing REF. The button mappings were randomly assigned for each trial. 2 When the participant responded, the circle representing the chosen option was 2 Subjects had button boxes in each hand when they were in the scanner. They were instructed to make choices by pressing a button in the hand corresponding to the option, as represented by the circle, they wanted. For example, if they wanted the reference option and the solid circle was on the right side of the screen in that trial, they could select it by pressing a button in their right hand. If 54 framed in a square to let the participant know that the their answer was recorded. The screen then advanced to a fixation cross for the remainder of the trial. Trial order and inter-stimulus intervals were optimized by Optsec2 for task regressor estimation e ciency (Dale (1999)) and organized into 5 runs. We also chose the options in order to ensure that each of the three conditions CONTROL, SCALING and BUNDLING had symmetrical sets of low, medium of high on-screen value options centered around REF. We also made sure that the distribution of value was similar across conditions. This was done to separate value-specific activity from task-specific activity. Figure 3.1: Three types of trial. The first is a single item, the second is two portions of the same item, the third is one portion each of two items. As will be explained below, we estimated the value of each option from the actual choices of each participant. The fMRI task however did not allow us to extract infor- mation regarding the relative value between any 2 on-screen options because these were not presented for a choice. To improve the estimation of value, we designed a third task implementedafterthescanningsession. Inthis post-fMRI task, participantswereshown two options, one on the left and one on the right. When the participant responded, by taping the preferred option, the screen advanced to a fixation cross for 0.25 seconds, and then to the next trial. The number of trials ranged from 300 to 500 and di↵ ered acrosssubjects. Theoptionswereselectedtoimprovethevalueestimatesof each option in the fMRI task. The procedures of the last two periods are represented in Figure 3.2. they wanted the on-screen option instead, they could select it by pressing a button corresponding to the hollow circle, which in that case would be a button in their left hand. 55 Figure 3.2: Experimental Design.Inthe fMRI task, each participant had to choose between an o↵ -screen reference (REF) option and an on-screen option. In the post- fMRI task, each participant had to choose between two on-screen options. All trials were self-paced. 3.2.3 MRI data acquisition Neuroimagingdatawascollectedusingthe3TSiemensMAGNETOMTim/Trioscanner at the Dana and David Dornsife Cognitive Neuroscience Imaging Center at USC with a 32-channelhead-coil. Participantslaidsupineonascannerbed, viewingstimulithrough a mirror mounted on head coil. Blood oxygen level-dependent (BOLD) response were measured by echo planar imaging (EPI) sequence with PACE (prospective acquisition correction) (TR = 2 s; TE = 25 ms; flip angle= 90; resolution = 3 mm isotropic; 64 x 64 matrix in FOV = 192 mm). A total of 41 axial slices, each 3 mm in thickness were acquired in an ascending interleaved fashion with no interslice gap to cover the whole brain. The slices were tilted on a subject-by-subject basis – typically 30deg from the AC-PC plane – to minimize signal dropout in the orbitofrontal cortex (Deichmann et al. (2003)). Anatomical images were collected using a T1-weighted three-dimensional magnetization prepared rapid gradient echo (MP-RAGE with TI = 900 ms; TR=1.95 s; TE: 2260 ms; flip angle = 9; resolution = 1 mm isotropic; 256 ⇥ 256 matrix in FOV = 256-mm) primarily for localization and normalization of functional data. These scans were co-registered with the participant’s mean EPI images. These images were 56 averaged together to permit anatomical localization of the functional activations at the group level. 3.2.4 MRI data preprocessing Image analysis was performed using FSL (Jenkinson et al. (2012)) algorithms organized inanipypepipeline(Gorgolewskietal.(2011)). Thestructuralimageswereskull-striped then aligned tothe standard Montreal Neurological Institute (MNI) EPI template using non-linear warping FSL-FNIRT (Andersson et al. (2007)). The functional images were motionandtimecorrected. TheywerespatiallysmoothedusingaGaussianKernelwith a full width at half-maximum of 5mm. We also applied a high-pass temporal filtering using a filter width of 120s. 3.2.5 Behavioral analysis In both the fMRI and the post-fMRI tasks, participants were asked to make a series of choices between two snack options. In the fMRI task, the first option was always the same o↵ -screen reference option denoted by REF while the second option was an on- screen variable option VAR j (j = {1,...,N}). We constructed a Random Utility Model (Clithero and Rangel (2013), McFadden (1973), Train (2003)) in which we assumed that the utility derived by option VAR j depends on the value of the food snack and a stochasticunobservederrorcomponent ✏ j . Formally,u(REF)= 0 +✏ 0 andu(VAR j )= j +✏ j . TheprobabilityofchoosingoptionVAR j isthereforeP j (q)=Pr[✏ 0 ✏ j < j q 0 ]. Assuming that the error terms are independent, identically distributed, and follow an extreme value distribution with cumulative density function F(✏ k )= exp( e ✏ k ) 57 for all k=0,j, then the probability that the participant chooses option VAR j is the logistic function P j (q)= 1 1+e ⇣ j 0 ⌘ The same procedure was applied to trials in the post-fMRI task where options were now all varying. In that task, the probability that the participant chooses option VAR j over VAR i is the logistic function P ji (q)= 1 1+e ⇣ j i ⌘ WethenconstructedalikelihoodfunctionandweusedMaximumLikelihoodEstimation techniques to retrieve parameters j given the observed choices. This procedure was implemented in Matlab with standard algorithms. For each individual, we also assigned an implicit ranking of all options based on these retrieved values. 3.2.6 Analysis of reaction times We recorded reaction times between the onset of the stimulus and the time at which a choice was made in each trial. We analyzed individual and group di↵ erences across conditions as well as trial-specific e↵ ects. In particular, we looked at whether trials deemed to be more di cult, as measured by a smaller distance between the value of the on-screen and o↵ -screen options, were also taking longer. 3.2.7 MRI data analysis We estimated several general linear models (GLMs) of BOLD responses. Each aspect of the task was encoded in a regressor for the GLM. To identify what signal was asso- ciated with a particular condition, we constructed indicator regressors that take value 58 1 whenever the participant is performing a trial within a condition and 0 otherwise. To identify the neural activity associated with the subjective value of the on-screen option, we created a parametric regressor that is equal to the value of the on-screen option and changes every time the on-screen option changes. When there is nothing on the screen, bothregressorsare0. Themodelsalsoincludemotionparameters(regressorsfor translation and rotation as well as artifact regressors controlling for quick jerking move- ments) and regressors for each run as nuisance regressors. All regressors were convolved with the canonical form of the hemodynamic response. The values in the regressors were applied from the onset of the stimulus until a choice was made (average duration, 1.47s). All of our GLMs took the general form: Y i =[H 1 (R a )]⇤ a i +R b ⇤ b i +e i Where Y i is the time-series of BOLD signal at each voxel i, H 1 is the hemodynamic response function (HDF) used by FSL Jenkinson et al. (2012), Smith et al. (2004) applied to the primary regressor matrix R a (each column is a primary regressor) and e i is a gaussian noise. The GLM solves for a i and b i to minimize the error e i . To analyze the influence of an indicator regressor the coe cients a i are contrasted against each other (CONTROL vs. SCALING for instance). These -contrasts are used to generate interpretable statistics. We considered the following models: Model (1) was a GLM used to identify the regions involved in value computation at the time of decision. To do this, we searched for areas in which the BOLD responses were correlated with value. This GLM consists of the following 4 regressors of interest: R 1 to R 3 were indicator regressors denoting CONTROL trials, SCALING trials and BUNDLING trials while R 4 was a parametric regressor tracking the value of the on- screen option. 59 Model (2) was a GLM used to conduct a conjunction analysis (Friston et al. (2005), Price and Friston (1997)) to assess di↵ erence in value-tracking across conditions. This model consists of 3 parametric regressors, one to track the value of the on-screen option in each condition, and 3 indicator regressors for CONTROL, SCALING and BUNDLING trials. Model(3)wasaageneralpsychophysiologicalinteraction(gPPI)model(DeMartino et al. (2013), McLaren et al. (2012)) designed to test di↵ erences in condition-dependent functional connectivity. We defined a region of interest (ROI) which we used as the seed for our analysis. The gPPI model searched for how and when other regions connected to that seed region during a specific condition, but not in any other condition. It has the general form: Y s = H 2 (x s ) Y s is the mean bold activity in a region of interest (ROI). If we preform a decon- volution of Y s with H 2 , Afni’s hemodynamic response function (Cox (1996), Cox and Hyde (1997)), we get x s , the implied neural activity in the seed region. ThentheBOLDsignalY i ineachvoxeliismodeledasthelinearcombinationofseed BOLD activity the convolved indicator regressors, the psychophysiological regressors, and the nuisance regressors. Y i = Y s ⇤ s i +... Mean BOLD signal in seed region [H 2 (R a )]⇤ a i +... Psychological contribution [H 2 (R a ⇤ x s )]⇤ c i +... Psychophysiological contribution R b ⇤ b i +... Nuisance contribution e i Error 60 The physiological regressor (Y i ) absorbs all of signal associated with constant func- tional connection with the seed ROI. The “psychological” regressors are same as the task indicator regressors form model (1). They absorbs all signal associated with the tasks. Each “psychophysiological” regressor is an element-wise product of a “psycho- logical” regressor (columns inR a ) and the vector of neural activity regressorx s .These regressors detect which brain activity correlates with the seed region brain activity dur- ing a specific task, but not at other times. We call this the task-dependent functional connectivity. Our seed region was a 6mm diameter sphere centered on MNI coordinates [-6,51,-6]. This was the point of peak vmPFC activity for the value regressor in a fMRI task analogous to ours (Kahnt et al. (2011)). We preferred to use this independent seed rather than our peak activity value region to avoid inference problems due to circular analysis (Kriegeskorte et al. (2009)). 3.2.8 Postprocessing After each GLM was fit to the image time-series, the -contrasts were combined at the subject level using a Fixed E↵ ects Model, then combined in a Mixed E↵ ects Model to create group level voxel-wise t-statistics. These t-statistics were corrected for false discovery rate (FDR) using threshold-free cluster enhancement (Smith et al. (2009)). Unless otherwise stated, all images are thresholded at p<0.02 FDR corrected. 3.3 Results 3.3.1 Behavioral results We counted very few missed trials resulting in no choice (1.48% of the trials) indicating that participants were attentive and had enough time to select their preferred option. 61 Estimated values and implicit ranking. We estimated the value of each option for each individual. The values were the best estimates given the observed choices. In principle, if a subject’s choices are well represented by the Random Utility Model, we should observe that most choices are consistent with estimates. For each individual, we generatedthechoicestheyshouldhavemadeinalltrialsiftheywerechoosingaccording to the value estimates and we compared with their actual choices. More precisely, we counted all choices that were not consistent with the value estimates (and henceforth withtheimplicitranking)andwecomputedthepercentageoftheseinconsistentchoices. We found that 87% of the choices of all subjects were consistent with implicit rankings in the fMRI task ( 88% in the CONTROL condition, 88% in the SCALING condition and 87% in the BUNDLING condition). Also 87% of choices were consistent in the post-fMRI task. These results indicate that value estimates were good proxies of values during choices in the scanner. Discrepancies between implicit and explicit ranking. Recall that the snacks that we included in the fMRI and post-fMRI sessions were selected in such a way that the dis- tributions of expected choices between REF and VAR in the three conditions would be balanced and comparable. This selection however was made based on the explicit rankings obtained in the pre-fMRI period and there was no guarantee that these rank- ings would line up with implicit rankings. We found that discrepancies existed gen- erally between the two rankings, suggesting that explicit rankings were not the best predictors of choices. However, overall, the two rankings were significantly correlated (Spearman=0.56 (p-value<0.0001) in CONTROL, 0.67 (p-value<0.0001) in SCAL- ING and 0.60 (p-value<0.0001) inBUNDLING) suggesting that the explicit ranking was a good predictor of choices in the scanner. 62 Values. Wefoundthat7(respectively6)participantsoutof25hadlinearpreferences in the SCALING condition (respectively BUNDLING). All others valued the combina- tion of items more than the sum of items, suggesting that value was super-additive. By regressing the value of each bundle on the values of the individual items, we found that the constant term was positive and significant (p< 0.05) for most participants with super-additive preferences, suggesting that bundled items were positively valued independently of their content. The value of a bundle in the SCALING condition was predicted by the value of the single item (p< 0.05). In the BUNDLING condition, it was often predicted by the value of only one of the single items, most of the time by the highest valued item. 3.3.2 Reaction times We found that it took on average longer to make decisions in the BUNDLING condition (mean=1.52s) compared to CONTROL (mean=1.43s) and SCALING (mean=1.37s). A t-test and a KS-test confirmed that reaction times were significantly longer in BUNDLING compared to CONTROL and SCALING (in both cases KS-test, p<0.001; t-test, p<0.0001). SCALING trials were taking slightly more time than CONTROL trials only according to KS-test (p<0.007). We also found that choosing the on-screen option was taking less time compared to the o↵ -screen option in all conditions (in each condition KS-test, p<0.001; t-test, p<0.0001). 3 To assess any specific e↵ ect of value on reaction times, we computed the absolute value of the di↵ erence between the rank of the o↵ -screen and on-screen options and we correlated it with reaction times. We found that reaction times were short in trials where the on-screen and the o↵ -screen option were ranked very di↵ erently and long in trials where they were close in ranks (Pearson= -0.15 in CONTROL, Pearson= -0.20 in SCALING and Pearson= -0.25 in BUNDLING, 3 Choices made with the right hand were significantly faster only in CONTROL trials. 63 p-value<0.0001). This e↵ ect was also found at the individual level, even though some- times less significant in particular in the CONTROL and SCALING conditions. In the BUNDLING conditions, subjects were spending significantly more time when options were close. 3.3.3 Regions correlating with subjective value Wehadthreepotentialvalueregressors: onebasedontheestimatedvalueofeachoption, one based on the implicit rank of each option and one based on the explicit rank of each option. Because estimated value and implicit rank contain the same information, both areequallygoodcandidatesfortheexercise. Becausetheexplicitrankhadaninferiorfit withtheactualchoices, itwasdominatedbytheothertwo. Wechosetousetheimplicit ranking, and we will report below results obtained under the alternative specifications. We identified value regions by estimating Model (1) based on the parametric re- gressor tracking the value of the on-screen option. We found significant activity in the mOFC, the vmPFC, the Precuneus, the Nucleus Accumbens (NA) and the left dlPFC thatcorrelatedwiththeestimatedvalueoftheonscreenoption, whichconfirmedearlier findings. We then estimated Model (2) and made a conjunction analysis to see whether the three conditions activated the same regions. We found that only the CONTROL value regressor showed significant activity in the vmPFC and only the BUNDLING value regressorshowedactivityinmanyregionsimplicatedinvaluetracking,includingdlPFC, SFG, fusiform, precuneus, mOFC, ACC, PCC (see tables 3.3 & 3.4). The SCALING value regressor showed no significant activation (min p-value = .32). This result was unexpected. However, it strongly suggested that di↵ erent calculations are performed under complex value-based decision-making. The activation patterns in relation with value are presented in Figure 3.3. 64 Region Side P-value MNI-X MNI-Y MNI-Z Precuneus 0.002 2 -32 40 0.002 -4 -36 40 0.002 0 -38 34 mOFC 0.004 -8 10 -14 vmPFC 0.004 -8 42 -10 0.005 8 42 -12 0.005 12 42 4 N. accumbens L 0.004 -10 10 -2 L 0.004 -10 6 -4 R 0.005 6 10 -2 SFG L 0.005 -20 10 48 dlPFC L 0.005 -20 58 6 L 0.005 -36 38 14 L 0.007 -36 4 32 L 0.007 -42 38 8 Amygdala L 0.005 -34 -14 -14 Table 3.1: Local minima in corrected p-value parametric value regressor. Thresholded for p 0.005 corrected. Minima in occipital cortex or white matter ex- cluded. Where cluster spanned multiple functional regions, a regional mask was used to locate the peak voxel within a region. mOFC; medial OrbitoFrontal Cortex, vmPFC; ventroMedial PreFrontal Cortex, SFG; Superior Frontal Gyrus, dlPFC; DorsoLateral PreFrontal Cortex Region Side P-value MNI-X MNI-Y MNI-Z vmPFC 0.003 2 54 -10 0.003 -4 44 -12 0.003 8 40 -16 0.004 2 46 -16 0.004 -8 34 -16 0.004 2 50 -18 MTG L 0.005 -62 -22 -18 Table 3.2: Local minima in corrected p-value parametric value regressor for CONTROL trials. Thresholded for p  0.005 corrected. Minima in occipital cor- tex or white matter excluded. Where cluster spanned multiple functional regions, a regional mask was used to locate the peak voxel within a region. vmPFC ;ventroMedial PreFrontal Cortex, MTG; MidTemporal Gyrus 65 Region Side P-value MNI-X MNI-Y MNI-Z dlPFC L 0.001 -36 8 42 L 0.001 -42 10 38 L 0.002 -48 4 44 L 0.002 -26 -6 44 L 0.002 -32 -4 42 L 0.002 -32 8 40 L 0.004 -42 38 2 L 0.006 44 34 12 L 0.006 38 36 6 L 0.009 40 26 12 R 0.006 56 0 28 R 0.008 64 2 26 R 0.008 44 -2 26 SFG L 0.003 -18 10 52 L 0.003 -14 24 44 L 0.003 -18 18 44 L 0.003 -18 30 22 L 0.003 -16 42 20 L 0.003 -20 36 18 Fusiform L 0.003 -30 -44 -24 L 0.003 -34 -44 -26 L 0.004 -26 -54 -14 L 0.004 -30 -64 -20 L 0.004 -26 -48 -22 Precuneus 0.003 -8 -56 62 0.004 -8 -50 56 IPS L 0.003 -22 -86 40 L 0.004 -14 -84 36 L 0.005 -18 -56 60 R 0.004 16 -60 52 R 0.004 24 -66 50 R 0.005 24 -62 62 R 0.005 30 -58 60 R 0.005 30 -54 50 R 0.005 22 -56 50 R 0.005 20 -78 44 R 0.005 30 -72 36 Table 3.3: Local minima in corrected p-value parametric value regressor for Bundling trials Part1. 