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Aggregating complaints

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Aggregating complaints

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Content 1
Aggregating Complaints
Joe Horton

A dissertation presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
in partial fulfilment of the requirement for the degree
DOCTOR OF PHILOSOPHY
(PHILOSOPHY)
May 2018

Supervised by:
Associate Professor Jonathan Quong
Associate Professor Jacob Ross
Professor Mark Schroeder
Professor Ralph Wedgwood

2
Abstract
Is there any number of people you should save from a moderately large burden, such as
paralysis, rather than saving one person from a very large burden, such as death? Is there any
number of people you should save from a very small burden, such as a headache, rather than
saving one person from a very large burden, such as death? If we answer ‘no’ and ‘no’, we
accept a non-aggregative moral view—a view on which benefits and burdens cannot be
interpersonally aggregated. If we answer ‘yes’ and ‘no’, we accept a partially aggregative
moral view—a view on which benefits and burdens can sometimes be interpersonally
aggregated. If we answer ‘yes’ and ‘yes’, we accept a fully aggregative moral view—a view
on which benefits and burdens can always be interpersonally aggregated.
Most people accept a partially aggregative moral view. In Chapters 1–3, I argue that
we should reject partially aggregative and non-aggregative views and accept a fully
aggregative view. In Chapters 4–5, I turn from the question of whether our moral view should
be aggregative to the question of what is should aggregate. I argue that, although our view
should be fully aggregative, it should not focus on well-being, as fully aggregative views
typically do. Instead, it should focus on complaints, as non-aggregative and partially
aggregative views typically do. I argue that complaints-based views have some important
advantages, and I defend them against Derek Parfit’s ‘Non-Identity Problem’.

3
Short Contents
Acknowledgments 8
Introduction 11
Chapter 1: Weighing Small Burdens 14
Chapter 2: Non-Aggregation, Partial Aggregation, and Risk 35
Chapter 3: Reconsidering Aggregation 62
Chapter 4: Count Complaints, Not Happiness 85
Chapter 5: The Non-Identity Problem 108
Addendum: Recent Developments 129
Bibliography 147

4
Long Contents
Acknowledgments 8
Introduction 11
Chapter 1: Weighing Small Burdens
1. The Close Enough View 14
2. Problems With CEV 15
3. Aggregate Relevant Claims 17
4. Problems With ARC 20
5. Avoid Inferior Claims 21
6. AIC and Option Dependence 25
7. AIC and Mixed Groups 27
8. AIC and Musical Chairs 30
9. Summary 33
Chapter 2: Non-Aggregation, Partial Aggregation, and Risk
0. Note 35
1. Introduction 36
2. Against Ex Ante MC 40
2.1. The Main Objection to Ex Ante MC 40
2.2. Frick’s Pluralist Response 42
3. What is Ex Post MC? 44
3.1. Moreau’s Proposal 44
3.2. Otsuka’s Proposal 46
3.3. Ex Post MC 50
4. Against Ex Post MC 51
4.1. Frick’s Objection to Ex Post MC 52
5
4.2. The Main Objection to Ex Post MC 54
5. Against Hybrid MC 57
6. Conclusion 58
Appendix: Strengthening the Objection to Ex Ante MC and Ex Ante PAMC 59
Chapter 3: Reconsidering Aggregation
1. Introduction 62
2. The Large Numbers Argument 64
3. Intuitions about My Villain Cases 66
4. Two Replies to the Large Numbers Argument 68
4.1. Voorhoeve’s Reply 68
4.2. Pummer’s Reply 70
5. Three More Arguments for Aggregation 76
5.1. The Common Practice Argument 76
5.2. The Spectrum Argument 79
5.3. The Heuristic Argument 81
6. Conclusion 83
Chapter 4: Count Complaints, Not Happiness
1. Introduction 85
2. Two Reasons to Prefer Complaints-Based Aggregative Views 87
2.1. The Permissibility of Self-Denial and Self-Harm 88
2.2. The Permissibility of Not Having Children 90
3. Contractualism v Teleology 92
4. Respecting the Separateness of Persons and the Unity of the Individual 93
4.1. A Dilemma for Traditional Aggregative Views 94
6
4.2. How Ex Ante Complaints-Based Aggregative Views Can Avoid
the Dilemma

98
4.3. Why Ex Post Complaints-Based Aggregative Views Cannot
Respect the Unity of the Individual

101
5. Avoiding Important Information 103
5.1. Ross’s Challenge 103
5.2. A Response to Ross 104
6. Summary 107
Chapter 5: The Non-Identity Problem
1. Introduction 108
2. The Non-Identity Problem: Mary’s Choice 109
2.1. Mary’s Choice 109
2.2. Let Mary Choose 111
3. The Non-Identity Problem: Future Catastrophe 115
3.1. Future Catastrophe 116
3.2. Catastrophe for Whom? 117
3.3. Human Extinction 120
4. Revenge of The Non-Identity Problem 122
4.1. Ross’s Challenge 122
4.2. A Response to Ross 123
5. Dissertation Summary 127
Addendum: Recent Developments
1. Introduction 129
2. Tomlin’s Argument 129
3. Tadros’s Response to Tomlin 133
7
3.1. Local Relevance 133
3.2. A Path Dependence Problem 134
3.3. A Dilemma 136
3.4. Sharpening the Horns 138
4. Tadros’s Response to Me 141
4.1. Recap: The Argument from Risk 141
4.2. Evaluating Sets of Acts 143
4.3. A Reply to Tadros 145
5. Summing Up (Pun Intended) 146
Bibliography 147

8
Acknowledgments

I owe my greatest debt and extend my foremost thanks to Jonathan Quong. I have worked
under his supervision since I first discovered philosophy as an undergraduate, and I would
not have embarked on and certainly not have completed this dissertation without his
guidance. He has given me more of his time and energy than I should have accepted. I could
not have hoped for a more inspiring and generous teacher, and I am immensely grateful.
I am also immensely grateful to the three other members of my dissertation
committee, Mark Schroeder, Ralph Wedgwood, and Jacob Ross. Mark gave me invaluable
feedback on multiple drafts of every chapter, and on every other paper that I wrote, despite
simultaneously supervising almost every other PhD student in the department. He helped me
understand the connections between my arguments and related issues in philosophy of
language, metaethics, and epistemology. And were it not for his suggestions on how to frame
my ideas, this dissertation would not be half as coherent. Ralph also gave me hugely
illuminating comments on multiple drafts, and indulged me in many hours of discussion
about my ideas. Without him pointing me towards papers that I should already have read, I
would have wasted months developing ideas that had already been developed by people
much more capable. Jake’s influence on the dissertation will be evident to anyone who reads
it. He challenged almost every argument that I tried, usually forcing extensive revisions or
lengthy responses. And on the few occasions that he agreed with my arguments, he was
almost always able to improve them. I have been continuously inspired by his philosophical
ingenuity, and the clarity and concision with which he approaches philosophical debate.
I owe a special thanks to Thomas Sinclair. I began my postgraduate work with Tom,
and working with him cemented my love of moral philosophy. Despite not being on my
committee, he gave me invaluable feedback on almost everything that I wrote.
9
I was lucky to write this dissertation alongside many amazing colleagues and friends.
I was kept sane, grounded, and often drunk by Mike Ashfield, Ara Astorian, Rima Basu,
Stephen Bero, Renee Jorgensen Bolinger, Alexander Dietz, Sean Donahue, Erik Encarnacion,
Maegan Fairchild, Paul Garofalo, August Gorman, Bixin Guo, Jennifer Head, Nathan
Howard, Nicola Kemp, Tatyana Kostochka, Nicholas Laskowski, Woo Ram Lee, Matthew
Leonard, Eleonore Neufeld, Daniel Pallies, Caleb Perl, Christa Peterson, Abelard Podgorski,
Alexander Sarch, Kenneth Silver, Aness Webster, and Jonathan Wright. As well as being
awesome people, they are all awesome philosophers, and many of the ideas in this
dissertation were stolen from them. Alex Dietz, Nathan, Nick, Dan, Abelard, and Jon gave
me constant help. Alex and Abelard had as much influence on my approach to philosophy as
anyone, setting standards of rigour and clarity that I can only strive to emulate. Deezy,
Nathan, and Jon need a special mention. I will miss them immensely.
I was also lucky to have the support of amazing friends back home. Tom Cuthbertson,
Will Astley, Kate Proctor, Gordon Ritchie, Hayley Barbary, Peter Norris, Sally Thirkettle,
Simon Wallis, Natasha Bray, Daniel Poole, Max Stanley, and my other friends in London and
Manchester welcomed me back every holiday and gave me much needed breaks from
philosophy. Anthony Taylor gave me breaks from the breaks.
I also thank the other supportive and inspiring faculty of the University of Southern
California philosophy department; the relentlessly patient administrative staff who helped me
out of many a tough spot; Erin, Monchichi, and Rabbit O’Donnell, who reminded me what
Los Angeles is really all about; Brian Carey, for many helpful discussions; the politics
department at the University of Manchester, where I began my postgraduate work; and the
philosophy department at University College London, where I finished this dissertation.
I have reserved my final and warmest thanks for my parents, Matthew Horton and
Wenda Fabian; my sisters, Alys Cooney and Eve Horton; and my wonderful partner, Emily
10
Lightowler. There were downs as well as ups over the last few years, and it was their
unwavering support and encouragement that got me through. Emily endured four years of a
transatlantic relationship so that this dissertation could be written. I hope she knows how
much I love her, and how grateful I am that she stuck with me.