66 Region Side P-value MNI-X MNI-Y MNI-Z Post-CS R 0.003 40 -28 42 R 0.004 52 -38 34 R 0.005 36 -38 54 R 0.005 38 -36 50 R 0.005 38 -42 48 ACC 0.003 -4 4 28 0.003 4 4 26 0.005 -12 -4 46 0.005 0 -2 50 0.009 -4 24 22 0.010 -2 28 30 Pre-CS R 0.005 58 -14 30 R 0.010 48 -12 26 Sup. Insual R 0.005 34 -8 12 R 0.005 38 0 8 R 0.005 42 -2 4 Frontal Pole L 0.006 -20 62 8 L 0.008 -18 56 4 Hypocampus L 0.006 -28 -2 -22 L 0.008 -30 -8 -22 V.Str. L 0.007 -30 -14 -6 L 0.010 -16 -24 16 mOFC 0.008 -4 24 -22 0.008 -6 12 -24 0.008 -2 8 -26 Amygdala L 0.008 -24 -8 -10 L 0.008 -24 -4 -16 L 0.008 -28 -18 -16 Table 3.4: Local minima in corrected p-value parametric value regressor for Bundling trials Part2. These tables contain many more minima because a lower threshold was needed to report the mOFC activation. dlPFC; DorsoLateral PreFrontal Cortex, SFG; Superior Frontal Gyrus, IPS;IntraParietal Sulcus, CS; Central Sulcus, ACC; antirior cingulate cortex, V.str.: Ventral Striatum, mOFC;medial OrbitoFrontal Cortex, vmPFC;ventroMedial PreFrontal.Cortex 67 Figure 3.3: Value tracking regions. A) Regions tracking value in the fMRI task (Model(1)). B)RegionstrackingvalueinCONTROL(Model(2)). C)Regionstracking value in BUNDLING (Model 2). See table 3.1 for all active regions. 3.3.4 Regions involved in complex conditions (SCALING and BUNDLING) We analyzed the e↵ ect of complexity by contrasting CONTROL trials with SCALING trials and BUNDLING trials separately. We found that the Default Mode Network (precuneus, TPJ) was deactivated during complex trials (Smith et al. (2009)) for a canonical map). This suggested that more attentiveness was required during those two conditions (Figure 3.4). 3.3.5 Regions involved in complex calculations (BUNDLING vs. SCALING) Weanalyzedthecondition-specifice↵ ectofBUNDLINGbycontrastingthesetrialswith SCALING trials. We found that the left and right infraparietal sulcus was significantly 68 Figure 3.4: Attentiveness is required in complex conditions. Compared to CON- TROL,bothSCALINGandBUNDLINGtrialshavesignificantlylessactivityinthepos- teriornodesoftheDefaultModeNetwork. Acanonicalmapofdefaultmorenetwork(A) fromSmithetal.(2009)appearsimilartocorrectedcontrastsofCONTROL>SCALING (B) and CONTROL>BUNDLING (C). There are no regions are significant for the con- trasts SCALING>CONTROL or BUNDLING>CONTROL. activated, as shown in Figure 3.6. Because this image is the result of a contrast between SCALING and BUNDLING, the activity cannot simply be caused by the tracking of twoitemsonthescreenasbothconditionshavethesamenumberofitemsonthescreen. This region is usually associated with calculation, arithmetic and numbers, suggesting that BUNDLING was requiring a computation ability. This e↵ ect was task specific and not sensitive to value. Unexpectedly, We also found significant activity in the fusiform gyrus (peak p value  0.005 see table 3.5). Similar activity has been reported in calculation tasks, and is attributed to letter-form recognition. Our fusiform activity was clearly not the resultofletterformrecognition,althoughitmightbecausedbythefactthatmoreitems 69 Figure 3.5: The contrast between the single-item-trial regressor and the re- gressors for scaled-option-trials and bundled-option-trials correlates the the canonical default mode network Smith et al. (2009). A voxelwise correlation between the correlation coe cient of 0.29 was calculated using fslcc. The p-value on a persons correlation is <10 308 . However, a Pearson correlation test assumes inde- pendent observations, which is never true in neuroimaging, especially after smoothing. addito salis grano, that’s still a good correlation and tiny p-value. require independent recognition in the BUNDLING task compared to the SCALING task. 3.3.6 Connectivity analysis With Model (3) we asses if any brain regions are di↵ erentially recruited to calculate value during di↵ erent task. The center of the vmPFC ROI Kahnt et al. (2011) is 10.05 mm from the vmPFC peak of our Value regressor (principally in the anterior direction). Our value regressor is highly significant at the center of the ROI (p = 0.01). We found that the dlPFC is functionally connected to the vmPFC, but only in the more complex conditions. The dlPFC was significantly activated when we contrasted BUNDLING and CONTROL, showing that as activity in the seed increased, activity in 70 Region Side P-value MNI-X MNI-Y MNI-Z fusiform L 0.002 -32 -58 -18 L 0.002 -32 -52 -20 R 0.005 30 -48 -20 IPS R 0.007 30 -62 44 R 0.007 30 -66 30 L 0.008 -24 -62 42 Table 3.5: Local minima in corrected p-value for BUNLDING>SCALING. Thresholded for p 0.01. Region Side P-value MNI-X MNI-Y MNI-Z dlPFC R 0.029 50 10 34 L 0.093 -44 24 30 Table 3.6: Local minima in corrected p-value for BUNDLING CONNECTIVITY >CONTROL CONNECTIVTY. Thresh- olded for p 0.1 corrected. dlPFC increased as well (Figure 3.7). A similar finding was made when we contrasted SCALING-CONTROL but to a lesser level of significance (p 0.25 corr). 3.3.7 Other analyses of interest We considered several variants of Model (1). First, we replaced the ”implicit ranking” value regressor by the estimated value regressor. We also repeated the analysis by considering the explicit ranking instead. The results presented here were qualitatively similar. We also considered a variant of Model (1) in which we replaced the on-screen value regressor by a chosen-value regressor. We did not find any significantly di↵ erent pattern of activity. We last constructed a variant of Model (1) that also included a regressor for task di culty, measured by the absolute value of the di↵ erence between the on-screen and the o↵ -screen option. No e↵ ect was associated with di culty. 71 Figure 3.6: Relative to SCALING, BUNDLING recruits regions associated with calculation. IPS activation in a neurosynth meta analysis for ‘calculation’(A) bares a striking resemblance to the BUNDLING>SCALING contrast(B). A contrast of meta analyses for ‘calculation’ and ‘saccades’ (C) also supports the claim that the IPS activityintheBUNDLING>SCALINGcontrastiscausedbycalculation-likecogitation. In (C) red regions are more associated with calculation and blue regions are more associated with saccades. 3.4 Discussion Our study provides novel insights about the computation of value in value-based decision-making involving bundles of goods. Value tracking of complex options. The most unexpected finding is that value track- ing regions are not tracking value similarly across conditions. Complexity requires attentiveness. The default mode network is active when a personisnotfocusedonatask(Davisetal.(2011),Raichle(2015),Raichleetal.(2001)) andithasalsobeenshowntobenegativelycorrelatedwithattentionnetworks(Greicius et al. (2003)) and the dlPFC in working memory tasks (Esposito et al. (2006), Piccoli etal.(2001)). TherelativeinactivationinregionsthatcorrelatewiththecanonicalDMN 72 Figure 3.7: The vmPFC is more connected to the dlPFC during BUNDLING trials than during CONTROL trials from gPPI. Both the right dlPFC (peak p-value = 0.029 corrected) and left dlPFC (peak p-value = 0.093 corrected) are signif- icantly greater in the contrast of the BUNDLING connectivity regressor than in the CONTROL connectivity regressor. in the SCALING and BUNDLING with respect to CONTROL, implies that subjects need to be more attentive when preforming those tasks. In the independent component analysis(ICA) studies that first identified networks like the DMN, they typically find opponent networks(Greicius et al. (2003), Raichle (2015)) which are active when the DMN is inactive; commonly referred to as the task positive network. We did not find any regions that were significantly more active in SCALING or BUNDLING compared to CONTROL. An absence of significant activity is always di cult to interpret, but it is unsurprising in this case if we suppose that subjects engaged with di↵ erent SCALING or BUNDLING trials with di↵ erent strategies. This would create a lot of heterogeneity ‘task positive’ response. Complexity requires calculation. The IPS is associated with many visio-spacial tasks including calculation, saccades, visual attention, language, reach, and grasp (Si- mon et al. (2002)). It is also known that the exact brain region associated with each of these abilities systematically varies between subjects based expertise (Desco et al. (2011)). Ideally, we could have run localizer tasks for each of these abilities in each subject and seen if which best fit with the parietal region implicated in the 73 BUNDLING>SCALING contrast. But our task was already pushing the limits of what could be expected from a subject. Instead,we’llcomparethatactivitywithabroadmeta-analysisofthesetasks. Figure 3.6showsabetweenaneurosynthmeta-analysisfor‘calculation’(A),acontrastofmeta- analysis for ‘calculation’>‘saccades’ (C), and the BUNDLING>SCALING contrast (B) (Yarkoni et al. (2011)). The contrast is much more similar to the meta analysis for ‘calculation’,implyingthatsomepsychologicalprimitiveofcalculationofwhatisdriving the activity in the BUNDLING>SCALING contrast. 4 Complexity requires working memory. A relationship between value tracking regions and dlPFC has been demonstrated in many studies. These studies all share a common denominator: participants need to choose between objects involving some degree of complexity and value cannot be simply computed by just looking at the objects. In our study, complexity refers to the SCALING condition and more so in the BUNDLING condition. The observed longer reaction times suggests that value is computed gradually in those conditions. Furthermore, the fact that mOFC and dlPFC are functionally connected in the complex conditions (and even more so when complexity increases) indicates that dlPFC may be supporting the longer accumulation ofinformationtocomputecomplexvalue. Thisfindingalsoshedslightonthereasonwhy dlPFC is not found consistently to activate in value-based decision-making paradigms. Its involvement requires a minimum level of complexity. 4 NeuroSynth meta-analyses for ‘arrhythmic’ and ‘number’ also bare a strong resemblance with the BUNDLING>SCALING contrast. 74 Bibliography S. N. Afriat. The Construction of Utility Functions from Expenditure. International Economic Review, 8(1):67–77, 1967. S. M. Albert and J. Du↵ y. Di↵ erences in Risk Aversion between Young and Older Adults., 2012. ISSN 2230-3561. URL http://www.pubmedcentral.nih. gov/articlerender.fcgi?artid=3852157{\&}tool=pmcentrez{\&}rendertype= abstract. J. Ameriks, A. Caplin, J. Leahy, and T. O. M. Tyler. Measuring Self-Control Problems. The American Economic Review, 97(3):966–972, 2007. J. L. R. Andersson, M. Jenkinson, and S. Smith. Non-linear registration aka Spatial normalisation. Oxford University, (June):22, 2007. URL http://fmrib.medsci.ox. ac.uk/analysis/techrep/tr07ja2/tr07ja2.pdf. B. J. Andreoni and C. Sprenger. Risk Preferences Are Not Time Preferences. The American Economic Review, 102(7):3357–3376, 2016. J. Andreoni and W. Harbaugh. Unexpected utility: Experimental tests of five key questions about preferences over risk. Mimeo University of Oregon, 0551296, 2009. URL http://econweb.ucsd.edu/{ ~ }jandreon/WorkingPapers/ AndreoniHarbaughUU.pdf. J. Andreoni and J. Miller. Giving According to GARP : An Experimental Test of the Consistency of Preferences for Altruism. Econometrica, 70(2):737–753, 2002. J. Andreoni and C. Sprenger. Estimating Time Preferences from Convex Budgets. The American Economic Review, 102(7):3333–3356, 2012. D. E. Astle and G. Scerif. Using developmental cognitive neuroscience to study be- havioral and attentional control. Developmental Psychobiology, 51(2):107–118, 2008. ISSN 00121630. doi: 10.1002/dev.20350. A. D. Baddeley. Working Memory. Science, 255(5044):556–559, 1992. 75 A. D. Baddeley and G. Hitch. Working memory, 1974. ISSN 00797421. URL http: //linkinghub.elsevier.com/retrieve/pii/S0079742108604521. S. C. Baker, C. D. Frith, R. S. Frackowiak, and R. J. Dolan. Ac- tive representation of shape and spatial location in man. Cerebral Cor- tex, 6(4):612–619, 1996. ISSN 1047-3211. doi: 10.1093/cercor/6.4. 612. URLhttp://www.biomednet.com/db/medline/96324314$\backslash$nhttp: //cercor.oxfordjournals.org/content/6/4/612.full.pdf. L. Battalio, R. C., Kagel, J. H., Winkler, R. C., Fisher, E. B., Basmann, R. L., Kras- ner. A test of consumer demand theory using obersvations of individual consumer purchases. Economic Inquiry, 11(4):411–428, 1973. T. Baumgartner, D. Knoch, P. Hotz, C. Eisenegger, and E. Fehr. Dorsolateral and ventromedial prefrontal cortex orchestrate normative choice. Nature neuroscience, 14 (11):1468–74, 2011. ISSN 1546-1726. doi: 10.1038/nn.2933. URL http://www.ncbi. nlm.nih.gov/pubmed/21964488. C. Bellemare, S. Kr¨ oger, and A. van Soest. Measuring Inequity Aversion in a Hetero- geneous Population Using Experimental Decisions and Subjective Probabilities. The Econometric Society, 76(4):815–839, 2008. K. Berman. Physiological activation of a cortical network during performance of the WisconsinCardSortingTest: Apositronemissiontomographystudy. Neuropsycholo- gia, 33(8):1027–1046, 1995. ISSN 00283932. doi: 10.1016/0028-3932(95)00035-2. D. Bernheim and A. Rangel. Beyond Revealed Preference: Choice-Theoretic Founda- tions for Behavioral Welfare. The Quarterly Journal Of Economics2, 124(1):51–104, 2009. T. Besedeˇ s, C. Deck, S. Sarangi, and M. Shor. Age E↵ ects and Heuristics in Decision Making. Review of Economics and Statistics, 94(2):580–595, 2012a. ISSN 0034- 6535. doi: 10.1162/REST a 00174. URL http://www.mitpressjournals.org/ loi/rest$\backslash$nhttp://search.ebscohost.com/login.aspx?direct= true{\&}db=eoh{\&}AN=1307285{\&}site=ehost-live$\backslash$nhttp: //www.mitpressjournals.org/doi/abs/10.1162/REST{\_}a{\_}00174. T. Besedeˇ s, C. Deck, S. Sarangi, and M. Shor. Decision-making strategies and per- formance among seniors. Journal of Economic Behavior and Organization, 81(2): 524–533, 2012b. ISSN 01672681. doi: 10.1016/j.jebo.2011.07.016. S. Bouwmeester and K. Sijtsma. Constructing a transitive reasoning test for 6- To 13-year-old children. European Journal of Psychological Assessment, 22(4):225–232, 2006. ISSN 10155759. doi: 10.1027/1015-5759.22.4.225. 76 H. Bradbury and T. M. Nelson. Transitivity and the patterns of children’s pref- erences. Developmental Psychology, 10(1):55–64, 1974. ISSN 0012-1649. doi: 10.1037/h0035538. URL http://content.apa.org/journals/dev/10/1/55. D. H. Brainard. The psychophysics toolbox. Spatial vision, 10:433–436, 1997. M. Brand and H. J. Markowitsch. Aging and decision-making: A neurocognitive per- spective. Gerontology, 56(3):319–324, 2010. ISSN0304324X. doi: 10.1159/000248829. T. S. Braver, J. D. Cohen, L. E. Nystrom, J. Jonides, E. E. Smith, and D. C. Noll. A parametric study of prefrontal cortex involvement in human working memory. Neu- roImage, 5(1):49–62, 1997. ISSN 1053-8119. doi: 10.1006/nimg.1996.0247. I. Brocas, T. D. Combs, J. D. Carillo, and N. Kodaverdian. Consistency in Simple vs . Complex Choices over the Life Cycle. Pre-press, 2016. S. G. Bronars. the Power of Nonparametric Tests of Preference Maximiza- tion. Econometrica, 55(3):693–698, 1987. ISSN 0012-9682. doi: 10.2307/ 1913608. URL http://search.ebscohost.com/login.aspx?direct=true{\&}db= bth{\&}AN=6849888{\&}site=ehost-live{\&}scope=site. S. Bruyneel, L. Cherchye, S. Cosaert, B. De Rock, and S. Dewitte. Are the smart kids more rational? CES - Discussion paper series DPS12.16, (December):1– 17, 2012. URL https://lirias.kuleuven.be/bitstream/123456789/370786/1/ DPS1216.pdf. P. E. Bryant and T. Trabasso. Transitive inferences and memory in young children. Nature, 232:456–458, 1971. ISSN 0028-0836. doi: 10.1038/232456a0. D. R. Burghart, P. W. Glimcher, and S. C. Lazzaro. An expected utility maximizer walks into a bar... Journal of Risk and Uncertainty, 46(3):215–246, 2013. ISSN 08955646. doi: 10.1007/s11166-013-9167-7. N. Camille, C. A. Gri ths, K. Vo, L. K.Fellows, and J. W. Kable. Ventromedial frontal lobe damage disrupts value maximization in humans. The Journal of Neuroscience, 31(20):7527–7532, 2011. M. Camus, N. Halelamien, H. Plassmann, S. Shimojo, J. O’Doherty, C. Camerer, and A. Rangel. Repetitive transcranial magnetic stimulation over the right dorsolateral prefrontal cortex decreases valuations during food choices. European Journal of Neu- roscience, 30(10):1980–1988, 2009. ISSN 0953816X. doi: 10.1111/j.1460-9568.2009. 06991.x. A. W. Cappelen, S. Kariv, E. Ø. Sørensen, and B. Tungodden. Is there a development gap in rationality ? Econometrica, (March):1–27, 2014. 77 K. A. Cappell, L. Gmeindl, and P. A. Reuter-Lorenz. Age di↵ erences in prefontal recruitment during verbal working memory maintenance depend on memory load. Cortex, 46(4):462–473, 2010. ISSN00109452. doi: 10.1016/j.cortex.2009.11.009. URL http://dx.doi.org/10.1016/j.cortex.2009.11.009. S. Carlson, S. Martinkauppi, P. R¨ am¨ a, E. Salli, A. Korvenoja, and H. J. Aronen. Distri- butionofcorticalactivationduringvisuospatialn-backtasksasrevealedbyfunctional magnetic resonance imaging. Cerebral cortex, 8:743–752, 1998. ISSN 1047-3211. doi: 10.1093/cercor/8.8.743. L. L. Carstensen and J. A. Mikels. At the Intersection of Emotion and Cognition. Cur- rentDirectionsinPsychologicalScience(Wiley-Blackwell),14(3):117–121,2005. ISSN 09637214. doi: 10.1111/j.0963-7214.2005.00348.x. URL 10.1111/j.0963-7214. 2005.00348.x. M. Castillo, D. Dickinson, and R. Petrie. Sleepiness, Choice Consistency, and Risk Preferences. Institute for the Study of Labor (IZA), (8709), 2014. URL http:// mason.gmu.edu/{ ~ }rpetrie1/Sleepy{\_}GARP{\_}June2014.pdf. E. Castle, N. I. Eisenberger, T. E. Seeman, W. G. Moons, I. a. Boggero, M. S. Grin- blatt, and S. E. Taylor. Neural and behavioral bases of age di↵ erences in per- ceptions of trust. Proceedings of the National Academy of Sciences of the United States of America, 109(51):20848–52, 2012. ISSN 1091-6490. doi: 10.1073/pnas. 1218518109. URL http://www.pubmedcentral.nih.gov/articlerender.fcgi? artid=3529090{\&}tool=pmcentrez{\&}rendertype=abstract. D. M. Cerella, John; Poon, Leonard W.; Williams. Age and the complexity Hypothesis. Aging in the 1980s: Psychological issues, pages 332–340, 1980. B. G. Charness and M.-c. Villeval. Cooperation and Competition in Intergenerational Experiments in the Field and the Laboratory. The American Economic Review, 99 (3):956–978, 2009. V. S. Chib, A. Rangel, S. Shimojo, and J. P. O’Doherty. Evidence for a common representationofdecisionvaluesfordissimilargoodsinhumanventromedialprefrontal cortex. The Journal of neuroscience, 29(39):12315–12320, 2009. ISSN 0270-6474. doi: 10.1523/JNEUROSCI.2575-09.2009. S. Choi, R. Fisman, D. Gale, and S. Kariv. Consistency and Heterogeneity of Individual BehaviorunderUncertainty. TheAmericanEconomicReview,97(5):1921–1938,2007. S. Choi, S. Kariv, W. M¨ uller, and D. Silverman. Who Is ( More ) Rational ? American Economic Review, 104(6):1518–1550, 2014. 78 K. Christo↵ , V. Prabhakaran, J. Dorfman, Z. Zhao, J. K. Kroger, K. J. Holyoak, and J. D. Gabrieli. Rostrolateral prefrontal cortex involvement in relational integration during reasoning. NeuroImage, 14(5):1136–1149, 2001. ISSN 1053-8119. doi: 10. 1006/nimg.2001.0922. J.A.ClitheroandA.Rangel. Combiningresponsetimesandchoicedatausinganeuroe- conomic model of the decision process improves out-of-sample predictions. Quarterly Journal of Economics, 91125:3, 2013. J. D. Cohen, S. D. Forman, T. S. Braver, B. J. Casey, D. Servan-Schreiber, and D. C. Noll. Activation of the prefrontal cortex in a nonspatial working memory task with functional MRI., 1994. ISSN 1065-9471. URL http://www.ncbi.nlm.nih.gov/ pubmed/9322207. J. D. Cohen, W. M. Perlstein, T. S. Braver, L. E. Nystrom, D. C. Noll, J. Jonides, and E. E. Smith. Temporal dynamics of brain activation during a working memory task.pdf, 1997. ISSN 0028-0836. J.Cox. OnTestingtheUtilityHypothesis. The Economic Journal, 107(443):1054–1078, 1997. R. W. Cox. AFNI: Software for Analysis and Visualization of Functional Magnetic Resonance Neuroimages. Computers and Biomedical Research, 29(3):162–173, 1996. ISSN 00104809. doi: 10.1006/cbmr.1996.0014. URL http://www.sciencedirect. com/science/article/pii/S0010480996900142. R. W. Cox and J. S. Hyde. Software tools for analysis and visualization of fMRI data. Nuclear Magnetic Resonance in Biomedicine, 10:171–178, 1997. ISSN 0952-3480. doi: 10.1002/(SICI)1099-1492(199706/08)10:4/5h171::AID-NBM453i3.0.CO;2-L. W. Crain. Theories of Development: Concepts and Applications. 6 edition, 2015. ISBN 9781317343219. C. E. Curtis and M. D’Esposito. Persistent activity in the prefrontal cortex during working memory. Trends in Cognitive Sciences, 7(9):415–423, 2003. ISSN 13646613. doi: 10.1016/S1364-6613(03)00197-9. A. M. Dale. Optimal experimental design for event-related fMRI. Human Brain Map- ping, 8(2-3):109–114, 1999. ISSN 1065-9471. doi: 10.1002/(SICI)1097-0193(1999)8: 2/3<109::AID-HBM7>3.0.CO;2-W. M. C. Davidson, D. Amso, L. C. Anderson, and A. Diamond. Development of cognitive control and executive functions from 4 to 13 years: Evidence from manipulations of memory, inhibition, and task switching. Neuropsychologia, 44(11):2037–2078, 2006. ISSN 00283932. doi: 10.1016/j.neuropsychologia.2006.02.006. 79 C. E. Davis, J. D. Hauf, D. Q. Wu, and D. E. Everhart. Brain function with complex decision making using electroencephalography. International Journal of Psychophysi- ology,79(2):175–183,2011. ISSN01678760. doi: 10.1016/j.ijpsycho.2010.10.004. URL http://dx.doi.org/10.1016/j.ijpsycho.2010.10.004. B. De Martino, S. M. Fleming, N. Garrett, and R. J. Dolan. Confidence in value-based choice. Nature Neuroscience, 16(1):105–110, 2013. ISSN 1097-6256. doi: 10.1038/nn. 3279. URL http://www.nature.com/doifinder/10.1038/nn.3279. S. de Wit, P. R. Corlett, M. R. Aitken, A. Dickinson, and P. C. Fletcher. Di↵ erential engagement of the ventromedial prefrontal cortex by goal-directed and habitual behavior toward food pictures in humans. The Journal of neuroscience : the o cial journal of the Society for Neuroscience, 29 (36):11330–8, 2009. ISSN 1529-2401. doi: 10.1523/JNEUROSCI.1639-09. 2009. URL http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid= 3443853{\&}tool=pmcentrez{\&}rendertype=abstract. M. Dean and D. Martin. Measuring Rationality with the Minimum Cost of Revealed Preference Violations. Mimeo Brown University, pages 1–27, 2014. ISSN 0034-6535. doi: 10.1162/REST a 00542. R. Deichmann, J. A. Gottfried, C. Hutton, and R. Turner. Optimized EPI for fMRI studiesoftheorbitofrontalcortex. NeuroImage, 19(2):430–441, 2003. ISSN10538119. doi: 10.1016/S1053-8119(03)00073-9. J. D. Demb, J. B., Desmond, J. E., Wagner, A. D., Vaidya, C. J., Glover, G. H., and Gabrieli. Semantic encoding and retrieval in the left inferior prefrontal - cortex: a functional MRI study of task di culty and process specificity. Journal of Neuro- science,, 15(9):5870–5878, 1995. M. Desco, F. J. Navas-Sanchez, J. Sanchez-Gonz??lez, S. Reig, O. Robles, C. Franco, J. A. Guzm??n-De-Villoria, P. Garc??a-Barreno, and C. Arango. Mathematically gifted adolescents use more extensive and more bilateral areas of the fronto-parietal network than controls during executive functioning and fluid reasoning tasks. Neu- roImage, 57(1):281–292, 2011. ISSN 10538119. doi: 10.1016/j.neuroimage.2011.03. 063. URL http://dx.doi.org/10.1016/j.neuroimage.2011.03.063. M. Donaldson. Conservation - What is the question.pdf. British Journal of Psychology, 23(2):199, 1982. A.Dove, S.Pollmann, T.Schubert, C.J.Wiggins, andD.YvesVonCramon. Prefrontal cortex activation in task switching: An event-related fMRI study. Cognitive Brain Research, 9(1):103–109, 2000. ISSN 09266410. doi: 10.1016/S0926-6410(99)00029-4. URL http://dx.doi.org/10.1016/S0926-6410(99)00029-4. 80 I. Dror, M. Katona, and K. Mungur. Age Di↵ erences in Decision Making: To Take a Risk or Not? Gerontology, 44(2):67–71, 1998. ISSN 0304- 324X. URL citeulike-article-id:7469855$\backslash$nhttp://users.ecs. soton.ac.uk/id/GERagedecisions.pdf. F. Echenique, S. Lee, and M. Shum. The Money Pump as a Measure of Revealed Preference Violations. Journal of Political Economy, 119(6):1201–1223, 2011. C. Engel. Dictator games: A meta study. Experimental Economics, 14(4):583–610, 2011. ISSN 13864157. doi: 10.1007/s10683-011-9283-7. R. W. Engle, S. W. Tuholski, J. E. Laughlin, and A. R. A. Conway. Working Memory , Short-Term Memory , and General Fluid Intelligence : A Latent-Variable Approach. Journal of Experimental Psychology, 128(3):309–331, 1999. F. Esposito, A. Bertolino, T. Scarabino, V. Latorre, G. Blasi, T. Popolizio, G. Tedeschi, S. Cirillo, R. Goebel, and F. Di Salle. Independent component model of the default- mode brain function: Assessing the impact of active thinking. Brain Research Bul- letin, 70(4-6):263–269, 2006. ISSN 03619230. doi: 10.1016/j.brainresbull.2006.06.012. E. Fehr, U. Fischbacher, and B. V. Rosenbladt. A nation-wide laboratory: Examining trust and trustworthiness by integrating behavioral experiments into representative surveys. Schmollers Jahrbuch, 122:519–542, 2003. ISSN 1556-5068. doi: 10.2139/ ssrn.385120. URL http://www.econstor.eu/handle/10419/20527. E. Fehr, H. Bernhard, and B. Rockenbach. Egalatarianism in young children. Nature, 454(28):1079–1084, 2008. L. K. Fellows. Orbitofrontal contributions to value-based decision making: Evidence fromhumanswithfrontallobedamage. Annals of the New York Academy of Sciences, 1239(1):51–58, 2011. ISSN 00778923. doi: 10.1111/j.1749-6632.2011.06229.x. L. K. Fellows and M. J. Farah. The role of ventromedial prefrontal cortex in decision making: Judgment under uncertainty or judgment per se? Cerebral Cortex, 17(11): 2669–2674, 2007. ISSN 10473211. doi: 10.1093/cercor/bhl176. P. F. Fevrier and M. Visser. A Study of Consumer Behavior Using Laboratory Data. Experimental Economics, 7:93–114, 2004. M. L. Finucane, P. Slovic, J. H. Hibbard, E. Peters, and C. K. Mert. Aging and decision-making competence : an analysis of comprehension and consistency Skills in OlderversusYoungerAdultsConsideringHealth-planOptions. Journal of Behavioral Decision Making, 164(February):141–164, 2002. 81 M. L. Finucane, C. K. Mertz, P. Slovic, and E. S. Schmidt. Task complexity and older adults’ decision-making competence. Psychology and aging, 20(1):71–84, 2005. ISSN 0882-7974. doi: 10.1037/0882-7974.20.1.71. R.Fisman,S.Kariv,andD.Markovits.IndividualPreferencesforGiving.TheAmerican Economic Review, 97(5):1858–1876, 2007. T. H. B. FitzGerald, B. Seymour, and R. J. Dolan. The Role of Human Orbitofrontal Cortex in Value Comparison for Incommensurable Objects. Journal of Neuroscience, 29(26):8388–8395, 2009. ISSN 0270-6474. doi: 10.1523/JNEUROSCI.0717-09.2009. URL http://www.jneurosci.org/cgi/doi/10.1523/JNEUROSCI.0717-09.2009. F. Fregni, F. Orsati, W. Pedrosa, S. Fecteau, F. A. M. Tome, M. A. Nitsche, T. Mecca, E. C. Macedo, A. Pascual-Leone, and P. S. Boggio. Transcranial direct current stim- ulation of the prefrontal cortex modulates the desire for specific foods. Appetite, 51 (1):34–41, 2008. ISSN 01956663. doi: 10.1016/j.appet.2007.09.016. K. J. Friston, W. D. Penny, and D. E. Glaser. Conjunction revisited. NeuroImage, 25 (3):661–667, 2005. ISSN 10538119. doi: 10.1016/j.neuroimage.2005.01.013. S. E. Gathercole, S. J. Pickering, B. Ambridge, and H. Wearing. The Structure of Working Memory From 4 to 15 Years of Age. Developmental Psychology, 40(2):177– 190, 2004. ISSN0012-1649. doi: 10.1037/0012-1649.40.2.177. URLhttp://doi.apa. org/getdoi.cfm?doi=10.1037/0012-1649.40.2.177. D. C. Geary. Origin of Mind: Evolution of Brain, Cognition, and General Intelligence. page 460, 2005. F. I. M. Gick, Mary L; Morris, Robin G; Craik. Task Complexity and Age Di↵ erences in Working Memory. Memory & Cognition, 16(4):353 – 361, 1988. V. Goel, B. Gold, S. Kapur, and S. Houle. The seats of reason? An imag- ing study of deductive and inductive reasoning. Neuroreport, 8(5):1305– 1310, 1997. ISSN 0959-4965. doi: 10.1097/00001756-199703240-00049. URL http://ovidsp.ovid.com/ovidweb.cgi?T=JS{\&}CSC=Y{\&}NEWS=N{\&}PAGE= fulltext{\&}D=ovftc{\&}AN=00001756-199703240-00049. T. E. Goldberg, K. F. Berman, K. Fleming, J. Ostrem, J. D. Van Horn, G. Esposito, V. S. Mattay, J. M. Gold, and D. R. Weinberger. Uncoupling cognitive workload and prefrontal cortical physiology: a PET rCBF study. NeuroImage, 7(4 Pt 1):296–303, 1998. ISSN 1053-8119. doi: 10.1006/nimg.1998.0338. K. Gorgolewski, C. D. Burns, C. Madison, D. Clark, Y. O. Halchenko, M. L. Waskom, and S. S. Ghosh. Nipype: a flexible, lightweight and extensible neuroimaging data processing framework in python. Front Neuroinform, 5, 2011. ISSN 1662-5196. doi: 10.3389/fninf.2011.00013. URL http://dx.doi.org/10.3389/fninf.2011.00013. 82 R. L. Gould, R. G. Brown, A. M. Owen, D. H. Ffytche, and R. J. Howard. fMRI BOLD response to increasing task di culty during successful paired associates learning. NeuroImage, 20(2):1006–1019, 2003. ISSN 10538119. doi: 10.1016/S1053-8119(03) 00365-3. C. L. Grady, M. V. Springer, D. Hongwanishkul, a. R. McIntosh, and G. Winocur. Age-related changes in brain activity across the adult lifespan. Journal of cognitive neuroscience, 18:227–241, 2006. ISSN 0898-929X. doi: 10.1162/089892906775783705. URL http://www.ncbi.nlm.nih.gov/pubmed/16494683. J. R. Gray, C. F. Chabris, and T. S. Braver. Neural mechanisms of general fluid intelli- gence. Nature neuroscience,6(3):316–22,2003. ISSN1097-6256. doi: 10.1038/nn1014. URL http://www.ncbi.nlm.nih.gov/pubmed/12592404. J. D. Greene, L. E. Nystrom, A. D. Engell, J. M. Darley, and J. D. Cohen. The neural bases of cognitive conflict and control in moral judgment. Neuron, 44(2):389–400, 2004. ISSN 08966273. doi: 10.1016/j.neuron.2004.09.027. M. D. Greicius, B. Krasnow, A. L. Reiss, and V. Menon. Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. PNAS, 100(1):253– 258, 2003. ISSN 00278424. doi: 10.1073/pnas.0135058100\r0135058100[pii]. URL http://www.ncbi.nlm.nih.gov/pubmed/12506194$\backslash$nPM:12506194. W.T. Harbaughand K.Krause. Children’sContributions inPublic Good Experiments: The Development of Altruistic and Free-riding Behaviors. Economic Inquiry, 38(1): 95–109, 2000. W. T. Harbaugh, K. Krause, and T. R. Berry. GARP for Kids : On the Development of Rational Choice Behavior. The American Economic Review, 91(5):1539–1545, 2001. W. T. Harbaugh, K. Krause, and L. Vesterlund. Risk Attitudes of Children and Adults : Choices Over Small and Large Probability Gains and Losses. Experimental Eco- nomics, 5(1):53–84, 2002. ISSN 1386-4157. doi: 10.1023/A:1016316725855. URL http://www.springerlink.com/index/KJ50QLU9DTA7WFL9.pdf. T. A. Hare, J. P. O’Doherty, C. F. Camerer, W. Schultz, and A. Rangel. Dissociating the Role of the Orbitofrontal Cortex and the Striatum in the Computation of Goal Values and Prediction Errors. The Journal of Neuroscience, 28(22):5623–5630, 2008. T. A. Hare, A. Rangel, and C. F. Camerer. Self-control in decision-making involves modulation of the vmPFC valuation system. Science, 324(5927):646–8, 2009. ISSN 1095-9203. doi: 10.1126/science.1168450. URL http://www.ncbi.nlm.nih.gov/ pubmed/19407204. 83 T. a. Hare, J. Malmaud, and A. Rangel. Focusing attention on the health aspects of foods changes value signals in vmPFC and improves dietary choice. The Journal of neuroscience : the o cial journal of the Society for Neuroscience, 31(30):11077– 87, 2011. ISSN 1529-2401. doi: 10.1523/JNEUROSCI.6383-10.2011. URL http: //www.ncbi.nlm.nih.gov/pubmed/21795556. A. Harris, T. Hare, and A. Rangel. Temporally Dissociable Mechanisms of Self-Control: Early Attentional Filtering Versus Late Value Modulation. Journal of Neuroscience, 33(48):18917–18931,2013. ISSN0270-6474. doi: 10.1523/JNEUROSCI.5816-12.2013. URL http://www.jneurosci.org/cgi/doi/10.1523/JNEUROSCI.5816-12.2013. B. G. W. Harrison, M. I. Lau, and M. B. Williams. Estimating Individual Discount Rates in Denmark : A Field Experiment. The American Economic Review, 92(5): 1606–1617, 2002. D. E. Henninger, D. J. Madden, and S. A. Huettel. Processing speed and memory mediate age-related di↵ erences in decision making. Psychology and aging, 25(2):262– 70, 2010. ISSN 1939-1498. doi: 10.1037/a0019096. URL http://www.scopus.com/ inward/record.url?eid=2-s2.0-77953982768{\&}partnerID=tZOtx3y1. A.Henri-Bhargava,A.Simioni,andL.K.Fellows.Ventromedialfrontallobedamagedis- ruptstheaccuracy,butnotthespeed,ofvalue-basedpreferencejudgments. Neuropsy- chologia, 50(7):1536–1542, 2012. ISSN 00283932. doi: 10.1016/j.neuropsychologia. 2012.03.006. URL http://dx.doi.org/10.1016/j.neuropsychologia.2012.03. 006. E. C. Hinton, S. Dymond, U. von Hecker, and C. J. Evans. Neural correlates of re- lational reasoning and the symbolic distance e↵ ect: Involvement of parietal cortex. Neuroscience, 168(1):138–148, 2010. ISSN 03064522. doi: 10.1016/j.neuroscience. 2010.03.052. URL http://dx.doi.org/10.1016/j.neuroscience.2010.03.052. H. S. Houthakker. Revealed Preference and the Utility Function. Economica, 17(66): 159–174, 1950. J. Houtman, Martijn and Maks. Determining all maximal data subsets consistent with revealed preference. Kwantitatieve methoden, 19:89—-104, 1985. C. A. Hutcherson, H. Plassmann, J. J. Gross, and A. Rangel. Cognitive Regula- tion during Decision Making Shifts Behavioral Control between Ventromedial and Dorsolateral Prefrontal Value Systems. Journal of Neuroscience, 32(39):13543– 13554, 2012. ISSN 0270-6474. doi: 10.1523/JNEUROSCI.6387-11.2012. URL http://www.jneurosci.org/cgi/doi/10.1523/JNEUROSCI.6387-11.2012. S. M. Jaeggi, M. Buschkuehl, J. Jonides, and W. J. Perrig. Improving fluid intelligence with training on working memory. Proceedings of the National Academy of Sciences, 105(19):6829–6833, 2008. ISSN 0027-8424. doi: 10.1073/pnas.0801268105. 84 M. Jenkinson, C. F. Beckmann, T. E. J. Behrens, M. W. Woolrich, and S. M. Smith. Fsl. NeuroImage, 62(2):782–790, 2012. ISSN 10538119. doi: 10.1016/j.neuroimage. 2011.09.015. T. Kahnt, J.Heinzle, S. Q. Park, and J.D. Haynes. Decodingdi↵ erent rolesfor vmPFC and dlPFC in multi-attribute decision making. NeuroImage, 56(2):709–715, 2011. ISSN 10538119. doi: 10.1016/j.neuroimage.2010.05.058. URL http://dx.doi.org/ 10.1016/j.neuroimage.2010.05.058. M. J. Kane and R. W. Engle. The role of prefrontal cortex in working-memory ca- pacity, executive attention, and general fluid intelligence: An individual-di↵ erences perspective. Psychonomic Bulletin & Review, 9(4):637–671, 2002. S. Kim and L. Hasher. The attraction e↵ ect in decision making: superior performance by older adults. The Quarterly journal of experimental psychology, 58A(1):120–33, 2005. ISSN 0272-4987. doi: 10.1080/02724980443000160. H. Kondo, N. Osaka, and M. Osaka. Cooperation of the anterior cingulate cortex and dorsolateralprefrontalcortexforattentionshifting. NeuroImage,23(2):670–679,2004. ISSN 10538119. doi: 10.1016/j.neuroimage.2004.06.014. S. Kovalchik, C. F. Camerer, D. M. Grether, C. R. Plott, and J. M. Allman. Aging anddecisionmaking: Acomparisonbetweenneurologicallyhealthyelderlyandyoung individuals. JournalofEconomicBehaviorandOrganization,58(1):79–94,2005.ISSN 01672681. doi: 10.1016/j.jebo.2003.12.001. N. Kriegeskorte, W. K. Simmons, P. S. F. Bellgowan, and C. I. Baker. Circular analysis in systems neuroscience: the dangers of double dipping., 2009. ISSN 1097-6256. J. K. Kroger, F. W. Saab, C. L. Fales, S. Y. Bookheimer, M. S. Cohen, and K. J. Holyoak. Recruitment of Anterior Dorsolateral Prefrontal Cortex in Human Reason- ing: A Parametric Study of Relational Complexity. Cerebral Cortex, 12(5):477–485, 2002. F. Krueger, M. V. Spampinato, M. Pardini, S. Pajevic, J. N. Wood, G. H. Weiss, S. Landgraf, and J. Grafman. Integral calculus problem solving: an fMRI investigation. Neuroreport, 19(11):1095–1099, 2008. ISSN 0959-4965. doi: 10.1097/WNR.0b013e328303fd85. URL {\textless}GotoISI{\textgreater}:// 000257728700003. D. J. Levy and P. W. Glimcher. The root of all value: A neural common currency for choice. Current Opinion in Neurobiology, 22(6):1027–1038, 2012. ISSN 18736882. doi: 10.1016/j.conb.2012.06.001. URL http://dx.doi.org/10.1016/j.conb.2012. 06.001. 85 S.Lewandowsky,K.Oberauer,L.-X.Yang,andK.H.Ecker,Ullrich. Aworkingmemory test battery for MATLAB. Behavioral Research Methods, 42(2):571–585, 2010. ISSN 1554-351X. doi: 10.3758/BRM.42.2.571. S. Lichtenstein and P. Slovic. Response-induced reversals of preference in gambling: An extendedreplicationinLasVegas. Journal of Experimental Psychology, 101(1):16–20, 1973. ISSN 0022-1015. doi: 10.1037/h0035472. J. A. List and D. L. Millimet. The Market: Catalyst for Rationality and Filter of Irrationality. The BE Journal of Economic Analysis & Policy, 8(1):Article 47, 2008. ISSN 1935-1682. doi: 10.2202/1935-1682.2115. S. Luo, G. Ainslie, D. Pollini, L. Giragosian, and J. R. Monterosso. Moderators of the association between brain activation and farsighted choice. NeuroImage, 59(2): 1469–1477, 2011. A. W. Macdonald, J. D. Cohen, V. A. Stenger, and S. Carter. Dissociating the Role of the Dorsolateral Prefrontal and Anterior Cingulate Cortex in Cognitive Control. American Association for the Advancement of Science, 288(5472):1835–1838, 2000. R. Mata, A. K. Josef, G. R. Samanez-Larkin, and R. Hertwig. Age di↵ erences in risky choice: A meta-analysis. Annals of the New York Academy of Sciences, 1235(1): 18–29, 2011. ISSN 00778923. doi: 10.1111/j.1749-6632.2011.06200.x. M. Mather. The emotion paradox in the aging brain. Annals of the New York Academy of Sciences, 1251(1):33–49, 2012. ISSN 00778923. doi: 10.1111/j.1749-6632.2012. 