11
Introduction
Is there any number of people you should save from a moderately large burden, such as
paralysis, rather than saving one person from a very large burden, such as death? Is there any
number of people you should save from a very small burden, such as a headache, rather than
saving one person from a very large burden, such as death? If we answer ‘no’ and ‘no’, we
accept a non-aggregative moral view—a view on which benefits and burdens cannot be
interpersonally aggregated. If we answer ‘yes’ and ‘no’, we accept a partially aggregative
moral view—a view on which benefits and burdens can sometimes be interpersonally
aggregated. If we answer ‘yes’ and ‘yes’, we accept a fully aggregative moral view—a view
on which benefits and burdens can always be interpersonally aggregated.
Should our moral view be non-aggregative, partially aggregative, or fully
aggregative? This question has considerable importance. Even if we as individuals rarely face
decisions about whether to help one group of people or another, such decisions are routinely
faced by political institutions, large corporations, and charitable organisations. And as voters,
customers, and potential donors, we are able to influence the decisions that these bodies
make. A striking class of examples is discussed in a recent policy document issued by the
World Health Organisation (WHO), titled ‘Making Fair Choices on the Path to Universal
Health Coverage’.
1
This document was published in response to requests for guidance from

1
World Health Organization, ‘Making Fair Choices on the Path to Universal Health Coverage: Final Report of
the WHO Consultative Group on Equity and Universal Health Coverage’, World Health Organization (2014).
Also see Alex Voorhoeve, Tessa T.T. Edejer, Lydia Kapiriri, Ole F. Norheim, James Snowden, Olivier Basenya,
Dorjsuren Bayarsaikhan, Ikram Chentaf, Nir Eyal, Amanda Folsom, Rozita Halina Tun Hussein, Cristian
Morales, Florian Ostmann, Trygve Ottersen, Phusit Prakongsai, Carla Saenz, Karima Saleh, Angkana
Sommanustweechai, Daniel Wikler, and Afisah Zakariah, ‘Three Case Studies in Making Fair Choices on the
Path to Universal Health Coverage’, Health and Human Rights Journal 18 (2016): 11–22.
12
over seventy countries attempting to extend health coverage across their citizens. Given
limited funding, these countries found themselves having to decide between rolling out basic
coverage to a large number of people and providing more extensive coverage to a smaller
number in greater need. In formulating its guidance, the WHO consulted not only with
empirical researchers about the likely effects of different decisions, but also with moral
philosophers about the acceptability of different kinds of aggregation.
2

Most people accept, or are tempted to accept, a partially aggregative moral view.
3
In
Chapter 1, I describe problems for the two most prominent partially aggregative views in the
literature, and then develop a new partially aggregative view, which I call Avoid Inferior
Claims (AIC). This new view avoids many of the standard problems with partially
aggregative views, and those that is does not avoid are not decisive.
In Chapter 2, I argue that, despite the appeal of AIC and partially aggregative views
more generally, we must reject all partially aggregative and non-aggregative views. I argue
that there is a problem with these views that has not been properly appreciated in the existing
literature: they have unacceptable implications in certain cases involving risk.
In Chapter 3, I argue that we should accept a fully aggregative view. Most people
reject fully aggregative views because they find it very counterintuitive that there is some
number of people you should save from a headache rather than saving one person from death.
I follow several other philosophers in arguing that our intuitions about cases involving very
large numbers of people are unreliable, because we cannot accurately imagine very large
quantities. I then defend this argument against some recent objections.
In Chapter 4, I turn from the question of whether our moral view should be
aggregative to the question of what it should aggregate. I argue that, although our view

2
I discuss the work of one of these philosophers, Alex Voorhoeve, in Chapter 1.
3
For evidence of this, see note 7 in Chapter 1.
13
should be fully aggregative, it should not focus on well-being, as fully aggregative views
typically do. Instead, it should focus on complaints, as non-aggregative and partially
aggregative views typically do.
In Chapter 5, I respond to an influential challenge to complaints-based views. This
challenge is due to Derek Parfit, and it is known as The Non-Identity Problem.
4
I argue that
our intuitions about the cases that Parfit uses to illustrate this problem are distorted in various
ways, and that when we consider purified versions of these cases, our intuitions change, and
the problem promptly disappears. I then respond to a revenge version of the problem
suggested to me in conversation by Jacob Ross.
As a whole, then, this dissertation constitutes a defence of a fully-aggregative,
complaints-based moral view. To my knowledge, it is the first such defence.

In an addendum, I discuss two recent developments in the literature on aggregation. Patrick
Tomlin has argued that partially aggregative views have implausible implications in cases in
which there are additions or subtractions to the groups of people that we can save.
5
I
summarise his argument and explain how it complements the risk-based argument that I
present in Chapter 2. Victor Tadros has subsequently responded to both Tomlin’s argument
and my risk-based argument.
6
I summarise his responses and argue that they fail.

4
Derek Parfit, Reasons and Persons (Oxford: Oxford University Press, 1987): Chapter 16.
5
Patrick Tomlin, ‘On Limited Aggregation’, Philosophy & Public Affairs 45 (2017): 232–260.
6
Victor Tadros, ‘Localised Restricted Aggregation’, Oxford Studies in Political Philosophy: forthcoming.
14
Chapter 1
Weighing Small Burdens

1. The Close Enough View
Is there any number of people you should save from paralysis rather than saving one person
from death? Is there any number of people you should save from a headache rather than
saving one person from death? Many people answer these questions ‘yes’ and ‘no’
respectively.
7
These judgments can be captured by the following view.

7
For philosophers giving these answers, see David Brink, ‘The Separateness of Persons, Distributive Norms,
and Moral Theory’, in R. G. Frey and Christopher W. Morris (eds.), Value, Welfare, and Morality (Cambridge:
Cambridge University Press, 1993): 252–289, at 270; Frances Kamm, Intricate Ethics (Oxford: Oxford
University Press, 2007): 297–298; T. M. Scanlon, What We Owe to Each Other (Harvard University Press,
1998): 238–241; Roger Crisp, ‘Equality, Priority, and Compassion’, Ethics 113 (2003): 745–763, at 754;
Michael Otsuka, ‘Saving Lives, Moral Theory, and the Claims of Individuals’, Philosophy & Public Affairs 34
(2006): 109–135, at 109; Larry Temkin, Rethinking the Good (Oxford: Oxford University Press, 2012): 26–34;
Dale Dorsey, ‘Headaches, Lives, and Value’, Utilitas 21 (2009): 36–58, at 36-38; and Alex Voorhoeve, ‘How
Should We Aggregate Competing Claims?’, Ethics 125 (2014): 64–87, at 64-65. For survey data showing that
these answers are also common among non-philosophers, see Frank Cowell, Marc Fleurbaey, and Bertil
Tungodden, ‘The Tyranny Puzzle in Welfare Economics: An Empirical Investigation’, STICERD Working
Paper PEP-5, Suntory and Toyota International Centres for Economics and Related Disciplines, London School
of Economics and Political Science (2010). Several philosophers have argued that we should answer ‘yes’ to the
second question. See Alastair Norcross, ‘Comparing Harms: Headaches and Human Lives’, in Philosophy &
Public Affairs 26 (1997): 135–167; Derek Parfit, ‘Justifiability to Each Person’, Ratio 16 (2003): 368–390; John
Broome, Weighing Lives (Oxford: Oxford University Press, 2004): 56–58; and John Halstead, ‘The Numbers
Always Count’, Ethics 126 (2016): 789–802. John M. Taurek has argued that we should answer ‘no’ to the first
question. See his ‘Should the Numbers Count?’, Philosophy & Public Affairs 6 (1977): 293–316.
15
The Close Enough View (CEV): A larger number of a smaller burden can morally
outweigh a smaller number of a larger burden if and only if these burdens are close
enough in size.
8

Though initially very plausible, CEV faces significant problems. In response to these
problems, Alex Voorhoeve has proposed a different way to capture the judgments that
motivate CEV.
9
In this paper, I show that Voorhoeve’s view also faces significant problems. I
then develop some of Voorhoeve’s arguments in a way that yields a more defensible view.

2. Problems With CEV
There are at least two problems with CEV.
10
Here is the first. Suppose that, by the relevant
standard of ‘close enough’, the burden of losing a finger is close enough in size to the burden
of losing a hand, and the burden of losing a hand is close enough in size to the burden of
death, but the burden of losing a finger is not close enough in size to the burden of death.
Suppose also that one million lost fingers morally outweighs one thousand lost hands, and
one thousand lost hands morally outweighs one death. If the ‘morally outweighs’ relation is
transitive, it follows that one million lost fingers morally outweighs one death. But because
the burden of a lost finger is not close enough in size to the burden of death, CEV implies

8
Scanlon proposes this view in What We Owe to Each Other, at 239–240. The relevant judgments can also be
captured by a view on which there is a size threshold such that any burden above the threshold morally
outweighs any number of burdens below the threshold. However, this view has the implausible implication that
you should save one person from the smallest burden just above the threshold rather than saving any number of
people from the largest burden just below the threshold even though these burdens are almost identical in size.
9
Voorhoeve, ‘How Should We Aggregate Competing Claims?’.
10
Parfit raises these problems in ‘Justifiability to Each Person’, at 384–385. In a footnote, he raises a third
problem, which I discuss below in Section 8. See ‘Justifiability to Each Person’, at 383 n. 16.
16
that one death morally outweighs any number of lost fingers. So CEV has the seemingly
incoherent implication that the ‘morally outweighs’ relation is intransitive.
11

Of course, we could deny the suppositions in the above argument. But that would not
solve the problem. If CEV is to capture the judgments that motivated it, there must be some
set of burdens B1, B2, and B3 such that B1 is close enough in size to B2, B2 is close enough
in size to B3, and B1 is not close enough in size to B3. Let x > y mean that x morally
outweighs y. CEV implies that there is some set of numbers n, m, and l such that n B1s > m
B2s > l B3s > n B1s. So CEV has the seemingly incoherent implication that the ‘morally
outweighs’ relation is intransitive. We can call this the incoherence problem.
Here is the second problem. Suppose CEV does imply that one million lost fingers >
one thousand lost hands > one death > one million lost fingers. Even if this were coherent, it
would give rise to the following problem. Suppose that you have three options: save one
person from death, save one thousand people from losing a hand, save one million people
from losing a finger. CEV implies that each option is morally outweighed by another option.
Presumably, it is wrong for you to choose an option that is morally outweighed by another
option. So CEV has the very implausible implication that every option is wrong.
Again, we could deny the suppositions in the above argument. But again, that would
not solve the problem. Let B1, B2, B3, n, m, and l, be such that, according to CEV, n B1s > m
B2s > l B3s > n B1s. Suppose that you have three options: save n people from B1, save m
people from B2, save l people from B3. CEV implies that each option is morally outweighed
by another option. Presumably, it is wrong for you to choose an option that is morally

11
I say only that this implication ‘seems’ incoherent because Larry Temkin has recently argued that this
implication might be coherent after all. See Temkin, Rethinking the Good. However, even Temkin is reluctant to
embrace this implication.
17
outweighed by another option. So CEV has the very implausible implication that every
option is wrong. We can call this the no permissible options problem.

3. Aggregate Relevant Claims
Voorhoeve argues that we should reject CEV in favour of the following view.
12

Aggregate Relevant Claims (ARC):
1. If you can save someone from a burden, she has a claim to your help.
2. Her claim is stronger (i) the greater the burden she faces and (ii) the worse off she
will be if you do not help her.
3. Two claims compete if and only if they cannot be jointly satisfied.
4. A claim is relevant if and only if it is sufficiently strong relative to the strongest
claim with which it competes.
13

5. Other things equal, you should satisfy the greatest sum of strength-weighted,
relevant claims.

ARC captures the judgments that motivated CEV. Suppose that you can either save
one person from death or save many people from paralysis. The person facing death has a
strong claim to your help, but so too does each of the people facing paralysis. Since the
claims to be saved from paralysis are close in strength to the claim to be saved from death,
they are relevant. So ARC implies that there is some number of people you should save from
paralysis rather than saving the one person from death.

12
Voorhoeve, ‘How Should We Aggregate Competing Claims?’.
13
This has the somewhat odd-sounding implication that people can have irrelevant claims to your help, so it is
important to keep in mind that Voorhoeve is using ‘claim’ and ‘relevant’ in a special, technical sense.
18
Suppose next that you can either save one person from death or save many people
from a headache. The person facing death has a strong claim to your help, while the people
facing a headache have only a weak claim. Since the claims to be saved from a headache are
not close in strength to the claim to be saved from death, they are not relevant. So ARC
implies that you should save the one person from death no matter how many people face
headaches.
ARC also avoids the incoherence problem. Suppose that a claim to be saved from
losing a finger is sufficiently strong relative to a claim to be saved from losing a hand, and a
claim to be saved from losing a hand is sufficiently strong relative to a claim to be saved
from death, but a claim to be saved from losing a finger is not sufficiently strong relative to a
claim to be saved from death. Suppose also that the sum of one million claims to be saved
from losing a finger is greater than the sum of one thousand claims to be saved from losing a
hand, and the sum of one thousand claims to be saved from losing a hand is greater than one
claim to be saved from death. It follows, by the transitivity of ‘greater than’, that the sum of
one million claims to be saved from losing a finger is greater than one claim to be saved from
death. But ARC is compatible with this implication. ARC implies not that claims against
losing a finger cannot sum to more than one claim to be saved from death, but rather that,
when claims to be saved from losing a finger compete with a claim to be saved from death,
the claims to be saved from losing a finger are not relevant, regardless of how great their
sum.
ARC also avoids the no permissible options problem. Suppose that you have three
options: save one person from death, save one thousand people from losing a hand, save one
million people from losing a finger. ARC implies that you should save the one thousand
people from losing a hand, for the one thousand claims to be saved from losing a hand sum to
19
more than the one claim to be saved from death, and the claims to be saved from losing a
finger are not relevant.
It might seem that ARC is ad hoc—reverse engineered to capture the judgments that
motivated CEV while avoiding its problems. But, as Voorhoeve argues, there is a plausible
rationale for ARC.
14
Suppose that you can either save one person from a burden B1 or save
yourself from a burden B2. Plausibly, if B2 is much smaller than B1, as when B2 is a
headache and B1 is death, you should be more concerned about the one person avoiding B1
than about yourself avoiding B2, and so you should save the one person. But if B2 is
sufficiently large relative to B1, as when B2 is paralysis and B1 is death, it is reasonable for
you to be more concerned about yourself avoiding B2, and so it is permissible for you to save
yourself. Suppose next that you can either save one person from B1 or save a group of people
from B2. We can plausibly extend the foregoing reasoning as follows. If B2 is much smaller
than B1, each of the people in the group should be more concerned about the one person
avoiding B1 than about herself avoiding B2, and so they should refuse to press a claim to
your help that competes with the claim of the one person. Since they should refuse to press a
claim, you should ignore their claims. But if B2 is sufficiently large relative to B1, it is
reasonable for each of the people in the group to be more concerned about herself avoiding
B2 than about the one person avoiding B1, and so it is reasonable for them to press a claim to
your help that competes with the claim of the one person. Since it is reasonable for them to
press a claim, you should take their claims into account. So, as ARC implies, the claims of
the group are relevant if and only if they are sufficiently strong relative to the claim of the
one person.

14
Voorhoeve, ‘How Should We Aggregate Competing Claims?’, at 70–76.
20
4. Problems With ARC
There are at least three problems with ARC. Here is the first. ARC holds that if a claim is not
sufficiently strong relative to the strongest competing claim, this claim is irrelevant
simpliciter. But why should this claim be irrelevant simpliciter, rather than irrelevant only to
the strongest competing claim? Suppose again that you can save one person from death, save
one thousand people from losing a hand, or save one million people from losing a finger. It is
plausible that, because the burden of losing a finger is much smaller than the burden of death,
it is unreasonable for the people who face losing a finger to press a claim that competes with
the claim of the person facing death. So it is plausible that the claims of the people who face
losing a finger are not relevant to the claim of the person facing death. But since the burden
of losing a finger is close enough in size to the burden of losing a hand, the people who face
losing a finger can still reasonably press a claim that competes with the claims of the people
who face losing a hand. So, contra ARC, the claims of the people who face losing a finger are
still relevant to the claims of the people who face losing a hand. We can call this the relative
relevance problem.
Here is the second problem. ARC has counterintuitive implications in cases in which
your options change.
15
Suppose again that you can save one person from death, save one
thousand people from losing a hand, or save one million people from losing a finger. ARC
implies that you should save the one thousand people from losing a hand. Suppose that you
are just about to save these people when the one person dies. With this person gone, the
strongest claim is a claim against losing a hand. Since a claim against losing a finger is close
enough in strength to a claim against losing a hand, the claims against losing a finger are now
relevant. And since one million claims to be saved from losing a finger sum to more than one

15
This problem is emphasised in Halstead, ‘The Numbers Always Count’, at 797–799.
21
thousand claims to be saved from losing a hand, ARC now implies that you should save the
one million people from losing a finger. So ARC has the counterintuitive implication that
whether you should save the one thousand people from losing a hand or the one million
people from losing a finger depends on how long the one person stays alive. We can call this
the option dependence problem.
16

Here is the third problem. As Voorhoeve acknowledges, ARC needs to be modified if
it is to have plausible implications in cases in which people within the same group face
different burdens.
17
Suppose that you can either save one person from a painful death or save
one other person from a fractionally less painful death and save one million people from
losing a finger. Intuitively, you should do the latter. But ARC implies that you should do the
former, for the claims to be saved from losing a finger are not relevant. We can call this the
mixed groups problem.

5. Avoid Inferior Claims
If we take seriously the rationale that Voorhoeve offers for ARC, but we also take seriously
the relative relevance problem, we should hold that a claim is never relevant or irrelevant
simpliciter, but rather relevant or irrelevant only relative to a specified set of claims. More
specifically, we should hold that a claim C is relevant to a set of claims S if and only if C is
sufficiently strong relative to the strongest claim in S.

16
It might seem that this problem is just a symptom of a more fundamental problem with ARC. The ostensibly
more fundamental problem is that ARC violates a principle known as the independence of irrelevant
alternatives (also known as basic contraction consistency). I discuss the relationship between the option
dependence problem and the independence of irrelevant alternatives in Section 6.
17
Voorhoeve, ‘How Should We Aggregate Competing Claims?’, at 66–67 and footnote 38.
22
Let us say that a set of claims S1 defeats a set of claims S2, and S2 is defeated by S1,
if and only if the claims in S1 that are relevant to S2 sum to more than the claims in S2 that
are relevant to S1. Suppose again that you can save one person from death, save one thousand
people from losing a hand, or save one million people from losing a finger. In this case, every
set of claims is defeated by another set. Since the claims to be saved from losing a finger are
much weaker than the claim to be saved from death, they are not relevant to this claim, and
so they are defeated by it. But the claims to be saved from losing a finger are still relevant to
the claims to be saved from losing a hand, and since one million claims to be saved from
losing a finger sum to more than one thousand claims to be saved from losing a hand, the
claims to be saved from losing a hand are defeated by the claims to be saved from losing a
finger. Finally, the claim to be saved from death is defeated by the one thousand claims to be
saved from losing a hand.
If we assume that it is wrong for you to satisfy a defeated set of claims, we now face
the no permissible options problem. This assumption is natural, for it is natural to think that if
one set of claims defeats another, the former morally outweighs the latter. But while natural,
this assumption is mistaken. Even if one set defeats another, these sets might be morally on a
par, for the former might be defeated by some other set. If every set is defeated by exactly
one other set, every set is morally on a par. And if every set is morally on a par, it is
permissible for you to satisfy any set. So what follows from the reasoning in the previous
paragraph is not that every option is wrong, but rather that every option is permissible.
We might now conclude that, when every set of claims is defeated by another set, it is
permissible for you to satisfy any set. But this conclusion needs to be qualified. Suppose that
you have four options: save one person from death, save one thousand people from losing a
hand, save one million people from losing a finger, save 900,000 people from losing a finger.
Here, every set of claims is defeated by at least one other set. But, plausibly, it would be
23
wrong for you to satisfy the 900,000 claims to be saved from losing a finger, given that you
could satisfy the one million claims to be saved from losing a finger instead.
I suggest that the reason it would be wrong for you to satisfy the 900,000 claims to be
saved from losing a finger is that this set of claims is not only defeated but also dominated. It
is dominated in the sense that there is another set, the one million claims to be saved from
losing a finger, that defeats it and defeats every set that it defeats. If a set of claims is not only
defeated but also dominated, it is morally inferior to every non-dominated set.
We have now arrived at the following view.