06471.x. M. Mather and L. L. Carstensen. Aging and motivated cognition: The positivity e↵ ect in attention and memory. Trends in Cognitive Sciences, 9(10):496–502, 2005. ISSN 13646613. doi: 10.1016/j.tics.2005.08.005. M. Mather and L. Nielsen. Emerging perspectives in social neuroscience and neuroe- conomics of aging. Social Cognitive and A↵ ective Neuroscience, 6(2):149–164, 2011. ISSN 17495016. doi: 10.1093/scan/nsr019. A. Mattei. Full-scale real tests of consumer behavior using experimental data. Journal of Economic Behavior & Organization, 43(4):487–497, 2000. ISSN 01672681. doi: 10.1016/S0167-2681(00)00132-3. B. R. McFadden, J. L. Lusk, J. M. Crespi, J. B. C. Cherry, L. E. Martin, R. L. Aupperle, and A. S. Bruce. Can neural activation in dorsolateral prefrontal cor- tex predict responsiveness to information? An application to egg production sys- tems and campaign advertising. PloS one, 10(5):e0125243, 2015. ISSN 1932-6203. doi: 10.1371/journal.pone.0125243. URL http://journals.plos.org/plosone/ article?id=10.1371/journal.pone.0125243. 86 D. McFadden. Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics, chapter 4, pages 105–142. 1973. ISBN 0127761500. doi: 10.1108/ eb028592. D. G. McLaren, M. L. Ries, G. Xu, and S. C. Johnson. A generalized form of context- dependent psychophysiological interactions (gPPI): A comparison to standard ap- proaches. NeuroImage, 61(4):1277–1286, 2012. ISSN 10538119. doi: 10.1016/j. neuroimage.2012.03.068. URL http://dx.doi.org/10.1016/j.neuroimage.2012. 03.068. P. N. C. Mohr, S. C. Li, and H. R. Heekeren. Neuroeconomics and aging: Neuro- modulation of economic decision making in old age. Neuroscience and Biobehavioral Reviews, 34(5):678–688, 2010. ISSN 01497634. doi: 10.1016/j.neubiorev.2009.05.010. URL http://dx.doi.org/10.1016/j.neubiorev.2009.05.010. J.R.Monterosso, G.Ainslle, J.Xu, X.Cordova, C.P.Domier, andE.D.London. Fron- toparietal cortical activity of methamphetamine-dependent and comparison subjects performing a delay discounting task. Human Brain Mapping, 28(5):383–393, 2007. ISSN 10659471. doi: 10.1002/hbm.20281. P. Nichelli, J. Grafman, P. Pietrini, D. Alway, J. C. Carton, and R. Miletich. Brain Activity in Chess Playing. Nature, 369(6477):191, 1994. ISSN 0028-0836. doi: 10. 1038/369191a0. URL {\textless}GotoISI{\textgreater}://A1994NM06700035. P. J. Olesen, H. Westerberg, and T. Klingberg. Increased prefrontal and parietal ac- tivity after training of working memory. Nature neuroscience, 7(1):75–9, 2003. ISSN 1097-6256. doi: 10.1038/nn1165. URL http://www.ncbi.nlm.nih.gov/pubmed/ 14699419. D.Osherson,D.Perani,S.Cappa,T.Schnur,F.Grassi,andF.Fazio. Distinctbrainloci in deductive versus probabilistic reasoning. Neuropsychologia, 36(4):369–376, 1998. ISSN 00283932. doi: 10.1016/S0028-3932(97)00099-7. D.G.Pelli. TheVideoToolboxsoftwareforvisualpsychophysics: transformingnumbers into movies. 10(4):437–443, 1997. M. Petrides. Frontal lobes and behaviour. Current Opinion in Neurobiology, 4(2): 207–211, 1994. ISSN 09594388. doi: 10.1016/0959-4388(94)90074-4. J. Piaget. Classes, relations et nombres: essai sur les groupement logistique et sur la reversibilite de la pense. Librairie Philosophique, 1942. J. Piaget. La psychologie de intelligence. Revue Philosophique de Louvain, 46(10): 225–227, 1948. J. Piaget, D. Elkind, and A. Tenzer. Six psychological studies. 1967. ISBN 0394704622. 87 T. Piccoli, G. Valente, D. E. J. Linden, M. Re, F. Esposito, A. T. Sack, and F. D. Salle. The default mode network and the working memory network are not anti-correlated during all phases of a working memory task. PLoS ONE, 10(4):1–16, 2001. ISSN 19326203. doi: 10.1371/journal.pone.0123354. H. Plassmann, J. O’Doherty, and A. Rangel. Orbitofrontal Cortex Encodes Willingness to Pay in Everyday Economic Transactions. Journal of Neuroscience, 27(37):9984– 9988, 2007. ISSN 0270-6474, 1529-2401. doi: 10.1523/JNEUROSCI.2131-07.2007. URL http://www.jneurosci.org/cgi/doi/10.1523/JNEUROSCI.2131-07.2007. J.-B. B. Pochon, R. Levy, J. B. Poline, S. Crozier, S. Leh´ ericy, B. Pillon, B. De- weer, D. Le Bihan, and B. Dubois. The Role of Dorsolateral Prefrontal Cortex in the Preparation of Forthcoming Actions: an fMRI Study. Cere- bral Cortex, 11(3):260–266, 2001. ISSN 14602199. doi: 10.1093/cercor/11.3. 260. URL http://www.ncbi.nlm.nih.gov/pubmed/11230097$\backslash$nhttp: //cercor.oxfordjournals.org/cgi/content/long/11/3/260. V. Prabhakaran, J. a. Smith, J. E. Desmond, G. H. Glover, and J. D. Gabrieli. Neural substrates of fluid reasoning: an fMRI study of neocortical activation during perfor- mance of the Raven’s Progressive Matrices Test. Cognitive psychology, 33(1):43–63, 1997. ISSN 0010-0285. doi: 10.1006/cogp.1997.0659. V. Prabhakaran, K. Narayanan, Z. Zhao, and J. D. Gabrieli. Integration of diverse information in working memory within the frontal lobe. Nature neuroscience, 3(1): 85–90, 2000. ISSN 1097-6256. doi: 10.1038/71156. URL http://www.ncbi.nlm. nih.gov/pubmed/10607400. C. J. Price and K. J. Friston. Cognitive conjunction: a new approach to brain activation experiments. NeuroImage, 5(4 Pt 1):261–70, 1997. ISSN 1053-8119. doi: 10.1006/nimg.1997.0269. URL http://www.sciencedirect.com/science/ article/pii/S105381199790269X. M. F. Rabinowitz, M. J. Grant, M. L. Howe, and C. Walsh. Reasoning in Middle Childhood: A Dynamic Model of Performance on Transitivity Tasks, 1994. ISSN 00220965. M. E. Raichle. The Brain’s Default Mode Network. Annual review of neuroscience, (April):413–427, 2015. ISSN 1545-4126. doi: 10.1146/annurev-neuro-071013-014030. URL http://www.ncbi.nlm.nih.gov/pubmed/25938726. M. E. Raichle, a. M. MacLeod, a. Z. Snyder, W. J. Powers, D. a. Gusnard, and G. L. Shulman. A default mode of brain function. Proceedings of the National Academy of Sciences of the United States of America, 98(2):676–682, 2001. ISSN 0027-8424. doi: 10.1073/pnas.98.2.676. 88 A.Rangel,C.Camerer,andP.R.Montague. Aframeworkforstudyingtheneurobiology of value-based decision making. Nature Reviews Neuroscience, 9(7):545–556, 2008. ISSN 1471-003X. doi: 10.1038/nrn2357. URL http://www.nature.com/doifinder/ 10.1038/nrn2357. A. Rangel, K. C. Armel, and A. Beaumol. The Computation of Decision Values in SimpleEconomicChoice.InNeuroeconomics: DecisionMakingandtheBrain: Second Edition, pages 0–36. 2013. ISBN 9780124160088. doi: 10.1016/B978-0-12-416008-8. 00008-5. J. Raven, J., Raven, J.C., and Court. Manual for Raven’s progressive matrices and vocabulary scales. 1998. N. Raz, U. Lindenberger, K. M. Rodrigue, K. M. Kennedy, D. Head, A. Williamson, C. Dahle, D. Gerstorf, and J. D. Acker. Regional brain changes in aging healthy adults: General trends, individual di↵ erences and modifiers. Cerebral Cortex, 15(11): 1676–1689, 2005. ISSN 10473211. doi: 10.1093/cercor/bhi044. D. Read and N. L. Read. Time discounting over the lifespan. Organizational Behavior and Human Decision Processes, 94(1):22–32, 2004. ISSN 07495978. doi: 10.1016/j. obhdp.2004.01.002. S. Rudorf and T. A. Hare. Interactions between Dorsolateral and Ventromedial Pre- frontal Cortex Underlie Context-Dependent Stimulus Valuation in Goal-Directed Choice. Journal of Neuroscience, 34(48):15988–15996, 2014. ISSN 0270-6474. doi: 10.1523/JNEUROSCI.3192-14.2014. URL http://www.jneurosci.org/cgi/doi/ 10.1523/JNEUROSCI.3192-14.2014. B.RypmaandM.D’Esposito. Isolatingtheneuralmechanismsofage-relatedchangesin human working memory. Nature neuroscience, 3(5):509–515, 2000. ISSN 1097-6256. doi: 10.1038/74889. P. A. Samuelson. A Note on the Pure Theory of Consumer’s Behaviour. Economica,5 (17):61–71, 1938. O. Simon, J. F. Mangin, L. Cohen, D. Le Bihan, and S. Dehaene. Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron, 33(3):475–487, 2002. ISSN 08966273. doi: 10.1016/S0896-6273(02)00575-5. R. Sippel. An experiment on the pure theory of consumer’s behaviour. Economic Journal, 107(444):1431–1444, 1997. ISSN 00130427. doi: Doi10.1111/1468-0297. 00231. URL {\textless}GotoISI{\textgreater}://WOS:A1997YC93200007. J. Smedslund. Transitivity of preference patterns as seen by preschool children. Scan- dinavian journal of psychology, 1(1):49–54, 1960. 89 S. M. Smith, M. Jenkinson, M. W. Woolrich, C. F. Beckmann, T. E. J. Behrens, H. Johansen-Berg, P. R. Bannister, M. De Luca, I. Drobnjak, D. E. Flitney, R. Niazy, J. Saunders, J. Vickers, Y. Zhang, N. De Stefano, J. M. Brady, and P. M. Matthews. AdvancesinfunctionalandstructuralMRimageanalysisandimplementationasFSL. NeuroImage, 23(S1):208–219, 2004. S.M.Smith,P.T.Fox,K.L.Miller,D.C.Glahn,P.M.Fox,C.E.Mackay,N.Filippini, K. E. Watkins, R. Toro, A. R. Laird, and C. F. Beckmann. Correspondence of the brain’sfunctionalarchitectureduringactivationandrest. Proceedings of the National Academy of Sciences of the United States of America, 106(31):13040–5, 2009. ISSN 1091-6490. doi: 10.1073/pnas.0905267106. URL http://www.ncbi.nlm.nih.gov/ pubmed/19620724. P. Sokol-Hessner, C. Hutcherson, T. Hare, and A. Rangel. Decision value computation in DLPFC and VMPFC adjusts to the available decision time. European Journal of Neuroscience, 35(7):1065–1074, 2012. ISSN 0953816X. doi: 10.1111/j.1460-9568. 2012.08076.x. M. Sutter and M. G. Kocher. Trust and trustworthiness across di↵ erent age groups. Games and Economic Behavior, 59(2):364–382, 2007. ISSN 08998256. doi: 10.1016/ j.geb.2006.07.006. K. Tentori, D. Osherson, L. Hasher, and C. May. Wisdom and aging: Irrational prefer- encesincollegestudentsbutnotolderadults. Cognition, 81(3), 2001. ISSN00100277. doi: 10.1016/S0010-0277(01)00137-8. K. E. Train. Discrete Choice Methods with Simulation. 2003. ISBN 9780511805271. doi: 10.1017/CBO9780511805271. URL http://books.google.com/books?hl= en{\&}lr={\&}ie=UTF-8{\&}id=F-{\_}gYALlfR4C{\&}oi=fnd{\&}pg=PA1{\&}dq= A+Method+of+Simulated+Moments+for+Estimation+of+Discrete+Response+ Models+without+Numerical+Integration{\&}ots=9DWej7aXID{\&}sig= KarLb58YdwvJ{\_}DH83Vg2RjimI3k$\backslash$nhttp://ebooks.cambridg. H. R. Varian. The Nonparametric Approach to Demand Analysis. Econometrica, 50 (4):945–973, 1982. H. R. Varian. Goodness-of-fit in optimizing models. Journal of Econometrics, 14 (October 1979):49–68, 1990. M. S. Visser and M. R. Roelofs. Heterogeneous preferences for altruism: Gender and personality, social status, giving and taking. Experimental Economics, 14(4):490—- 506, 2011. M. S. Visser, W. T. Harbaugh, and N. H. Mocan. An Experimental Test of Criminal Behavior Among Juveniles and Young Adults. (12507), 2006. doi: 10.3386/w12507. URL http://www.nber.org/papers/w12507. 90 R. E. Wright. Aging, divided attention, and processing capacity. Journal of Geron- tololgy, 36(5):605–614, 1981. T. Yarkoni, R. A. Poldrack, T. E. Nichols, D. C. Van Essen, and T. D. Wager. Large- scale automated synthesis of human functional neuroimaging data. Nature Methods, 8(8):665–670, 2011. ISSN 1548-7091. doi: 10.1038/nmeth.1635. URL papers:// fd97edd0-de1d-401e-87f3-202830b99eeb/Paper/p14347. L. Zamarian, H. Sinz, E. Bonatti, N. Gamboz, and M. Delazer. Normal aging a↵ ects decisions under ambiguity, but not decisions under risk. Neuropsychology, 22(5):645– 657, 2008. ISSN 0894-4105. doi: 10.1037/0894-4105.22.5.645. 91 Appendix A Appendix A1. Example of direct violation in a triplet of trials of treatment S - 6 t a 12 t c 0 12 t b 12 t a 0 12 t c 12 t b 0 12 q 2 q 1 0 Figure A.1: Trials (a 12 vs. a 0 12 ), (b 12 vs. b 0 12 ), (c 12 vs. c 0 12 ) In the example of Figure A.1, no pair of trials satisfies condition (i) of Definition 1, so there cannot be a direct violation between any pair of trials. Suppose now that a 12 is chosen over a 0 12 , b 12 is chosen over b 0 12 and c 12 is chosen over c 0 12 .Since q a 0 x >q b x for all x and q b 0 x >q c x for all x,wehave a 12 a 0 12 b 12 b 0 12 c 12 .Since q c 0 x >q a x for all x, we have c 12 c 0 12 a 12 . This forms a contradiction to the maximization of monotonic and transitive preferences. 92 Notice that the key reason we have a direct violation between triplets of trials but not between any pair of trials is that q b 0 2 <q a 2 and q a 0 2 <q c 2 . This issue would not arise if, instead of a discrete number of alternatives we were to o↵ er subjects the entire budget set. Appendix A2. List of all food items (with portions) used in the experiment Almond (2); Barbecue popped potato chip (1); Cashew (2); Cheddar cracker (2); Mini cheese sandwich cracker (1); Citrus gum drop (2); Roasted gorgonzola cracker (2); Gummy bears (2); Popcorn (2); M&M (2); Dark chocolate peanut butter cup (1); Mini chocolate-covered pretzel (1); Mini Oreo (1); Onion-flavored corn snack, “Funyuns” (1); Peanut (3); Pistachio (2); Potato chip (1); Mini pretzel (1); Pretzel nugget (2); Sweet potato chip (1); Yogurt-covered raisin (1); Appendix A3. Individual analysis The aggregate results suggest that complexity a↵ ects the ability to make consistent choices di↵ erentially across individuals. E↵ ects are stronger among OA and may be attributable to declines in working memory. Yet, behavior is heterogeneous even in the OA group indicating that aging is either not a↵ ecting all subjects similarly or that some subjects are capable of developing strategies to remain consistent. A3.1. A random utility model (RUM) Inordertobetterunderstandindividualdi↵ erences, weestimatearandomutilitymodel (RUM) for each subject in each treatment. Specifically, in treatment S, each subject i in each trial o chooses between a bundle on the left (l) of the screen, denoted by BU l , 93 and a bundle on the right (r) of the screen, denoted by BU r . A decision is obtained by comparing the utility derived from each option. We assume that utility depends linearly on the observable quantities of the goods 1 and 2, as well as on a stochastic unobserved error component ✏ k i , k = l,r. Formally: u io (BU l )= i1 q l 1o + i2 q l 2o +✏ l i and u io (BU r )= i1 q r 1o + i2 q r 2o +✏ r i where q k jo is the quantity of good j = {1,2} in bundle k = {l,r} of trial o.The probability of individual i choosing option BU l in trial o is therefore: P l io =Pr h i1 q l 1o + i2 q l 2o +✏ l i > i1 q r 1o + i2 q r 2o +✏ r i i =Pr h ✏ r i ✏ l i < i1 (q l 1o q r 1o )+ i2 (q l 2o q r 2o ) i and P r io =1 P l io . We assume that error terms are i.i.d. and follow an extreme value dis- tribution: thecumulativedistributionfunctionoftheerrortermis F i (✏ k i )= exp( e ✏ k i ). Therefore, the probability that subject i chooses option BU l is the logistic function: P l io (q l 1o q r 1o ,q l 2o q r 2o )= 1 1+e ⇣ i1 (q l 1o q r 1o )+ i2 (q l 2o q r 2o ) ⌘. 94 For each individual i the parameters to estimate are i1 and i2 , which we achieve by maximum likelihood. 5 A similar model is estimated in treatment C. The bundle on the left is made of goods s and w while the bundle on the right is made of goods p and s. The utilities are now: u io (BU l )= is q l so + iw q l wo +✏ l i and u io (BU r )= ip q r po + is q r so +✏ r i and the probability that subject i chooses option BU l is the logistic function: 6 P l io (q l wo ,q l so q r so ,q r po )= 1 1+e ⇣ iw q l wo + is (q l so q r so ) ip q r po ⌘. We estimate the parameters for each individual in each treatment. We then predict the choice in each trial given the estimated parameters and we count the number of misclassified trials. Importantly, we find that misclassification rates in each treatment are strongly correlated with the number of violations (Pearson coe cient = .77 in treat- mentS and .77 in treatmentC). This suggests that the classification level of RUM is a 5 We obtain O observations. The log-likelihood is therefore xxxIB check subscript k (and other subscripts) in Log L xxxIB: logL ik = O X o=1 log h P l io (q l 1o q r 1o ,q l 2o q r 2o )1 l +[1 P l io (q l 1o q r 1o ,q l 2o q r 2o )][1 1 l ] i where 1 l =1ifBU l is chosen and 1 l =0ifBU r is chosen. 6 The log-likelihood is now xxxIB again check subscript k (and other subscripts) in Log L xxxIB: logL ik = O X o=1 log h P l io (q l wo ,q l so q r so ,q r po )1 l +[1 P l io (q l wo ,q l so q r so ,q r po )][1 1 l ] i 95 reliable proxy for GARP consistency: subjects who are not well predicted by the model are inconsistent. Finally, notice that RUM presupposes more errors when the di↵ erence inutilitybetweenthetwobundlesissmall, whichmeansthatitisalsorelatedtoseverity of violations. 7 It is therefore natural that we also find a significant correlation between severity of violations and misclassification rates (Pearson coe cient = .52 in treatment S and .32 in treatment C). A3.2. Clustering We then use RUM misclassification data to group individuals with the objective of finding common patterns of behavior. For each individual, we compute the percentage of misclassified trials given the maximum likelihood estimation of the RUM model in treatments S and C, respectively. Contrary to violation counts, these two percentages are comparable between treatments. They provide two interpretable measures related to, but not based on, violations that we can use to cluster our subjects. We consider a model-based clustering method to identify the clusters present in our population. We retain two measures: the % of RUM misclassifications in S, and the di↵ erence between the % of RUM misclassifications in C and the % of RUM misclassifications in S. We opt for this second measure (rather than simply % of RUM misclassifications in C) because of the importance of understanding the treatment e↵ ect between simple and complex choices. A wide array of heuristic clustering methods are commonly used, however they 7 To check the specification of the model, we ran a Probit regression of the probability of correct classification as a function of the absolute utility di↵ erence |BU r BU l |. As predicted by RUM, most subjects have positive coe cients (better classification when utility di↵ erences are large). Also, subjects with negative coe cients are those with highest number of violations, that is, those for which RUM is not well specified. Finally, as another robustness check, we correlated RUM misclassifications with GARP violations DC and IC separately, and obtained the same results. 96 usuallyrequirethenumberofclustersandtheclusteringcriteriontobesetex-anterather than endogenously optimized. Mixture models, on the other hand, treat each cluster as acomponentprobabilitydistribution. Thus, thechoicebetweennumbersofclustersand models can be made using Bayesian statistical methods (Fraley and Raftery, 2002). We implement our model-based clustering analysis with the Mclust package in R (Fraley and Raftery, 2006). We consider ten di↵ erent models with a maximum of nine clusters each, and determine the combination that yields the maximum Bayesian Information Criterion (BIC). For our data, the ellipsoidal, equal shape model that endogenously yields three clusters maximizes the BIC. Table A.1 provides summary statistics of the three clusters. The first two rows display the average percentage of RUM misclassifications in S and C by subjects in each cluster, the variables used for the clustering. The next two rows present the composition of YA and OA in each cluster. The last five rows summarize the average performance within each cluster in the consistency task (GARP violations) and the tests (WM and IQ). Clusters are ordered from smallest to largest in the percentage of misclassified observations. Cluster 1 is characterized by almost no misclassification inS and few inC.Cluster 2 also exhibits limited misclassifications in bothS andC (although more than cluster 1). Cluster 3 has substantial misclassifications in both treatments. The first surprising finding is the allocation of OA and YA across clusters. Given our previous results, one would expect more YA in cluster 1 and more OA in cluster 2. We find the reverse. Cluster 3 is a mix of subjects. 