Avoid Inferior Claims (AIC):
1. If you can save someone from a burden, she has a claim to your help.
2. Her claim is stronger (i) the greater the burden she faces and (ii) the worse off she
will be if you do not help her.
3. Let S1 and S2 be any two sets of claims. Let C be any claim in S1. C is relevant to
S2 if and only if C is sufficiently strong relative to the strongest claim in S2.
4. S1 defeats S2 if and only if the claims in S1 that are relevant to S2 sum to more
than the claims in S2 that are relevant to S1.
5. S1 dominates S2 if and only if S1 both defeats S2 and defeats every set of claims
that S2 defeats.
6. Other things equal, you should satisfy a non-defeated set of claims, unless every
set is defeated, in which case you should satisfy a non-dominated set.

AIC captures the judgments that motivated CEV. Since a claim to be saved from
paralysis is close in strength to a claim to be saved from death, a claim to be saved from
paralysis is relevant to a claim to be saved from death, and so some number of claims to be
24
saved from paralysis defeats one claim to be saved from death. So AIC captures the judgment
that there is some number of people you should save from paralysis rather than saving one
person from death. Since a claim to be saved from a headache is not close in strength to a
claim to be saved from death, a claim to be saved from a headache is not relevant to a claim
to be saved from death, and so one claim to be saved from death defeats any number of
claims to be saved from a headache. So AIC captures the judgment that there is no number of
people you should save from a headache rather than saving one person from death.
It might be objected that AIC does not fully capture the second judgment. Suppose
that you have the following sequence of options: save one person from death, save many
people from a burden smaller than but just close enough in size to death, save many more
people from a burden smaller than but just close enough in size to the previous burden, …,
save an enormous number of people from a headache. AIC implies that every set of claims in
this sequence is defeated by the next set of claims, apart from the claims to be saved from a
headache, which are defeated by the one claim to be saved from death. Since every set of
claims is defeated by another set, and no set is dominated, AIC implies that it is permissible
for you to satisfy any set. So AIC implies that, in this case, it is permissible for you to save an
enormous number of people from a headache rather than saving one person from death.
I am not persuaded that there is a problem here. I have a strong intuition that, given a
straight choice between saving one person from death and saving many people from a
headache, you should save the one person from death. But when I consider the sequence case
described above, I lack any clear intuition about what you should or should not do. Others
have told me that they feel the same way. Plausibly, we lack any clear intuition in the
sequence case because it is intuitive that each option is defeated in something like the way
that AIC implies. If that is right, the sequence case actually supports AIC.
25
I have argued that if we take seriously the rationale that Voorhoeve offers for ARC,
and we also take seriously the relative relevance problem, we are led to AIC. I have also
argued that AIC adequately captures the judgments that motivated CEV. We should now
consider how AIC fares against the option dependence problem and the mixed groups
problem.

6. AIC and Option Dependence
As reflection on the sequence case suggests, AIC is vulnerable to the option dependence
problem. Suppose again that you can save one person from death, save one thousand people
from losing a hand, or save one million people from losing a finger. AIC implies that,
because each set of claims is defeated by another set, and no set is dominated, it is
permissible for you to satisfy any set. Suppose that you initially decide to save the one
thousand people from losing a hand, but just as you are about to save them, the one person
dies. With this person gone, the one million claims to be saved from losing a finger are no
longer defeated. So AIC now implies that you should save the one million people from losing
a finger. So AIC has the counterintuitive implication that whether it is permissible for you to
save the one thousand people from losing a hand rather than the one million people from
losing a finger depends on how long the one person stays alive.
Is this a decisive problem for AIC? That depends on whether the implication just
described remains counterintuitive even when we keep in mind the rationale for AIC. I
suggest that the counterintuitiveness of this implication is at least mitigated. When I keep in
mind the rationale for AIC, I can reason myself into accepting that the presence or absence of
the person facing death really does make a difference to which of the other sets of claims it is
permissible for you to satisfy. After all, the presence or absence of the person facing death
makes a difference to which of the other sets of claims is defeated.
26
Of course, Voorhoeve could, and in fact does, defend ARC against the option
dependence problem in just the same way.
18
But as we have seen, the rationale that
Voorhoeve offers for ARC much better supports AIC. So appealing to this rationale to
mitigate the counterintuitiveness of option dependence is more powerful when AIC is the
view that we are defending.
It might now be objected that the option dependence problem is just a symptom of a
more fundamental problem. The ostensibly more fundamental problem is that AIC violates a
principle known as the independence of irrelevant alternatives (also known as basic
contraction consistency). According to this principle, if it is permissible for you to choose an
option O from an option set S, it is permissible for you to choose O from any subset of S
containing O. AIC violates this principle by implying that it is permissible for you to save
one thousand people from losing a hand given the option set {save one person from death,
save one thousand people from losing a hand, save one million people from losing a finger},
but wrong for you to save one thousand people from losing a hand given the subset {save one
thousand people from losing a hand, save one million people from losing a finger}.
However, it is not clear why it should be a problem that AIC violates the
independence of irrelevant alternatives. This principle is typically appealed to in social choice
theory and decision theory, and even in those domains it is controversial. There is no obvious
reason to think that our moral view should satisfy this principle. Suppose you believe that,
when buying wine for a dinner party, it is wrong to buy the cheapest bottle in the shop. This
view might be implausible for all sorts of reasons, but it does not seem to be a special
problem that it violates the independence of irrelevant alternatives, by implying that it is

18
Voorhoeve, ‘How Should We Aggregate Competing Claims?’, at 78–79.
27
permissible for you to buy a $5 bottle given the option set {$4 bottle, $5 bottle, $6 bottle},
but wrong for you to buy a $5 bottle given the subset {$5 bottle, $6 bottle}.
19

I tentatively conclude that the option dependence problem is not a decisive problem
for AIC.

7. AIC and Mixed Groups
Like ARC, AIC needs to be modified if it is to have plausible implications in cases in which
people within the same group face different burdens. Suppose that you can either save one
person from a painful death or save one other person from a fractionally less painful death
and save one million people from losing a finger. Intuitively, you should do the latter. But
AIC implies that you should do the former, for the claims to be saved from losing a finger are
not relevant.
In a footnote addressing this problem, Voorhoeve suggests that, if people in the same
group face different burdens, so long as at least one claim in the group is relevant, the weaker
claims in the group become relevant too. If we modify AIC to incorporate this suggestion,
AIC gets the right result in the case just described. Since the claim to be saved from a
fractionally less painful death is relevant, the claims to be saved from losing a finger become
relevant too, and so the claim to be saved from a painful death is defeated.

19
This example is inspired by examples in Amartya Sen, ‘Internal Consistency of Choice’, Econometrica 61
(1993): 495–521. Some philosophers have argued that we can save the independence of irrelevant alternatives
from these counterexamples by individuating options more finely. See John Broome, Weighing Goods
(Blackwell, 1995): chapter 5; and Michael Neumann, ‘Choosing and Describing: Sen and the Independence of
Irrelevant Alternatives’, Theory and Decision 63 (2007): 79–94. If we allow that options can be individuated
more finely, neither ARC nor AIC will violate the independence of irrelevant alternatives. See Voorhoeve,
‘How Should We Aggregate Competing Claims?’, at 78–79. However, allowing that options can be
individuated more finely risks making the independence of irrelevant alternatives trivial.
28
However, this way of modifying AIC seems ad hoc. And there are cases in which it
has counterintuitive implications. Suppose that you can either save two people from a painful
death or save one other person from a fractionally less painful death and save an enormous
number of people from a headache. Intuitively, you should save the two people from a
painful death, no matter how many people face a headache. But the modified version of AIC
implies otherwise. Since the claim to be saved from a fractionally less painful death is
relevant, the claims to be saved from a headache become relevant too, and enough of these
claims will sum to more than the two claims to be saved from a painful death.
I propose that we explain our judgments about these cases by appeal to the following
notion of secondary relevance. A claim C in a set of claims S1 is (qua member of S1)
secondarily relevant to a set of claims S2 if and only if C is sufficiently strong relative to the
difference between the sum of the claims in S1 that are relevant to S2 and the sum of the
claims in S2 that are relevant to S1. In the former case, the claims against losing a finger are
secondarily relevant to the claim against a painful death, because they are sufficiently strong
relative to the difference between the claim against a painful death and the claim against a
fractionally less painful death. In the latter case, the claims against a headache are not
secondarily relevant to the two claims against a painful death, because they are not
sufficiently strong relative to the difference between the sum of the two claims to be saved
from a painful death and the one claim to be saved from a fractionally less painful death.
I think that this notion of secondary relevance can be supported by an extension of our
rationale for AIC. Suppose that you can either satisfy a set of claims S1 or satisfy a set of
claims S2 and also save yourself from a burden B. Plausibly, whether it is permissible for you
to do the latter depends not only on the difference between the sum of the claims in S1 that
are relevant to S2 and the sum of the claims in S2 that are relevant to S1, but also on the size
of this difference relative to the size of B. If the sum for S1 is much larger than the sum for
29
S2 and B is sufficiently small, you should satisfy S1. If the sum for S1 is not much larger
than the sum for S2 and B is sufficiently large, it is permissible for you to satisfy S2 and save
yourself from B. Suppose next that it is me, rather than you, who must decide what happens. I
can either satisfy S1 or satisfy S2 and also save you from B. Plausibly, it is reasonable for
you to press a claim to my help if and only if it would be permissible for you to choose to
satisfy S2 and save yourself from B rather than satisfying S1. It follows that it is reasonable
for you to press a claim to my help if and only if your claim to be saved from B is sufficiently
strong relative to the difference in strength between the sum of the claims in S1 that are
relevant to S2 and the sum of the claims in S2 that are relevant to S1.
If we accept this notion of secondary relevance, we should modify AIC as follows.

Avoid Inferior Claims + (AIC+):
1. If you can save someone from a burden, she has a claim to your help.
2. Her claim is stronger (i) the greater the burden she faces and (ii) the worse off she
will be if you do not help her.
3. Let S1 and S2 be any two sets of claims. Let C be any claim in S1. C is relevant to
S2 if and only if C is sufficiently strong relative to the strongest claim in S2.
4. C is (qua member of S1) secondarily relevant to S2 if and only if C is sufficiently
strong relative to the difference between the sum of the claims in S1 that are
relevant to S2 and the sum of the claims in S2 that are relevant to S1.
20

20
If further orders of relevance are needed, we can define them as follows: C is (qua member of S1) n-order
relevant to S2 if and only if C is sufficiently strong relative to the difference between the sum of the claims in
S1 that are relevant to, secondarily relevant to, …, or (n-1)-order relevant to S2 and the sum of the claims in S2
that are relevant to, secondarily relevant to, …, or (n-1)-order relevant to S1.
30
5. S1 defeats S2 if and only if the claims in S1 that are relevant or secondarily
relevant to S2 sum to more than the claims in S2 that are relevant or secondarily
relevant to S1.
6. S1 dominates S2 if and only if S1 both defeats S2 and defeats every set of claims
that S2 defeats.
7. Other things equal, you should satisfy a non-defeated set of claims, unless every
set is defeated, in which case you should satisfy a non-dominated set.

8. AIC and Musical Chairs
I will end by responding to a final objection to AIC. This objection is due to Derek Parfit,
who presses it against a closely-related view.
21
My response to the objection is largely a
reproduction of a response from Voorhoeve and Larry Temkin, but having recourse to the
notion of secondary relevance that I defined in the previous section makes a crucial part of
this response much more persuasive.
22

Parfit first asks us to imagine a choice between the following two outcomes, each
involving the same one hundred people, P1–P100:
23

Outcome (1) Outcome (2)
P1 at welfare level 1 P2 at welfare level 1
P2 at welfare level 2 P3 at welfare level 2

21
Parfit, ‘Justifiability to Each Person’, at 383 note 16. Parfit repeats this objection in his On What Matters:
Volume 2 (Oxford: Oxford University Press, 2011): at 208.
22
Voorhoeve, ‘How Should We Aggregate Competing Claims?’, at 82–86; and Temkin, Rethinking the Good,
at 440–442.
23
Parfit labels this case ‘Musical Chairs’, hence the title of this section.
31
P3 at welfare level 3 …
… P100 at welfare level 99
P100 at welfare level 100 P1 at welfare level 100

According to AIC, P1 has a strong claim that you choose (2), for she is so much worse off
under (1), while everyone else has only a very weak claim that you choose (1), for they are
only very slightly worse off under (2). Since the very weak claims are not relevant to the
strong claim, AIC implies that, given the choice between (1) and (2), you should choose (2).
Parfit thinks that this is a mistake. There is, he claims, no morally relevant difference
between (1) and (2). They both contain the same total amount of welfare, the worst-off
person is just as badly off in (1) as the worst-off person is in (2), and the same goes for the
second-worst-off person, the third-worst-off person, and so on up to the best-off person. The
only difference between (1) and (2) is that in (1) P1 finds herself at the bottom of the pack
rather than at the top. And, Parfit claims, P1 ‘has no right to be at the top.’
However, like Temkin and Voorhoeve, I find it quite intuitive that you should choose
(2) over (1). After all, it is much more important for P1 that you choose (2) than it is for
anyone else that you choose (1). And given the opportunity, each of the other people would
be morally required to forego an extra one unit of welfare so that P1 could have an extra 99
units. These seem to me powerful moral reasons to choose (2) over (1). So it seems to me
that, contra Parfit, this kind of example actually supports AIC.
Perhaps in anticipation of the foregoing response, Parfit goes on to strengthen his
objection. He asks us to imagine a choice like the following:

Outcome (1) Outcome (2)
P1 at welfare level 2 P2 at welfare level 1
32
P2 at welfare level 3 P3 at welfare level 2
P3 at welfare level 4 …
… P100 at welfare level 99
P100 at welfare level 101 P1 at welfare level 100

P1 still has a very strong claim that you choose (2). And though everyone else now has a
stronger claim than before, their claims are still not strong enough to be relevant. So AIC
again implies that you should choose (2). This, Parfit thinks, is implausible. As he sees it, the
important difference between (1) and (2) is that the total welfare in (1) is 100 units greater
than in (2). This difference, he thinks, gives you decisive moral reason to choose (1).
Again, like Temkin and Voorhoeve, I am not persuaded by this objection. As before,
it is much more important for P1 that you choose (2) than it is for anyone else that you
choose (1). And given the opportunity, each of the other people would be morally required to
forego an extra two units of welfare so that P1 could have an extra 98 units. These seem to
me powerful moral reasons to choose (2) over (1).
Parfit might now point out that we can make his objection even stronger. We can keep
increasing the amount of welfare that everyone else must forego for P1 to be at the top of the
pack until it becomes implausible that you should choose (2) over (1). However, as we
increase the amount of welfare that everyone else must forego, we also increase the strength
of their claims. Eventually, some of the other people will have claims that are relevant to the
claim of P1. And once just one other claim becomes relevant, other, weaker claims will
33
become secondarily relevant.
24
So AIC+ will begin implying that you should choose (1) over
(2) long before it becomes implausible that you should choose (2) over (1).
25

9. Summary
Many people judge both that there is some number of people you should save from paralysis
rather than saving one person from death, and that there is no number of people you should
save from a headache rather than saving one person from death. These judgments can be
captured by appeal to CEV, but CEV faces both the incoherence problem and the no
permissible options problem.
In response to these problems, Voorhoeve has argued that we should capture the
judgments that motivated CEV by appeal to ARC. There is a plausible rationale for ARC, and
it avoids both the incoherence problem and the no permissible options problem. However,
ARC faces the relative relevance problem, the option dependence problem, and the mixed
groups problem.
I have argued that if we take seriously Voorhoeve’s rationale for ARC, and we also
take seriously the relative relevance problem, we are led to AIC. This view adequately
captures the judgments that motivated CEV, and though it is vulnerable to the option
dependence problem, this problem is not decisive, given the plausibility of the rationale for
AIC.
Like ARC, AIC needs to be modified if it is to have plausible implications in cases in
which people within the same group face different burdens. I have proposed AIC+ as a

24
If needed, we could also appeal to further orders of relevance, as defined above in footnote 13.
25
Voorhoeve makes the same point in defence of ARC. See his ‘How Should We Aggregate Competing
Claims?’, at 86 n. 38. However, in making this point, he relies on the alternative account of secondary relevance
that I argued against in Section 7.
34
reasonable modification. This view has plausible implications in the relevant cases, and it is
supported by an extension of the rationale for AIC. It also allows us to provide a more
persuasive responsive to a further objection that Parfit has pressed against views like AIC.

35
Chapter 2
Non-Aggregation, Partial Aggregation, and Risk
*

0. Note
In Chapter 1, I described problems for the two most prominent partially aggregative views in
the literature, and then developed a new partially aggregative view, which I called Avoid
Inferior Claims (AIC). This new view avoids many of the standard problems with partially
aggregative views, and those that is does not avoid are not decisive.
In this chapter, I argue that, despite the appeal of AIC and partially aggregative views
more generally, we must reject all partially aggregative and non-aggregative views. I argue
that there is a problem with these views that has not been appreciated in the existing
literature: they have unacceptable implications in certain cases involving risk. I conclude that
we should reconsider the prospects for aggregative views. That is my task in Chapter 3.
I should note a change in terminology between Chapter 1 and this chapter. In Chapter
1, I developed a partially aggregative view that focuses on ‘claims’. In this chapter, I describe
non-aggregative and partially aggregative views not in terms of claims but rather in terms of
‘complaints’. A person has a complaint against an act A just in case there is some act B that
would help her more, and her complaint is stronger (i) the more B would help her relative to
A and (ii) the worse off A would leave her absolutely. We can think of complaints as the flip
side of claims: if you are in a position to help someone, we can say either that she has a claim
to your help, or that she has a complaint against you not helping her. Thus, each of the

*
For helpful comments and discussion, I am grateful to Renee Jorgensen Bolinger, David Boonin, Alexander
Dietz, Nathan Robert Howard, Nicola Kemp, Nicholas Laskowski, Alexander Sarch, Thomas Sinclair, Anthony
Taylor, Jonathan Wright, and the editors at Philosophy & Public Affairs. I am especially grateful to Abelard
Podgorski, Jonathan Quong, Jacob Ross, Mark Schroeder, and Ralph Wedgwood.
36
partially aggregative views that I discussed in Chapter 1 can be restated in terms of
complaints.
Why the shift in terminology? I used the claims terminology in Chapter 1 because
much of the literature on partially aggregative views uses this terminology and I wanted the
connections between Chapter 1 and the literature to be clear. I switch to the complaints
terminology in this chapter for the following reason: I will here be considering the
implications that non-aggregative and partially aggregative views have in cases involving
risk. When we apply these views to cases involving risk, we can apply them either ex ante or
ex post. If we apply them ex ante, it makes no difference whether we use the terminology of
claims or complaints. But if we apply them ex post, the complaints terminology is much more
intuitive. Since I want to consider the possibility of applying these views ex post, I use that
terminology throughout this chapter and the chapters that follow.