97 Cluster 1 Cluster 2 Cluster 3 % RUM misclassifications in S 3.2 (0.6) 16.2 (0.5) 36.5 (5.0) % RUM misclassifications in C 12.7 (1.4) 17.0 (1.2) 40.4 (5.3) Number of YA 13 30 7 Number of OA 20 15 10 Number of violations in S 1.3 (0.6) 3.6 (1.6) 48.1 (9.6) Number of violations in C 29.6 (9.7) 18.1 (6.3) 189.2 (47.0) Number of violations in A 1.6 (0.4) 0.9 (0.3) 4.7 (1.0) Working Memory test 173.3 (5.1) 187.0 (4.2) 169.8 (8.3) IQ test 9.8 (0.4) 10.2 (0.4) 9.2 (0.8) standard errors in parentheses Table A.1: Summary statistics by cluster. When we consider performance in the choice tasks and tests, we notice that cluster 3 stands out as a group of inconsistent subjects exhibiting a large number of GARP violations and low performance in WM and IQ tests. These subjects also fail our trivial trials much more frequently than the rest of the subjects. Not surprisingly, the vast majority of minimizers (6 in treatment S and 5 in treatment C) belong to this cluster. Clusters 1 and 2 are composed of relatively consistent subjects and di↵ er mostly in thewaytheirbehaviorcomparesbetweentreatments. IntreatmentS,subjectsincluster 1 are very well-classified and have almost no violations while subjects in cluster 2 are slightly more inconsistent. In treatment C, subjects in cluster 1 decrease significantly in their performance while subjects in cluster 2 remain more consistent. Overall, cluster 2 is a group of “consistently consistent” subjects. By contrast, subjects in cluster 1 are remarkably consistent in S but significantly less in C. Figure A.2 provides two di↵ erent representations of the three clusters. In the left graph, clusters 1, 2, and 3 are displayed according to the % of RUM misclassifications in 98 treatmentsSandC(rows1and2inTableA.1). 8 Intherightgraph, thesesamesubjects and clusters are represented based on a log transformation of the average number of violations in treatmentsS andC (rows 5 and 6 in Table A.1). Figure A.2: Cluster representation. Misclassified trials (left) and number of violations (right) in treatmentsS andC. xxx These figures need work, 1) we can barely see the di↵ erences in black and white print and 2) x- and y-axis should be of equal length xxx Clusters are clearly di↵ erentiated in the left graph. This is is not surprising since the variables are, up to a transformation, the ones used for grouping the individuals. The figure highlights the di↵ erencesacrossclustersemphasizedabove: smallpercentageofRUMmisclassifications in both treatments for cluster 1, slightly larger in S for cluster 2, and a substantial fraction of misclassifications for cluster 3 in both treatments. 8 Recall that the exact variables used to group the individuals are % of RUM misclassifications in S and di↵ erence between the % of RUM misclassifications inC andS. Our display helps visual clarity (both measures are between 0 and 100) while keeping the essence of the clustering. 99 More interestingly, the right graph also shows clear di↵ erences across clusters. Clus- ter 1 has (with a few exceptions) almost no violations in S and some in C,cluster2 has a more even distribution of violations between S and C than cluster 1, and cluster 3 is, again, an outlier in both types of violations. This reasonable mapping is quite remarkable given that subjects are not clustered on the basis of that variable. It sug- gests a tight relationship between classification by RUM and GARP violations. It also suggests that the transition from the simple to the complex situation is more di cult for individuals in cluster 1 than for those in cluster 2. We investigate this issue in more detail in the next section. Finally, we find that subjects in cluster 1 have significantly worse working memory scores than subjects in cluster 2 (p-value = .040); they also have lower IQ scores but the di↵ erence is not statistically significant. This suggests a relationship between working memory and the ability to remain consistent as the complexity of the task increases. A3.3. Simple choice rules The extreme degree of consistency and lack of misclassifications by cluster 1 subjects in treatment S (26 subjects out of 33 have zero violations), together with the fact that manyofthemareintheOApopulationandperformsignificantlyworseinCissomewhat puzzling. ExaminingthevalueestimatesoftheRUMmodel(the ij -coe cients)inmore detail, we find that for some subjects one value estimate inS and two value estimates in C are close to 0. These are subjects whose behavior is consistent with maximizing the quantityoftheirmostpreferreditem. Forsomeothersubjects, thevalueestimatesofall goods are almost identical to each other. These are subjects for whom goods are perfect 100 substitutes, so that their behavior is consistent with maximizing the total quantity in the bundle. These two choice strategies are clearly consistent with the maximization of monotonic and transitive preferences, resulting in high degrees of consistency. At the same time, subjects with these types of preferences do not need to perform sophisticated mental trade-o↵ s between items and, instead, can use simple choice rules. We therefore hypothesize that having these specific preferences may potentially explain why cluster 1 exhibits such an extremely high level of consistency in treatmentS. With this idea in mind, we construct two simple choice rules for subjects in clusters 1 and 2: H (for highest), where the subject maximizes the quantity of one of the items in the bundle (presumably, the one with highest value) andT (for total) where the subject maximizes the total quantity in the bundle (presumably because goods are perfect substitutes). We assign typeH (T)toasubjectif(i)theruleH (T) generates the same xxxIB the same or fewer??? xxxIB number of misclassifications as RUM and (ii) this number is smaller than 3 in treatmentS and smaller than 10 in treatmentC. These arbitrary thresholds are simply meant to reflect the nature of a quick and simple choice rule that can be implemented with “few” errors. Otherwise, we assign type O to the subject (for other). In other words, we assume that the 33 subjects in cluster 1 and 45 subjects in cluster 2 maximize a well defined utility function, linear in the goods present in the bundle, but that they make some errors. As we know from sections A3.1 and A3.2, this is a reasonable description of behavior by subjects in those clusters. We then divide the sample into three types, depending on whether the optimal choice given their preferences can be implemented with a simple rule (typesH andT) or not (type 101 O). Table A.2 summarizes the number of subjects of each type by cluster. We also add in parentheses the average number of violations for type O subjects (since violations are typically very small for types H and T, the numbers are omitted). Cluster 1 Cluster 2 HT O HT O Treatment S 27 5 1 (0) 1 10 34 (3.9) Treatment C 10 4 19 (46.7) 7 3 35 (21.4) Table A.2: Types of preferences by subjects in clusters 1 and 2 All but one subjects in cluster 1 have preferences consistent with a simple rule in treatment S, mostly H. More than half of these subjects change their strategy in treatment C and are there best classified as type O. By contrast, only one-quarter of subjects in cluster 2 have a preference consistent with a simple rule and there is no treatment e↵ ect. It is remarkable to see such sharp di↵ erences across clusters of choices consistent with simple rules, even though subjects are not grouped based on that dimension. Our conjecture is that simple rules are more natural in treatment S, where the same goods are o↵ ered in both bundles: if one good is strongly preferred, the subject can lexicographically settle for it (type H); if both goods are of similar value, the subject can focus on total quantities (type T). In treatment C, subjects are forced to compare “apples to oranges” so simple rules are less intuitive to implement. 9 Subject are more likely to explicitly trade-o↵ the di↵ erent alternatives, which explains why more of them 9 Interestingly, the majority of subjects make significantly more violations when one specific item is common, which suggests that trade-o↵ s are more or less di cult depending on the composition of bundles. 102 are better classified as type O. Finally, since trade-o↵ s are di cult, type O subjects have significantly more violations than either typeH orT subjects. A3.4. Summary Overall, the individual analysis reveals interesting insights regarding the preferences and strategies of our subjects. First, a structural model (RUM) – where utility depends linearly on the quantities of goods in each bundle and the subject chooses the bundle that yields the highest utility – provides a good fit for a majority of subjects, but by no means for all of them. Second, a cluster analysis based on RUM misclassifications suggests three distinct groups. The RUM provides a reasonably good fit for two groups of subjects (clusters 1 and 2) and a poor fit for the last one (cluster 3). Third and as expected, RUM misclassifications are correlated with GARP violations. Subjects in cluster 3 perform badly in both treatments of the consistency task, whereas subjects in clusters 1 and 2 perform reasonably well. Surprisingly, however, cluster 1 (the group with the fewest RUM misclassifications) has more violations in treatment C than does cluster 2. The composition is also di↵ erent: two-thirds of subjects in cluster 1 are OA whereas two-thirds of subjects in cluster 2 are YA. Fourth, an analysis of simple rules of behavior consistent with utility maximization sheds light on the di↵ erences in age composition and consistency across tasks between clusters 1 and 2. Cluster 1 is mostly composed of OA who use a simple rule in treatment S (maximize the amount of the preferred good), resulting in extremely consistent behavior. Their consistency decreases substantiallyintreatmentC,possiblyduetothedi cultyofimplementingasimplerule when the bundles contain di↵ erent goods. By contrast, cluster 2 is mostly composed 103 of YA who use simple rules significantly less often but perform better value-quantity tradeo↵ s. These subjects make slightly more consistency mistakes in S but less in C. Finally, a conjecture consistent with the results presented here is that some subjects who are aware of their compromised working memory and fluid intelligence (mostly OA) resort to simple choice rules. Such strategies can be applied in the simple treatment but not in the complex one. This explanation is reasonable and appealing, however it requires the supporting evidence of new experiments. 104 Appendix B Design and Procedures TheexperimentwasreviewedandapprovedbytheIRBoftheUniversityofSouthern California. It was conducted through tablet computers and the tasks were programmed with the Psychtoolbox software, an extension of Matlab. Participants. We recruited 134 children from the elementary school at the Lycee International of Los Angeles, a private elementary school. We ran 18 sessions, each with 5 to 10 subjects and lasting between 1 and 1.5 hours. Sessions were conducted in a classroom at the school. In our tasks, children had to make choices between options involving goods. To make sure that options were desirable by all participants, we organized sessions by gender and age group: kindergarten to second grade boys, kindergarten to second grade girls, third to fifth grade boys, and third to fifth grade girls. Goods were all toys or stationary, for each of the age-gender groups. As a control, we ran 7 sessions with 51 undergraduate students. These were conducted in the Los AngelesBehavioralEconomicsLaboratory(LABEL)inthedepartmentofEconomicsat the University of Southern California. For the undergraduate population, participants 105 were recruited from the LABEL subject pool. Instead of toys or stationary, we used snack foods. A description of the distribution of our participants is reported in Table B.1. Grade Kinder. 1st 2nd 3rd 4th 5th Und.Grad. Male 12 12 15 20 11 6 22 Female 7 16 11 9 8 7 29 Total 19 28 26 29 19 13 51 Table B.1: Sample description. Each participant completed three di↵ erent types of tasks. In Ranking tasks, partic- ipants had to rank 7 options from most preferred to least preferred. We distributed 7 cards to each participant, on each of which was a picture of one of the options. Partic- ipants were instructed to rank these cards on a ranking board attached to their desk. 10 Anexperimenterthentransferredtherankingsontothetablets. TherewerethreeRank- ing tasks. In the Goods-Ranking task, options were toys. In the Social-Ranking task, options were sharing options between self and another child of the same age and gender in another school. The sharing options contained di↵ erent amounts of one single good. To ensure this good was desirable, we selected the toy that was ranked as first favorite in the Goods-Ranking task. Last, in the Risk-Ranking task, options were lotteries. In each lottery, the participant could earn a given number of toys with a given probability. Probability was represented by a circle with outcomes shown in white and 10 The ranking board had a green smiling face on the far right and a yellow non-smiling face on the far left, under which they were to place their most and least favorite cards, respectively. Previous studies have reported successful use of a smiley-face scale (e.g. Roedder et al., 1983; Neelankavil et al., 1985). We explained to subjects that in the case that they liked two or more cards ”exactly the same,” they were to place the cards in the same area. 106 green, with the relative size of the green area corresponding to the probability of win- ning the good(s). Each circle corresponded to a spinner wheel. 11 Again, to select that options were desirable, we chose the one that was ranked second in the Goods-Ranking task. In Choice tasks, participants were presented with all pairwise combinations of the options in the corresponding Ranking task. We will refer to these tasks as Goods- Choice task, Social-Choice task 12 and Risk-Choice task. In each trial, one option was displayed on the left and one on the right on the screen of the tablet. The partic- ipant could select the preferred option or report to be indi↵ erent between them. The combinations were presented randomly, both in terms of trial order and in terms of left-right presentation. 13 These tasks are represented in Figure 2.1 and the specific op- tions are displayed in Figures B.1, B.2 and B.3. In each Choice task, the 21 trials were followed by an attention trial. In this trial, subjects were presented with their most frequently and least frequently chosen options from the preceding 21 trials. 14 For analysis, participants also completed a Transitive Reasoning task. This task was designed to measure levels of transitive reasoning. Several tasks have been proposed in the literature (Bouwmeester and Sijtsma (2006)). It has been established that tasks 11 Previous experiments on risk with children have used a similar design with a spinner wheel (Huber and Huber, 1987; Reyna and Ellis, 1994; Schlottmann and Anderson, 1994; Harbaugh et al., 2002). 12 This task is a modified dictator game, similar to those in Andreoni and Miller (1998) or Harbaugh and Krause (2000). 13 This was done to ensure that any e↵ ects we might have found could not be attributable to the order of the trials or of the left-right order of the goods. 14 As the 21 choices are being made, the computer tallies selections ”for” and ”against” each of the options as follows: each time a given option is selected it receives 1 point and the other receives 0 point. Each time the indi↵ erence button is selected, both options receive 0.5 point. At the end of the 21st trial, the tally for each option is summed and the options with the most and least points are determined. In case of a tie, one option is chosen randomly. 107 Figure B.1: Options used in the Goods-Choice and Goods-Ranking tasks. with simultaneous presentation of premises are easier than those with sequential pre- sentation of premises, and tasks with physical content are at least as easy as those with verbal content (Bouwmeester and Sijtsma (2004)). In order to test the relation between transitive choice and transitive reasoning devoid of memory or operational reasoning re- quirements, we opted for a new design and we constructed a test that does not require memory and is visually represented. The task consisted of seven questions of varying di culty. Each of the seven questions consisted of two premises represented in two vignettes, and a third vignette with a response prompt. For each premise, participants were told that the animals shown in the vignette were at a party and the oldest wore a hat. They had to determine which animal in the third vignette should wear the hat. This is illustrated in Figure B.4. Three of the seven questions did not require transitive 108 Figure B.2: Options used in the Social-choice and Social-ranking tasks. Partic- ipants were presented with choices involving sharing rules between them and other. For elementary school each token represented a toy, which was personalized for each par- ticipants to ensure they liked it. For undergraduate students, each token represented $2. reasoning and were included to test whether participants were paying attention. These are referred to as ”pseudotransitivity” trials (Bouwmeester and Sijtsma (2006)). The remaining four did require transitive reasoning. Of the four transitivity questions, two of them were less di cult and two were more di cult. Allsubjectscompletedthetaskinthesameorder: (1)Goods-Choicetask,(2)Goods- Ranking task, (3) Transitive Reasoning task, (4) Social-Choice task, (5) Social-Ranking task,(6)Risk-Choicetaskand(7)Risk-Rankingtask. Alltaskswereuntimed. Uponthe completion of a given task by all subjects, instructions for the next task were given. We toldthesubjectsthattheirrankingsintheGoods-Rankingtaskwasimportanttoensure 109 Figure B.3: Options used in the Risk-choice and Risk-ranking tasks. Partici- pants were presented with choices involving lotteries. For elementary school each token represented a toy, which was personalized for each participants to ensure they liked it. For undergraduate students, each token represented $2. that they would play with their preferred items in the rest of the experiment and would thereforecollect thetoys theylikedbest. We didnot incentivizedthe othertwo Ranking tasksnor theTransitiveReasoningtask. ToincentivizeeachChoice task, onechoice was randomly selected by the computer and subjects received their selection in that trial. The incentive structure was explained accessibly through a simple analogy. 15 For the Social-Choice task, we explained that each participant had been paired with another student, of their same gender and grade level, from another school in Los Angeles. 