1. Introduction
Many of our acts benefit some people and burden others. According to some moral views,
when all other things are equal, we are morally required to act in the way that maximizes the
sum of benefits minus burdens.
26
We can say that these views are aggregative. The most
well-known aggregative view is Utilitarianism, but there are others.
27

26
The ‘all other things equal’ clause allows these views to accommodate moral constraints. See Robert Nozick,
Anarchy, State, and Utopia (Blackwell Publishing, 2003): 28–30.
27
For example, Prioritarianism. See Derek Parfit, ‘Equality and Priority’, Ratio 10 (1997): 202–221.
37
Aggregative views tend to have counterintuitive implications in cases in which we
must choose between imposing large burdens on each of a few people and imposing small
burdens on each of many.
28
T. M. Scanlon offers the following illustration.
29

Transmitter Room: Jones has suffered an accident in a TV broadcasting station and is
receiving extremely painful electric shocks. If you turn off the power, a huge number
of viewers will miss the second half of the World Cup final.

Intuitively, you are morally required to turn off the power, no matter how many viewers there
are. But aggregative views imply that, if there are enough viewers, you are morally required
to leave the power on, for the burden imposed on Jones will be less than the sum of the
burdens that would be imposed on each of the viewers.
Scanlon suggests that what matters in Transmitter Room is not the sum of benefits
minus burdens that you could bring about, but rather the strength of the individual complaints
that could be made against your act. Jones could make a much stronger individual complaint
against you leaving the power on than any of the viewers could make against you turning the
power off. That seems to be why you are morally required to turn the power off, no matter
how many viewers there are.

28
We might try to avoid these implications by arguing that the different burdens are incommensurable. See
James Griffin, Well-Being: Its Meaning, Measurement, and Moral Importance (Oxford University Press, 1989):
75–92. However, this move leads to other problems. See Alastair Norcross, ‘Comparing Harms: Headaches and
Human Lives’, Philosophy & Public Affairs 26 (1997): 135–167; and Larry Temkin, Rethinking the Good:
Moral Ideals and the Nature of Practical Reasoning (Oxford University Press, 2012): 45–52.
29
T. M. Scanlon, What We Owe to Each Other (Harvard University Press, 1998): 235.
38
This line of reasoning has led Scanlon and many other philosophers to reject
aggregative views and accept some version of what we can call Minimax Complaint, or MC.
According to this view, when we would not be violating any moral constraints, we are
morally required to act in the way that minimizes the strongest individual complaint.
30

In sections 2–5, I argue that MC must be rejected because it has implausible
implications in certain cases involving risk. In these cases, we can apply MC either ex ante,
by focusing on the complaints that could be made based on the prospects that an act gives to

30
Scanlon, What We Owe to Each Other, chapter 5. Scanlon’s view departs from the simple version of MC in
three main ways. First, his view is concerned not directly with acts, but rather with principles that regulate acts.
Second, on his view, ‘a person could reasonably reject a principle on the grounds that it treated him or her
unfairly.’ Third, on his view, ‘principles must be considered within the framework of other principles which are,
for the moment, being held constant, and possible grounds for rejection are shaped by these background
principles.’ See p. 229. As far as I can tell, these departures from the simple version of MC do not protect
Scanlon’s view from the objections that I raise below. For further defence and discussion of MC, see T. M.
Scanlon, ‘Contractualism and Utilitarianism’, in Amartya Sen and Bernard Williams (eds.), Utilitarianism and
Beyond (Cambridge University Press, 1982): 103–128; Thomas Nagel, Mortal Questions (Cambridge
University Press, 2012): chapter 8; Thomas Nagel, Equality and Partiality (Oxford University Press, 1991);
Sophia Reibetanz, ‘Contractualism and Aggregation’, Ethics 108 (1998): 296–311; Michael Otsuka, ‘Saving
Lives, Moral Theory, and the Claims of Individuals’, Philosophy & Public Affairs 34 (2006): 109–135; Aaron
James, ‘Contractualism’s (Not So) Slippery Slope’, Legal Theory 18 (2012): 263–292; Alex Voorhoeve, ‘How
Should We Aggregate Competing Claims?’, Ethics 125 (2014): 64–87; Rahul Kumar, ‘Risking and Wronging’,
Philosophy & Public Affairs 43 (2015): 27–51; Michael Otsuka, ‘Risking Life and Limb’, in I. Glenn Cohen,
Norman Daniels, and Nir Eyal (eds.), Identified Versus Statistical Lives (Oxford University Press, 2015): 77–93;
and Johann Frick, ‘Contractualism and Social Risk’, Philosophy & Public Affairs 43 (2015): 175–223.
39
people, or ex post, by focusing on the complaints that could be made based on the actual
results that an act has for people. I argue that MC has implausible implications either way.
31

It might seem unnecessary to offer a new argument against MC, since there is an
obvious objection to this view. According to this objection, MC has the implausible
implication that we are morally required to save one person from a large burden, such as
death, rather than any number of people from a slightly smaller burden, such as permanent
paralysis. But proponents of MC are not persuaded by this objection. They argue that MC can
be modified to permit the aggregation of complaints whenever opposing complaints are, as
with death and permanent paralysis, sufficiently close in strength.
32
We can call this modified
view Partially Aggregative MC, or PAMC. My objections to MC will also apply to PAMC.
I end by suggesting that cases involving risk will pose serious problems not just for
MC, but also for non-aggregative and partially aggregative views more generally. I conclude
that we should reconsider the prospects for aggregative views.

31
For a defence of the view that we should apply MC ex ante, see James, ‘Contractualism’s (Not So) Slippery
Slope’; Kumar, ‘Risking and Wronging’; and Frick, ‘Contractualism and Social Risk’. For a defence of the view
that we should apply MC ex post, see Scanlon, What We Owe to Each Other, chapter 5; Reibetanz,
‘Contractualism and Aggregation’; and Otsuka, ‘Risking Life and Limb’. Scanlon has recently switched to the
ex ante view, and he credits Frick’s paper with changing his mind.
32
See F. M. Kamm, Morality, Mortality: Volume 1 (Oxford University Press, 1998): 111–119; Scanlon, What
We Owe to Each Other, p. 232; and Voorhoeve, ‘How Should We Aggregate Competing Claims?’. For
criticisms of this kind of view, see Derek Parfit, ‘Justifiability to Each Person’, Ratio 16 (2003): 368–390; and
John Halstead, ‘The Numbers Always Count’, Ethics 126 (2016): 789–802. Alex Voorhoeve replies to these
criticisms in ‘Why One Should Count Only Claims with Which One Can Sympathize’, Public Health Ethics 10
(2017): 148–156.
40
2. Against Ex Ante MC
I now begin my critique of MC. Again, I argue that MC must be rejected because, whether
we apply it ex ante or ex post, it has implausible implications in certain cases involving risk.
In this section, I assume that we should apply MC ex ante, by focusing on the complaints that
could be made based on the prospects that an act gives to people. I present two cases, each
involving risk, that together illustrate a decisive reason to reject ex ante MC. I then reject a
response to this argument suggested by Johann Frick.

2.1. The Main Objection to Ex Ante MC
Suppose that in

Villain 1: A villain has kidnapped two children, C1 and C2. He will either (1) cut one
hand off C1, or (2) run a lottery that gives C2 a one-in-a-billion chance of death. You
must choose which.

I take it that you are morally required to choose (2), imposing a tiny chance of death on C2 to
spare C1 from losing a hand.
33
For ex ante MC to capture this judgment, a complaint against
certainly losing a hand must be stronger than a complaint against a one-in-a-billion chance of
death.
Suppose next that in

33
It might be claimed that you should refuse to make a choice, for then your hands are clean. To block this
response, we can suppose that if you refuse to make a choice, the villain will destroy the world.
41
Villain 2: A villain has kidnapped C1 and ten billion other children. He will either (1)
cut one hand off C1, or (2) randomly select and kill ten of the other children. You
must choose which.

Clearly, you are morally required to choose (1), imposing the loss of a hand on C1 to spare
ten other children from death. But ex ante MC implies otherwise. If you choose (2), though
you ensure that ten of the ten billion children will die, you impose on each of these children
only a one-in-a-billion chance of death. We have just seen that a complaint against certainly
losing a hand is stronger than a complaint against a one-in-a-billion chance of death. So C1
has a stronger complaint against (1) than any of the other children has against (2). So ex ante
MC has the implausible implication that you are morally required to choose (2).
34

The more general problem is this: ex ante MC has the implausible implication that we
are morally required to do what we know will be very bad for many people rather than what
we know will be much less bad for a few people whenever we have sufficiently low credence
about who the former people are.
Notice that this objection cannot be avoided by appeal to PAMC. A complaint against
certainly losing a hand is much stronger than a complaint against a one-in-a-billion chance of
death. Since these complaints are not close in strength, PAMC cannot allow us to aggregate
the ten billion complaints against a one-in-a-billion chance of death in a way that might
outweigh the complaint against losing a hand. So ex ante PAMC has the same implication as
ex ante MC.
Why do these views fail to capture our intuitions about cases like Villain 2, where a
risk is dispersed across a very large group of people? I suggest that the root of the problem is

34
A similar objection is presented in Reibetanz, ‘Contractualism and Aggregation’, 302–303.
42
the restriction on aggregation, and more specifically, the refusal to allow that many small
risks can combine to morally outweigh a much larger individual burden. But before we
accept that diagnosis, we should consider some other possibilities.