16 15 Subjects were instructed to make honest choices about which goods they liked, because the com- puter kept track of what they chose and put all of these choices in a bag, after which it did the equivalent of ”closing its eyes” and ”picking one of the goods from the bag.” In the situation that they liked the two goods ”exactly the same,” they were instructed to select the button displayed between the two goods. As we explained to subjects, this was analogous to telling the computer to make the choice of which good went into the bag on their behalf. 16 Undergraduate were paired with a subject of another session, matched for gender. 110 Figure B.4: Transitive Reasoning Task. The animal wearing the hat is the oldest in each vignette on the left. The participant has to answer in the vignette on the bottom right by choosing the animal he thinks is the oldest given the information on the left, or by reporting it cannot be known (?). We explained that the selected sharing would actually be implemented: we would go to other school and deliver to the other student the goods that were represented in that sharing option. 17 . For undergraduate participants, toys were replaced by money amounts. For the Risk-Choice task, we explained that their choice in the selected trial would be implemented and that the corresponding spinner wheel would be spun by a blindfolded assistant at the end of the session that day. If the spinner arrow landed in the green part of the wheel, the subject would win the number of goods associated to that choice. Otherwise, they would not win any goods from this task. This was implemented at the end of each session. For undergraduate participants, toys were also replaced by money amounts. Before leaving, we collected demographic information consisting in ”gender”, ”grade”, ”number of younger siblings” and ”number of older siblings”. All participants also received a fixed show-up fee. Children received their 17 The shared items were delivered to Foshay elementary school, a public school in LAUSD. 111 highest ranked item in the Goods-Ranking task while Undergraduate students received $5. .0.0.1 Analysis of transitivity violations We collected data from all participants in the Goods-Choice and Goods-Ranking tasks. The tablets did not record the choices of two subjects in the Risk-Choice and Risk- Ranking tasks and one subject in the Social-Choice and Social-Ranking tasks. In what follows, we group participants in four categories: Kindergarten and 1st graders in age group K-1st, 2nd and 3rd graders in age group 2nd-3rd, 4th and 5th graders in age group 4th-5th and Undergraduate students in age group U. Transitivity violations. We measured consistency by counting the number of transi- tive violations (hereafter TV). A choice is intransitive if a participant reveals to prefer optionA to optionB and optionB to optionC but not optionA to optionC. Intran- sitivity can be detected by considering all possible triplets of options and inspecting the choices made in the Choice-Tasks. Intransitivity is then measured by the number of triplets that produce a violation. Considering triplets is enough to account for all violations of transitivity. Given we allowed participants to express indi↵ erence between options, we allocated 0.5 violation to triplets in case of weak violations, that is when we observed choices such that A was chosen over B and B was chosen over C but A was indi↵ erent to C. We first counted the number of times choices between triplets of items were intransitive for each child in each choice-task and we then computed the 112 average number of violations by age group and choice-task. The results are represented in Figure 2.2. In the Goods domain, we found a significant improvement between consecutive age- groups, with the oldest group of children being at the same level of performance as undergraduate students. More specifically, participants in K-1st showed significantly more violations than participants in 2nd-3rd (p-value=0.0050), participants in 2nd- 3rd showed significantly more violations participants in 4th-5th (p-value=0.0355) but participants in 4th-5th did not have significantly more violations than participants in U (p-value=0.0835). In the Social domain, a similar pattern was observed. More specifically, TV counts were significantly di↵ erent between the K-1st age group and the 4th-5th age group (p-value=0.01620), between the K-1st age group and U age group (p-value=0.0002) and between the 2nd-3rd age group and the U age group (p- value=0.0048) while all other TV counts were not statistically significantly di↵ erent. In the Risk domain however, there was no apparent improvement. No age-group of elementary children had significantly more violations than U. When we compared TV counts across domains, we found that participants in the K-1st age group had significantly more violations in the Goods domain than in the Social domain (p=0.0017). A similar result held for the 2nd-3rd age group but it was less pronounced (p=0.0234). Analysis of transitivity in the goods domain. We used the explicit ranking elicited in the Goods-Ranking task to assess which options were more frequently involved in transitive violations as a function of their ranking. For each triplet of options involving 113 a violation, we assigned a score of 1 to each of the 3 corresponding pairwise choices. Each pair of options was then allocated the percentage of times this pair was involved in a violation (the number of times it obtained a score of one over all possible times). By repeating the exercise for all participants and averaging over all of them, we obtained thepercentageoftimesviolationsweredetectedinchoicesbetweenoptionsrankedxand y in each age group. Naturally, these corresponded to di↵ erent specific items since each participant had his own x and y preferred items. Figure 2.3 represents the color-coded result of this exercise. Darker color are used to represent fewer violations. Next, we studied the marginal sensitivity to violations to know if some choices were more consistent than others, and if so, why. Na¨ ıvely, we might expect that highly consistent choices are easy to make. Easiness might be just a matter of picking what we like. Or it might be a matter of avoiding what we do not like. Assuming that option ranksderivedfromtheexplicitrankingsgiveaproxyforoptionvalues, themorevaluable options should be those with higher ranks. If consistency is only driven by choosing what is liked, it should not matter what the lower ranked option is, and if consistency is only driven by avoiding what is liked least, then it should not matter what the higher ranked option is. We tested this conjecture by analyzing how consistency changes if we marginally change the rank of the higher or lower ranked option. Intuitively, in Figure 2.3, if participants are making choices in a given cell and exhibit a certain level of consistency, how much more (or less) consistent they become by moving one cell to the right (changing the rank of the higher ranked item but not the lower ranked item) 114 or by moving one cell up (changing the rank of the lower ranked item but not the higher ranked item). More specifically, we considered every pair of adjacent boxes in the same row and we determined the di↵ erence in violations between a box and the box to the right of it. We then computed the average di↵ erence over all pairs of boxes and reported this number as the left-right gradient of the vector in the corner of Figure 2.3 for each age group. A vector with a larger x-coordinate means a greater increase in violations when the higher ranked option is one rank closer to the lower ranked option. We did the same with every pair of adjacent boxes in the same column to determine the up-down gradient so that a vector with a larger y-coordinate means a greater increase in violations when the lower ranked option is one rank closer to the higher ranked option. As expected, the vector of all four age-groups have upper right gradients, indicating more violations when options are ranked more closely in either dimension. It also implies that highest violations occur between items of intermediate ranks (3, 4, 5). The left graph of Figure B.5 presents a heat-map of all vectors in the Goods domain and confirms the increase in violations when the higher and lower ranked options are closer to each other. Finally, a t-test confirms that both the x- and y-coordinates are positive and significantly di↵ erent from 0 (p-value<0.01) overall and for all age groups, with the exception of the x-coordinate in the K-1st age-group. Overall, in the Goods domain, all groups were significantly driven by the rank of the lower ranked option, and all groups except K-1st were driven by the rank of the higher ranked option. 115 Goods Social Risk Figure B.5: Sensitivity analysis Analysis of transitivity in the social domain. An option in the Social domain can be decomposed in three attributes that can be visually assessed through counting: the reward to self, the reward to other and the total reward. When comparing attributes, a participant can use three simple rules: pick the maximum, pick the minimum or be indi↵ erent. A participant could apply a rule to a single attribute (a policy such as “pick option with maximum reward for self”); a participant could alternatively apply a rule to one attribute then move to a second attribute and apply a possibly di↵ erent rule (a policy such that “pick option with maximum reward for self and if they are the same, pick option with maximum total reward”). We counted 16 such policies but only 3 were used: ”maximize own amount, then minimize amount of other” ”maximize own amount, then maximize amount of other” and ”maximize own amount irrespective of what’s the other is collecting”. We counted all participants who complied exactly with any such policy and those who made exactly one mistake with respect to it. We will call these participants heuristic users or simple policy users. Among them, 62% chose the heuristic ”maximize own amount, then minimize amount of other”. We removed them 116 fromoursampleandwewereleftwith125participants. WecomputedTVcountsbyage group and found that the results were not significantly di↵ erent from those obtained in the Goods domain. The development of consistency followed the same pattern: participants in the K-1st age group were significantly more inconsistent than all older participants (p-value=0.0060 for the comparison with 2nd-3rd, p-value=0.0080 for the comparisonwith4th-5thandp-value<0.0001forthecomparisonwithU).Participants in the 2nd-3rd age group showed significantly more violations than participants in the U age group (p-value=0.01441) and participants in the 4th-5th age group were not significantly di↵ erent from participants in the U age group. This is represented in Figure 2.4. We also repeated the heat-map analysis we performed on the Goods-Choice task. The result is represented in Figure 2.5(A). We also performed the same marginal sensitivity to violations analysis as in the Goods domain after removing heuristic users. The x-coordinates were positive and significantly di↵ erent from 0 (p-value<0.01) overall and for all age groups except for participants in the K-1st age group. However and contrary to the Goods domain, the y-coordinates were not significantly di↵ erent from 0 for any age-group. It suggests that participants had a very clear idea of what they liked best but a less clear idea of what theylikedleast. Theresultcanalsobeseenintheheatmaprepresentationofthevectors (Figure B.5). Overall, in the Social domain, no groups were driven by the rank of the higher ranked option, but all groups except for the K-1st age group were driven by the rank of the lower ranked option. 117 Analysis of transitivity in the risk domain. The procedure to elicit simple policies was the same. In the Risk domain, there are two attributes to attend, reward amount and probability, and three simple rules, pick the maximum, pick the minimum or remain indi↵ erent. We counted 6 policies but only 4 were ever used: ”maximize the amount ir- respective of the probability”, ”maximize the probability, then maximize the amount”, ”minimize the amount irrespective of the probability, and ”minimize the probability irrespective of the amount”. We counted all participants who complied exactly with any such policy as well as those who made exactly one mistake with respect to a policy. Among those, 87% chose the policy ”maximize the amount irrespective of the proba- bility”. We removed them from our sample and we were left with 128 subjects. We analyzedTVcountsagainandwefoundthatallparticipantsfromtheelementaryschool had significantly more violations than participants in the U group (p-value=0.0019 for the comparison with K-1st, p-value=0.0050 for the comparison with 2nd-3rd and p- value=0.0153 for the comparison with 4th-5th) but they performed at the same level with each other. This is represented in Figure 2.4. We also repeated the heat-map analysis. The result is represented in Figure 2.5(B). Again, we performed a marginal sensitivity analysis after removing heuristic users and we found the opposite result than in the Social domain: y-coordinates were sig- nificantly di↵ erent from 0 overall and for two age-groups (4th-5th and U,t-testp- values<0.05) whereas x-coordinates were not di↵ erent from 0 in any age group (see Figure B.5). It means that in the Risk domain, participants had more consistent rank- ings when their least favorite option was involved than when their most favorite option 118 was involved. Overall, in the Risk domain, no one was driven by the rank of the lower ranked option; 4th-5th and U were driven by the rank of the higher ranked option. Transitivity violations across domains. The aggregate analysis of TV indicated that consistency improves with age. We addressed the question of how individual scores vary across domains to assess whether participants who commited relatively more violations in one domain were also those who committed relatively more violations in a di↵ erent domain. Saiddi↵ erently,wewantedtoknowifconsistencywasdriven(atleastpartially) byacommonfactororwhetheritresultedfromthedevelopmentofdomainspecificskills. When considering the full sample, we found that TV in the Goods and Risk domains were not correlated while TV in the Goods and Social or TV in the Risk and Social domainswere(Pearsoncoe cient=0.38and0.3respectivelyp-value<0.00001forboth). Whenweremovedheuristicusers,wefoundthattransitivityviolationsweresignificantly correlated across domains (Pearson coe cient =0.33, p-value=0.001 between the Goods and Risk domains, Pearson coe cient=0.40, p-value<0.0001 between the Goods and Social domains and Pearson coe cient=0.49, p-value <0.0001 between the Risk and Social domains) suggesting that participants’ consistency was at least partially driven by the development of a skill useful in all domains. Comparison with random play. To assess whether participants committing many violations might have been acting randomly, we simulated random players. Depending on the probability we assigned to their expressing indi↵ erence, the number of TV was between8and10,substantiallyabovetheactualnumbersobtainedevenamongthemost 119 inconsistent participants. This was consistent with earlier literature on consistency in children (Harbaugh et al. (2001)). .0.0.2 Other measures of choice consistency Choice reversals and choice removals. We computed two measures of violation severity foreachsubject. Thefirstofthesecountsthenumberofchoicesthatneedtobereversed to restore transitivity. To compute that number, an algorithm sequentially changes the choices made in each trial, and computes atransitivity violation score after each change. If the score is 0 at any point, the algorithm stops. After all single trials have been exhausted, the algorithm repeats the procedure over pairs of trials, then triplets and so on. We found that choice reversals followed a similar pattern across age groups as TV (Figure B.6), and were highly correlated to it in the goods-choice-task (Pearson = 0.95, Spearman = 0.98, p<0.0001), in the Social-Choice task (Pearson = 0.93, Spearman = 0.98, p< 0.0001), and in the Risk-Choice task (Pearson = 0.92, Spearman = 0.95, p < 0.0001). The second of these severity measures counts the number of choices that need to be removed to restore transitivity. We used an algorithm similar to that for counting choice reversals. As with choice reversals, this measure also closely reflects the age patterns observed with TV (see Figure B.7) and also highly correlated with TV for all three Choice tasks. Implicit ranking and choice noisiness. From a subject’s selections in a Choice task, it is possible to extract their implicit ranking for the options in that task. We computed this ranking by tallying their selections ”for” and ”against” each of the options as 120 Choice Reversals per Subject K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group Goods Social Risk Choice-Task Figure B.6: Choice reversals across domains and age. follows: each time a given option was selected or indi↵ erence was expressed, 1 point or 0.5 point was added to the running tally of that option, respectively. The tallied points for each option were summed, and the options were ordered according to this sum, giving the subject’s implicit ranking. The subject’s choices are then checked for inconsistencies against their implicit ranking. For each choice, a score of 1, 0.5, or 0 was possible. Suppose the tally of choices produced the following revealed ranking in order of lowest to highest tally score: C, G, B, A, E, F, D. Now consider the trial o↵ ering a choice between options A and B. If A was chosen over B, the subject was consistent with their implicit ranking and receives a score of 0 for that trial. If instead, the indi↵ erence button was selected, the subject was weakly inconsistent with their revealed ranking and received a score of 0.5 for that trial. If B was chosen over A instead, the subject 121 K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group Choice Removals per Subject Goods Social Risk Choice-Task Figure B.7: Choice removals across domains and age. was inconsistent with their revealed ranking and received a score of 1 for that trial. We called the overall score a Classification error. Notwithstanding the endogeneity issues with this measure (we use choices to extract a ranking then check that ranking against the very choices that were used to create it), it provides a measure of choice noisiness. As can be seen in Figure B.8, the age pattern of choice inconsistencies with revealed rankings closely resembles that of TV: participants who make more transitivity violations are those who are more “noisy” (make more mistakes) around their implicit ranking. Explicit vs. implicit ranking. Theimplicitrankingisrevealedbychoicesanddoesnot need to coincide with the explicit ranking elicited in a Ranking task. We computed for each participant and each task a measure of distance between those rankings. Suppose 122 K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group ICR per Subject Goods Social Risk Choice-Task Figure B.8: Classification errors (all subjects). for instance that a participant made choices in a Choice task so that their implicit ranking for options A-G was 3,5,1,7,4,6,2. Suppose now that their explicit rank was 2, 6,1, 7, 4, 5, 3. We assigned to each option a discrepancy score, namely the di↵ erence between its rank in the implicit and the explicit ranking (e.g. option A was assigned 3-2=1) and we computed a discrepancy score as the average of all option discrepancies scores. Figure B.9 describes those scores by domain and age group. As can be seen from the graph, these closely followed the pattern of TV. In the goods domain, the ability to chooseaccordingtoone’sexplicitlydisclosedpreferenceswasfoundtograduallydevelop. The pattern was similar in the Social domain. However, discrepancies remained at all ages in the Risk domain suggesting a persistent inability to draw choices from explicit preferences. 