2.2. Frick’s Pluralist Response
In response to a related objection to ex ante MC, Johann Frick suggests ‘scaling back the
ambitions’ of MC.
35
Rather than accepting MC as a view about what we are morally required
to do all-things-considered, we could accept it as a view about one category of pro tanto
moral reasons. According to this scaled-back version of the view, which we can call
MCweak, when every alternative to an act would produce a stronger individual complaint,
this gives us a pro tanto moral reason to perform this act. As Frick emphasises, this pro tanto
moral reason could be outweighed by other pro tanto moral reasons, such as those deriving
from aggregative considerations or from consequentialist considerations about the goodness
of outcomes.
MCweak can avoid the objection that I pressed against ex ante MC. Recall Villain 2.

Villain 2: A villain has kidnapped C1 and ten billion other children. He will either (1)
cut one hand off C1, or (2) randomly select and kill ten of the other children. You
must choose which.

MCweak implies only that you have a pro tanto moral reason to choose (2). It is plausible that
this complaints-based moral reason is outweighed by the aggregative and consequentialist

35
Frick, ‘Contractualism and Social Risk’, 212–223.
43
moral reasons in favour of choosing (1). Thus, MCweak is compatible with the claim that you
are morally required to choose (1).
But MCweak is vulnerable to a closely related objection. Suppose that in

Villain 3: A villain has kidnapped C1 and one billion other children. He will either (1)
break three of C1’s fingers, or (2) randomly select one of the other children and break
four of his fingers. You must choose which.

I take it that you are morally required to choose (1), imposing three broken fingers on C1 to
spare another child from four broken fingers. But you have a very strong complaints-based
reason to choose (2), since a complaint against certainly having three fingers broken is much
stronger than a complaint against a one-in-a-billion chance of having four fingers broken, and
you have only a very weak consequentialist reason to choose (1), since an outcome in which
one child has four fingers broken is only slightly worse than an outcome in which one child
has three fingers broken. So for MCweak to yield the intuitively correct result in this case, we
must claim that even a very strong complaints-based reason is outweighed by even a very
weak consequentialist reason. And once we allow that, accepting MCweak will make no
difference, or only a very slight difference, to what we are morally required to do.
It is worth considering a slight revision to Villain 3. Suppose that the villain will
either (1) break three of C1’s fingers, or (2) randomly select one of the other children and
break three (rather than four) of his fingers. It seems to me that you have equal moral reasons
to choose each option. If that is right, MCweak is not just inconsequential, but also false, for
it implies that you have an extra complaints-based moral reason to choose (2).
36

36
In an appendix to this chapter, I show that my objections to ex ante MC and ex ante PAMC can be greatly
strengthened.
44

3. What is Ex Post MC?
In the previous section, I assumed that we should apply MC ex ante, by focusing on the
complaints that could be made based on the prospects that an act gives to people. As I have
said, there is an alternative. We might instead apply MC ex post, by focusing on the
complaints that could be made based on the actual results that an act has for people. In this
section, I try to clarify this idea, and I explain how it avoids the objection that I pressed
against ex ante MC. In the next section, I argue that ex post MC must be rejected, because
there are other cases involving risk in which it has implausible implications.

3.1. Moreau’s Proposal
Recall Villain 2.

Villain 2: A villain has kidnapped C1 and ten billion other children. He will either (1)
cut one hand off C1, or (2) randomly select and kill ten of the other children. You
must choose which.

Sophia Moreau (formerly Sophia Reibetanz) suggests that, in this kind of case, it is a mistake
to simply apply MC ex ante.
37
She writes,

As long as we know that acceptance of a principle [directing us to perform some act]
will affect someone in a certain way, we should assign that person a complaint that is
based upon the full magnitude of the harm or benefit, even if we cannot identify the

37
Reibetanz, ‘Contractualism and Aggregation’, 304.
45
person in advance. It is only if we do not know whether acceptance of a principle will
affect anyone in a certain way that we should allocate each individual a complaint
based upon his expected harms and benefits under that principle.

On this proposal, because we know that, if you choose (2), ten children will die, we should
assign ten children a complaint against certainly dying. Since this complaint is stronger than
C1’s complaint against certainly losing a hand, given this proposal, MC implies that you are
morally required to choose (1), which is clearly the right result.
Moreau’s proposal is sometimes taken to be a statement of the view that we should
apply MC ex post.
38
But there are at least two problems with her proposal.
First, on Moreau’s proposal, it is often mysterious both who we are assigning
complaints to and why we are assigning these complaints to anyone. For example, in Villain
2, Moreau’s proposal directs us to assign a complaint against certainly dying to ten of the ten
billion children. But which ten children should we assign this complaint to? And why should
we assign this complaint to any of them, when none of them actually faces certain death? (I
return to these questions in the next subsection.)
Second, on Moreau’s proposal, it is only when we know that an act will burden
someone in some way that we should assign this person a complaint based upon the full
magnitude of the burden. If we do not know how an act will affect people, we are to ‘allocate
each individual a complaint based upon his expected harms and benefits’. This feature of the
proposal leaves it vulnerable to a version of the objection that I pressed against ex ante MC.
Suppose that in

38
See, for example, Frick, ‘Contractualism and Social Risk’, 185.
46
Villain 4: A villain has kidnapped C1 and one hundred billion other children. He will
either (1) cut one hand off C1, or (2) randomly select two hundred of the other
children and then flip a coin to decide whether to kill them. You must choose which.

I take it that you are morally required to choose (1), imposing the loss of a hand on C1 rather
than risking the lives of two hundred children on a coin flip. But even on Moreau’s proposal,
MC implies otherwise. If you choose (2), there is a one-in-two chance that no one will die.
Since we do not know whether anyone will die, on Moreau’s proposal, we should assign each
of the one hundred billion children a complaint ‘based upon his expected harms and benefits’.
And that means assigning each of these children a complaint against a one-in-a-billion chance
of death. Since a complaint against certainly losing a hand is stronger than a complaint
against a one-in-a-billion chance of death, it follows that C1 has a stronger complaint against
(1) than any of the other children has against (2). So even on Moreau’s proposal, MC has the
implausible implication that you are morally required to choose (2).
39

3.2. Otsuka’s Proposal
Michael Otsuka suggests a way of extending Moreau’s proposal.
40
He writes,

[Suppose] we do not know that anyone would end up with a complaint of premature
death in [some] scenario, but we are 95% certain that someone would end up with

39
We can make this objection even stronger. Suppose that, if you choose (2), the villain will decide whether to
kill the two hundred children by running a lottery that favours killing them ninety percent of the time. It now
seems even clearer that you are morally required to choose (1). But we still do not know that choosing (2) will
result in any deaths, so on Moreau’s proposal, MC still implies that you are morally required to choose (2).
40
Otsuka, ‘Risking Life and Limb’, 88.
47
such a complaint. I propose that, rather than following [Moreau’s] advice [by
assigning each person a complaint ‘based upon his expected harms and benefits’], we
should instead posit a complaint of premature death in this scenario, where this
complaint is discounted in a manner that tracks the probability that someone would
suffer this fate. When applied to the scenario in question, there would be the
following case against being exposed to risk. There is a 95% chance that someone
would be killed as the result of such exposure, and a 5% chance that nobody would be
killed. Since the risk of death falls short of certainty … we should register a strong
complaint on behalf of that one victim, whoever in particular he may end up being,
who is 95% certain to exist. But we should discount this complaint by 5% to reflect
the chance that nobody would suffer any harm.

Otsuka seems to be suggesting the following way of applying MC. When we know that there
is a risk that an act would impose a particular burden on someone, even if we do not know
who this someone is, we should posit a complaint against this act based on the full magnitude
of this burden, and then discount this complaint by the probability that someone will
experience this burden. We are then morally required to act not in the way that minimizes the
strongest individual complaint, but rather in the way that minimizes the strongest probability-
discounted individual complaint.
As I explain in the next subsection, Otsuka’s proposal is not quite the right way to
apply MC ex post. But it is on the right track. It gets us the intuitively correct result in each of
the cases that we have considered so far. Recall Villain 4.

48
Villain 4: A villain has kidnapped C1 and one hundred billion other children. He will
either (1) cut one hand off C1, or (2) randomly select two hundred of the other
children and then flip a coin to decide whether to kill them. You must choose which.

On Otsuka’s proposal, we reason as follows. If you choose (1), C1 will certainly lose a hand.
So we posit a complaint against (1) based on losing a hand and then discount this complaint
by the probability that C1 will actually lose a hand. Since the probability is one, this means
not discounting this complaint at all. If you choose (2), there is a one-in-two chance that two
hundred children will die. So we posit a complaint against (2) based on death and then
discount this complaint by the probability that anyone will actually die. Since the probability
is one in two, this means reducing the strength of this complaint by half. We then compare a
complaint against losing a hand with a complaint that has half of the strength of a complaint
against death. Plausibly, the latter complaint is stronger. So it follows that you are morally
required to choose (1), which is clearly the right result.
Otsuka worries that his proposal suffers from the first problem that I raised for
Moreau’s proposal.
41
He notes that on his proposal, we are often required to posit a complaint
even though ‘no particular flesh-and-blood person would have a complaint’. The bearer of
this complaint, he suggests, is in some respects ‘akin to a fictional character rather than an
actual flesh-and-blood human being.’ And, he writes, ‘one might question whether the
complaints of such abstract entities, who are other than actual persons, have moral force.’
Why should what we are morally required to do be determined in part by ‘the phantom
complaint of a purely abstract entity’?

41
Otsuka, ‘Risking Life and Limb’, 84–86.
49
A possible answer to this question is that, because the universe is largely
deterministic, really there is a fact about which person would experience the relevant burden,
and so really there is a fact about to whom the corresponding complaint belongs. Otsuka does
not appeal to this answer, and rightly so. If his proposal depended on the universe being
deterministic, it would not apply in a non-deterministic universe, or in any case in which
things are objectively risky. So in a non-deterministic universe, and in any case in which
things are objectively risky, we would have to apply MC ex ante. So we would get the
intuitively wrong result in versions of my cases in which the villain selects the children using
a non-deterministic lottery.
Otsuka’s actual answer to this question is brief and opaque. He writes,

I believe that the answer to this question is that the complaint … is not the complaint
of an indeterminate person along the lines of a fictional character. … Rather the
indeterminacy of the person is simply the lack of determinacy to which of the …
scenarios would have been the upshot, where each scenario involves the killing of an
actual flesh-and-blood [person].
42

I am not sure what Otsuka has in mind here. But there is a way of interpreting his proposal on
which it avoids the charge of assigning phantom complaints to purely abstract entities. We
need to distinguish between ex ante complaints, which are complaints based on the prospects
that an act gives to people, and ex post complaints, which are complaints based on the actual
results that an act has for people. When we apply MC ex ante, we ignore ex post complaints
and aim to minimize the strongest ex ante complaint that could be made against our act.

42
Otsuka, ‘Risking Life and Limb’, 86.
50
Otsuka’s proposal can be seen as directing us, instead, to ignore ex ante complaints and aim
to minimize the strongest ex post complaint that our act generates. So, in Villain 4, when we
posit a complaint against (2) based on death, we are not assigning this complaint to anyone.
We are simply taking into account that, if you choose (2), there is a one-in-two chance that
this act will generate an ex post complaint based on death.
43

3.3. Ex Post MC
As I mentioned before, Otsuka’s proposal is not quite the right way to apply MC ex post. We
can see this by considering a slightly more complicated case. Suppose that in

Villain 5: A villain has kidnapped C1 and C2. He will either (1) impose a 50-unit
burden on C1, or (2) flip a coin to decide whether to impose a 98- or a 99-unit burden
on C2. You must choose which.

I take it that you are morally required to choose (1), imposing a 50-unit burden on C1 in order
to spare C2 from a burden of roughly twice the size. On Otsuka’s proposal, however, MC
implies otherwise. If we take the ex post complaints that might be generated by (2) and
discount each by the probability of it being generated, the strongest resulting complaint has
strength 49.5. Since the strongest probability-discounted complaint against (1) is 50, it
follows, on this way of applying MC, that you are morally required to choose (2).
I suggest that the proper way to apply MC ex post is as follows. We consider each
possibility that might result from an act, take the strongest ex post complaint in each
possibility, discount this complaint by the probability of this possibility obtaining, and then

43
I take it that by presenting ex post MC in this way, we avoid the second set of objections that Frick presses
against this view in ‘Contractualism and Social Risk’, 194–201.
51
sum the results. The final result is the expected strongest ex post complaint of the act. We are
then morally required to act in the way that minimizes the expected strongest ex post
complaint.
In Villain 5, there are two possibilities that might result from (2): either C2 will have
an ex post complaint of strength 98, or he will have an ex post complaint of strength 99. If we
take these complaints, discount each by the probability that it is generated, and then sum the
results, we get a complaint of strength 98.5. This is the expected strongest ex post complaint
of (2). Since this complaint is almost twice as strong as the expected strongest ex post
complaint of (1), ex post MC correctly implies that you are morally required to choose (1).
As we have just seen, the modified proposal departs from Otsuka’s proposal in cases
like Villain 5. But these proposals have the same implications, and apply in roughly the same
way, in cases like Villain 2 and Villain 4, where there is only one ex post complaint that
might be generated by each of the acts available to us. In what follows, we need consider
only these simpler cases, so the difference between the modified proposal and Otsuka’s
proposal will not matter.

4. Against Ex Post MC
In the previous section, I tried to clarify what it means to apply MC ex post, and I explained
how ex post MC avoids the objection that I pressed against ex ante MC. In this section, I
argue that ex post MC must be rejected, because there are other cases involving risk in which
it has implausible implications. I begin by responding to a risk-based objection to ex post MC
suggested by Frick. I then present what seems to me a stronger objection.

52
4.1. Frick’s Objection to Ex Post MC
In the course of defending an ex ante version of MCweak, which I argued against in section
two, Frick presses an objection against ex post MC. He asks us to consider the following
case.
44

Virus: A terrible virus threatens one million young children. If we do nothing, the
virus will kill all of them. We must choose between mass producing one of two
vaccines (capacity constraints prevent us from producing both). Vaccine 1 is certain
to save every child’s life, but the vaccine does not offer complete protection, so each
child will end up with one paralysed leg. Vaccine 2 is risky. It gives each child a
0.999 chance of surviving the virus completely unharmed, but for every child, there is
a 0.001 chance that the vaccine will be ineffective, in which case the child will die. So
we can expect that, if we choose Vaccine 2, around one thousand of the children will
die.

Frick thinks that we are morally required to choose Vaccine 2, even though, if we do, around
one thousand of the children will die. In defence of this judgment, he writes,

In real life, we often impose social risks that closely resemble that of choosing
Vaccine 2. Thus, it is commonly deemed morally unproblematic to systematically
inoculate young children against certain serious but nonfatal childhood diseases
where there is a remote chance of fatal side effects from the inoculation itself. But this
is not because it is unlikely that inoculation will ever lead to disaster for some

44
Frick, ‘Contractualism and Social Risk’, 181–182.
53
unlucky children. Given the large number of children inoculated each year, it is a
statistical certainty that some number of them will develop fatal complications.
45

Frick then argues that while ex ante MC is compatible with the claim that we are morally
required to choose Vaccine 2, ex post MC is not. He argues as follows. It is better to face a
one-in-a-thousand chance of death than to lose the use of a leg. So it is in the ex ante interest
of each child that we choose Vaccine 2. So each child has an ex ante complaint against
Vaccine 1 and no ex ante complaint against Vaccine 2. So ex ante MC implies that we are
morally required to choose Vaccine 2. But choosing Vaccine 2 would almost certainly
generate a number of ex post complaints based on death. Since each of these complaints
would be much stronger than an ex post complaint based on losing the use of a leg, ex post
MC implies that we are morally required to choose Vaccine 1.
I think there are at least two ways for proponents of ex post MC to answer this
objection.
First, they could adopt an ex post version of PAMC and hold that a complaint against
losing the use of a leg is sufficiently close in strength to a complaint against death for PAMC
to permit the aggregation of these complaints.
46
It is plausible that one million complaints
against losing the use of a leg together outweigh one thousand complaints against death, so
ex post PAMC is compatible with the claim that we are morally required to choose Vaccine
2. Frick might respond to this suggestion by reducing the burden that Vaccine 1 imposes on
each of the children until the ex post complaint that would be generated by Vaccine 1 is no
longer close in strength to the ex post complaint that would be generated by Vaccine 2. But

45
Frick, ‘Contractualism and Social Risk’, 185–186.
46
Voorhoeve defends a version of PAMC on which these complaints would indeed be sufficiently close in
strength. See his ‘How Should We Aggregate Competing Claims?’, 70–75.
54
once the burden imposed by Vaccine 1 is sufficiently reduced, it will be much less clear that
we are morally required to choose Vaccine 2.
Second, recall that to avoid a version of the objection that I pressed against ex ante
MC, Frick suggested adopting an ex ante version of MCweak. Proponents of ex post MC
could avoid Frick’s objection by making the same move.
47
That is, they could adopt an ex
post version of MCweak. According to this view, when every alternative to an act has a
stronger expected strongest ex post complaint, this gives us a pro tanto moral reason to
perform this act. As Frick emphasises, this pro tanto moral reason could be outweighed by
other pro tanto moral reasons, such as those deriving from aggregative or consequentialist
considerations. Since it is plausible that the aggregative and consequentialist moral reasons in
favour of choosing Vaccine 2 would outweigh any complaints-based moral reason in favour
of choosing Vaccine 1, ex post MCweak is compatible with the claim that we are morally
required to choose Vaccine 2.

4.2. The Main Objection to Ex Post MC
I think that there is a stronger risk-based objection to ex post MC. I will now present three
cases that together illustrate this objection.
Suppose that in

Villain 6: A villain has kidnapped C1. He will either (1) cut one hand off C1, or (2)
run a lottery that gives C1 a one-in-a-billion chance of death. You must choose which.

47
I owe this suggestion to Jonathan Quong.
55
I take it that you are morally required to choose (2), exposing C1 to a tiny chance of death to
spare him from losing a hand. For ex post MC to capture this judgment, an ex post complaint
based on losing a hand discounted by probability one must be stronger than an ex post
complaint based on death discounted by probability one in a billion.
Suppose next that in

Villain 7: A villain has kidnapped one billion children. He will either (1) cut one hand
off each child, or (2) randomly select and kill one of the children. You must choose
which.

It is not obvious what you should do in this case. But ex post MC implies that you are
morally required to choose (1), for (2) is certain to generate an ex post complaint based on
death, and that complaint is clearly stronger than an ex post complaint based on losing a
hand.
Here comes the problem. Suppose that in

Villain 8: A villain has kidnapped one billion children. For each child, the villain will
either (1) cut one hand off this child, or (2) give this child a ticket for a lottery with
one billion unique tickets. You must choose between these options for each child in
turn. You know that, after you have chosen for all of the children, the villain will
randomly select one of the one billion lottery tickets and then