123 K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group Discrepancy Score per Subject Goods Social Risk Choice-Task Figure B.9: Discrepancies between explicit and implicit rankings (all sub- jects). Explicit rankings and choices. As an additional measure, we evaluated inconsisten- cies between choices in Choice tasks and the explicit ranking elicited in the Ranking tasks. This measure was computed in a similar fashion as for inconsistencies with re- spect to explicit rankings. In the goods domain, we found that participants in the K-1st and2nd-3rd age groups had relatively more di culty making choices consistent with their explicit rankings compared to older participants (p-values < 0.0334 for all comparisons). A similar story held qualitatively in the Social domain except that the participants in the K-1st and 2nd-3rd age groups were not significantly di↵ erent from each other, nor were the older participants in groups 4th-5th and U, suggesting a less gradual development of the ability to choose from an explicit ranking. We found that 124 inconsistencies in the Social domain were following the same trend as inconsistencies in the Goods domain after removing heuristic users. In the Risk domain, we found that the level of inconsistencies was high and the same across all subjects: they were not able to make choices consistent with their explicit rankings. This result changed when we removedheuristicusers: participantswhodidnotuseheuristicswerebecomingmoreca- pable over time to express their explicit rankings in their choices. Nevertheless the level of discrepancies remained higher than in the goods domain for all ages. Inconsistencies are illustrated in Figure B.10. K & 1 st 2 nd & 3 rd 4 th & 5 th U Age Group ICE per Subject Goods Social Risk Choice-Task Figure B.10: Inconsistencies with respect to explicit ranking (all subjects) Relationship between measures of consistency. Our measures were all highly corre- lated: a high number of transitivity violations was associated with a high number of inconsistencies between explicit rankings and choices (Pearson=0.79, p-value<0.0001 125 in the Goods domain, Pearson=0.72, p-value<0.0001 in the Social domain and Pear- son=0.69, p-value<0.0001 in the Risk domain), which was captured by a high dis- crepancy between implicit and explicit ranking (Pearson=0.61, p-value<0.0001 in the Goods domain, Pearson=0.60, p-value<0.0001 in the Social domain and Pearson=0.54, p-value<0.0001 in the Risk domain) and a large misclassification error between actual choices and the closest ranking consistent with it (Pearson=0.95, p-value<0.0001 in the Goods domain, Pearson=0.93, p-value<0.0001 in the Social domain and Pearson=0.93, p-value<0.0001 in the Risk domain). These results were very similar if we removed heuristic users. Overall, although we feel that TV is the best measure of choice consistency, the results presented in the main text are robust to other measures of violations or incon- sistent decision-making. Intransitivity was associated to the inability to make choices consistent with rankings, either implicit or explicit. .0.0.3 Other analysis of choices Indi↵ erence. We checked whether age had an influence on the tendency to be indi↵ erent and whether this was associated with TV. In the Goods domain, we found that the number of indi↵ erence choices decreased over time from an average of 3.8 indi↵ erent choices in K-1st to an average of 1.9 among U. Participants from K to 5th grades were less often indi↵ erent in the social task but they were more often indi↵ erent than participants in the U age group. We counted fewer indi↵ erences in the risk domain 126 among all children and no trend in reducing those indi↵ erence choices. This is reported in Table B.2. Grade Goods Social Risk K-1st 3.81 (0.54) 2.04 (0.47) 1.53 (0.59) 2nd-3rd 3.09 (0.47) 2.47 (0.54) 1.31 (0.45) 4th-5th 2.19 (0.42) 2.50 (0.60) 1.94 (0.53) U 1.86 (0.23) 1.12 (0.28) 1.49 (0.35) Table B.2: Indi↵ erences. However, we also found that triplets involving indi↵ erent choices were less likely to result in transitivity violations for all ages in the goods and Social domains (t-tests, p-values< 0.0093). This result was also true for participants in the K-1st age group (p-value=0.0272) and the U age group (p-value=0.0007). Reaction times and choices. We found that reaction times in trials involving viola- tions were longer compared to reaction times in trials involving no violations. This was true in all age groups and in all domains (KS test, p-value=0.015 for K-1st age group in the risk domain, p-value=0.010 for2nd-3rd in risk and p-value<0.0001 for all other age groups and domains) suggesting that participants were more confused when they ended up making a violation. We also found that reaction times were usually longer when participants pressed the indi↵ erence button compared to when they made a selec- tion (KS test, p-value<0.0001 for age groups above the 2nd-3rd age group). However, among trials in which the indi↵ erence button was pressed, those involved in a violation took slightly less time thanks those not involved in a violation (KS test, p-value=0.053). This was consistent with the results obtained regarding indi↵ erence: participants were 127 spending more time in those choices where they ended up hitting the indi↵ erence button and avoiding a violation. Last, heuristics users were quicker than non heuristic users (KS test, p-value< 0.0001). These additional measures confirmed the fact that intransitivity was associated with confusion, which decreased with age. .0.0.4 Heuristic users From the 60 subjects who used heuristics in the Social domain and the 57 who used heuristics in the Risk domain, we found that only 19 used heuristics in both domains. We also compared TV in the Goods domain by heuristics users and non heuristics users and we found no significant di↵ erence. Therefore, centration and the development of the value-based decision-making system appeared to be uncorrelated. However, we found that heuristic users were very distinguishable from non heuristic users in terms of discrepancies between implicit and explicit rankings (t-test p-value< 0.0001 in both risk and social). This means that they were explicitly revealing preferences that were not supported by their choices (hence implicit rankings). .0.0.5 Evolution of preferences Evolution of preferences in the social domain. We found that lexicographic preferences were common in the social domain. The most common policy was to maximize reward for self but its usage changed over time. Indeed, the preference for giving seemed to be developing: small children tended to maximize their own reward systematically 128 and, other things being equal, they also preferred smaller rewards for others. Older participants however selected larger reward for others. Interestingly, we did not find any evidencethat participantswereusingthee cient policy (maximizingsocial welfare) but we found that they came closer to that policy as they aged, with participants in the 4th-5th age group being similarly close to the e cient policy as participants in the U group (di↵ erences between these two groups were not significant). Thefavoriteoption, asrevealedbyimplicitrankings, alsochangedovertime. Indeed, for all ages, Option (4,0) and Option (3,3) were the most popular but the frequency of (4,0) decreased while the frequency of (3,3) increased with age (Table B.3). The least favorite options changed over time as well. For all ages Options (0,4) and (0,5) were the least popular but the frequency of (0,5) tended to decrease while the frequency of (0,4) tended to increase. Option (4,0) Option (3,3) K-1st 0.64 0.32 2nd-3rd 0.40 0.58 4th-5th 0.50 0.50 U 0.33 0.73 Table B.3: Revealed preferred options in the Social domain (from implicit rankings) Our Social-Choice task was also rich enough to study the evolution of prosocial behavior. In particular, we could study whether participants were prosocial (chose (3,3) over (3,1)), willing to share (chose (3,1) over (4,0)) or were envious (chose (0,4) over (0,5)). We could therefore conduct a similar analysis as in Fehr et al. (2008) and determine a type for each subject as a combination of decisions in these 3 choices. As in 129 Fehr et al. (2008), a participant was ”strongly egalitarian” if he/she chose (3,3), (3,1) and (0.4) and ”weakly egalitarian” if he/she chose (3,3), (4,0) and (0,4). A participant was ”strongly generous” if he/she chose (3,3), (3,1) and (0,4) and ”weakly generous” if he/she chose (3,3), (4,0) ad (0,4); last a participant was ”spiteful” if he/she chose (3,1), (4,0) and (0,5). We found similar results as in Fehr et al. (2008) for the range of ages in common between the two studies: young children were mostly spiteful, consistent with the centration hypothesis, while older children were mostly egalitarian, consistent with a more integrative reasoning. Our oldest participants were dominantly generous. This result is represented in Figure B.11. Figure B.11: Evolution of Prosocial behavior. Evolution of preferences in the risk domain. Wefoundthatlexicographicpreferences were also common in the Risk domain. The most common policy was to maximize reward but, as in the Social domain, its usage changed over time. More than 20% of participants in the K-1st and 2nd-3rd age groups used it against less than 10% in the 4th-5th and U age groups. We chose the Maximization of expected value (E(V)) as a 130 template of integrative reasoning but strictly speaking no participant maximized E(V). Only two subjects were one step away from it and they both had transitivity violations. For each participant, we counted the number of choices that maximized E(V) and we averaged this count across participants in each Choice task and each age-group. We found that participants in the K-1st, 2nd-3rd and 4th-5th age groups were making significantly more choices inconsistent with the maximization of E(V) compared to participants in the U age group. In particular, after removing heuristic users, we found that each group of children used policies that were farther away from E(V) compared to participants in the U age group (t-test, p-value<0.0001 for comparison with K-1st, p-value=0.0036 for comparison with 2nd-3rd and p-value=0.0029 for comparison with 4th-5th). When looking at the favorite option revealed by implicit rankings, we found that children were transitioning gradually (Table B.4) from the option involving the largest quantity(12, 12.5%)totheoptionexhibitingthelargestexpectedvalue(5,50%). Across all ages, option (1,100%) was the least favorite option for most children. Interestingly, we also found that option (12, 12.5%) was the most favorite option of many and the least favorite of others at the same time. Option (12,12.5%) Option (5,50%) K-1st 0.57 0.13 2nd-3rd 0.44 0.35 4th-5th 0.28 0.53 U 0.16 0.82 Table B.4: Revealed preferred options in the Risk domain (from implicit rankings) 131 These results taken together showed that behavior was changing from choices con- sistent with very simple policies to choices resulting from trade-o↵ s and integrative thinking. The centration e↵ ect observed in young participants made them appear self- ish in the social domain and risk lover in the risk domain. These attitudes changed with age. .0.0.6 Catch trials. Remember that catch trials were o↵ ering a choice between the most and least preferred options of a participant in the 21 pairwise choices of each Choice task. If a subject was payingattention, theyshouldchoosetheirmostfrequentlychosenoptionovertheirleast frequently chosen option. In that trial, a subjects received a catch score of 1, 0.5, or 0 if they selected their least frequently chosen option, the indi↵ erence button, or their most frequently chosen option, respectively. We found that most children were attentive: 70% in K-1st, 76% in 2nd-3rd, 84% in 4th-5th and 100% U answered correctly all catch trials. Most of those who failed got a 0.5 attention score, and no children failed all 3. We also found that performance on attention trials and TV was correlated in the Goods-choice-task (Pearson = 0.54, Spearman = 0.43, p-value< 0.0001), in the Social- choice-task (Pearson = 0.40, Spearman = 0.20, p-value< 0.01), and in the Risk-choice- task (Pearson = 0.36, Spearman = 0.32, p-value < 0.0001), suggesting a relationship between the ability to choose consistently and attention mechanisms. In the same lines, discrepancies between explicit and implicit rankings were correlated in all domains with catch trials (Pearson=0.3769, p-value<0.0001 in the Goods domain, Pearson=0.3152, 132 p-value<0.0001 in the Social domain and Pearson=0.2670, p-value=0.0003 in the Risk domain). These results suggest that attentiveness as measured by catch trials was a strong predictor of intransitivity and it was also strongly associated with the ability to choose according to explicit rankings .0.0.7 Transitive reasoning We counted for each participant the number of mistakes accumulated in each level of di culty of the transitive reasoning task. In all three levels of di culty of the reasoning task, the K-1st group, 2nd-3rd group, and 4th-5th group accrued significantly more errors on average than the U group (p-value<0.001, p-value<0.05, and p-value<0.05, respectively). Participants in the K-1st group made more mistakes on the most dif- ficult reasoning trials than they did on the easy or medium trials (p-value=0.02 and p-value=0.0001). Participants in the 2nd-3rd group also made more mistakes on the di cult trials as compared to the easy trials (p-value=0.0002). Within the 4th-5th and U age groups however, the average error counts were similar across trial di culty. These results are summarized in Figure B.12. We found that performance in the transitive reasoning task was correlated with attentiveness. This was true for all levels of di culty (Pearson coe cient=0.2156, p- value=0.0032 for all trials and Pearson coe cient=0.1996, p-value=0.0065 for all the most di cult trials). We also found that it was correlated with the level of discrepan- cies between implicit and explicit rankings in all domains (Pearson coe cient=0.3314, 133 p-value<0.0001 in the Goods domain, Pearson coe cient=0.2033, p-value=0.0056 in the Social domain and Pearson coe cient=0.0.1725, p-value =0.0195 in the Risk do- main). Last, we found that catch trials in the Goods domain and age were predictors of performance in most di cult trials (Table B.5). Figure B.12: Performance in the reasoning task. Model 1 Catch trial Goods 0.370 (*) Catch trial Social 0.0420 Catch trial Risk 0.560 Heuristic usage risk -0.005 Heuristic Usage social -0.014 Dummy K-1 0.776 (***) Dummy 2-3 0.194 Dummy 4-5 0.191 Constant 0.133 R-squared 0.281 Table B.5: Complex transitive reasoning determinants (all subjects) Overall, transitive reasoning was associated with the same explanatory variables as transitive decision-making. 134 .0.0.8 The determinants of transitive choices Relationship between TV and demographic variables. Given TVs covary across domains, we looked for possible common explanatory variables of intransitivity. To this end, we ran OLS regressions treating transitivity violations in each domain as the variable to explain by demographic characteristics. Those included the age group, gender, the number of younger siblings and the number of older siblings. We found that the only significant explanatory variable for transitivity violations was the age group. Moving from an age group to the next was associated with a decreased number of transitivity violations for all three choice tasks; this was significant in the Goods-Choice task (p- value < 0.001) and Social-Choice task (p-value < 0.001) and not significant in the Risk-Choice task (p-value = 0.921). These results were unchanged when we removed heuristic users. Relationship between TV and developmental variables. We ran OLS regressions on the full sample to assess the explanatory power of mistakes in transitive reasoning on transitivity violations in each domain. We found that mistakes in transitive reasoning were not associated with violations in the Risk domain. They were correlated with violations in the Goods and Social domain but significance levels dropped as we con- trolled for other explanatory variables such as age and attentiveness. These however werehighlysignificantaswellasthetendencytouseheuristics. Theresultsarereported in Tables B.6, B.7 and B.8. Overall, TVwasbestpredictedinalldomainsbytheperformanceincatchtrialsand the ability to make choices consistent with explicit rankings. It was further predicted 135 by centration in the Social and Risk domains. Transitive reasoning, even though it was correlated with TV, failed to predict any TV result after controlling for these other explanatory variables. Model 1 Model 2 Model 3 Model 4 TR mistakes 0.878 (***) 0.393 (**) 0.297 (*) 0.188 Dummy K-1 3.049 (***) 2.497 (***) 1.376 (**) Dummy 2-3 1.383 (**) 0.824 0.221 Dummy 4-5 0.146 -0.139 -0.275 Catch trial 3.460 (***) 2.565(***) Discrepancies 2.397 (***) Constant 1.359 (***) 0.693 (*) 0.708 (**) -0.403 # obs 185 185 185 185 R-squared 0.127 0.242 0.359 0.485 Table B.6: Transitivity violations in the Goods domain Model 1 Model 2 Model 3 Model 4 Model 5 TR mistakes 0.359 (***) 0.115 0.0685 0.0163 0.0610 Dummy K-1 1.492 (***) 1.176 (**) 0.775(*) 0.860 (**) Dummy 2-3 0.738 (*) 0.418 -0.034 -0.146 Dummy 4-5 0.215 0.048 0.031 -0.198 Catch trial 1.937 (***) 1.330 (***) 1.207 (***) Discrepancies 1.654 (***) 0.707(***) Heuristics usage 0.304 (***) Constant 0.894 (***) 0.531 (*) 0.538 (**) -0.213 -0.603 (**) # obs 184 184 184 184 184 R-squared 0.045 0.103 0.187 0.364 0.475 Table B.7: Transitivity violations in the Social domain 136 Model 1 Model 2 Model 3 Model 4 Model 5 TR mistakes 0.216 0.265 0.179 0.027 0.254 Dummy K-1 -0.358 -0.957 -0.947 -0.157 Dummy 2-3 0.0694 -0.523 -0.149 0.552 Dummy 4-5 0.765 0.457 0.598 0.671 Catch trials 3.579 (***) 1.796 (***) 1.250 (**) Discrepancies Risk 2.237 (***) 1.540 (***) Heuristic Risk 0.268 (***) Constant 2.510(***) 2.390 (***) 2.403 (***) 0.592 -0.741 (*) # obs 183 183 183 183 183 R-squared 0.008 0.022 0.157 0.416 0.500 Table B.8: Transitivity violations in the Risk domain 137

Abstract (if available)

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Value-based decision-making in complex choice: brain regions involved and implications of age

PDF

The evolution of decision-making quality over the life cycle: evidence from behavioral and neuroeconomic experiments with different age groups

PDF

Toward a more realistic understanding of decision-making

PDF

Homeostatic imbalance and monetary delay discounting: effects of feeding on RT, choice, and brain response

PDF

Sequential decisions on time preference: evidence for non-independence

PDF

Deciphering the variability of goal-directed and habitual decision-making

PDF

Behabioral and neural evidence of state-like variance in intertemporal decisions

PDF

Effect of mindfulness training on attention, emotion-regulation and risk-taking in adolescence

PDF

Value based purchasing: decision-making processes underlying hospital acquisitions of orthopedic devices

PDF

Brain and behavior correlates of intrinsic motivation and skill learning

PDF

Perceptual and computational mechanisms of feature-based attention

PDF

Demographic and clinical covariates of sensorimotor processing

PDF

Reacting to the negative consequences of your decisions: an ATSS comparison of cognitive and affective reactions in older versus younger adults

PDF

Post-investigation experiences of families with complex needs at risk of maltreatment: an examination of need, matched services, and changes in need

PDF

Beyond revealed preferences: how gender, relative socioeconomic status, and social norms drive happiness and behavior

PDF

Behavioral and neural evidence of incentive bias for immediate rewards relative to preference-matched delayed rewards

PDF

A perceptual model of evaluative knowledge

PDF

Noradrenergic mechanisms of arousal-enhanced memory selectivity

PDF

Unbounded utility

PDF

Impact of enhanced efficacy expectation on motor learning in individuals with Parkinson’s disease

Asset Metadata

Creator Combs, Thomas Dalton (author)

Core Title Neuroeconomic mechanisms for valuing complex options

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Neuroscience

Publication Date 08/02/2016

Defense Date 05/05/2016

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

Tag Decision making,Development,Generalized Axiom of Revealed Preference,neuroeconomics,Neuroscience,OAI-PMH Harvest,Value,value based decision making

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Monterosso, John (committee chair), Brocas, Isabelle (committee member), Coricelli, Giorgio (committee member)

Creator Email tcombs@usc.edu,tdaltoncombs@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-294047

Unique identifier UC11281013

Identifier etd-CombsThoma-4717.pdf (filename),usctheses-c40-294047 (legacy record id)

Legacy Identifier etd-CombsThoma-4717.pdf

Dmrecord 294047

Document Type Dissertation

Format application/pdf (imt)

Rights Combs, Thomas Dalton

Type texts

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA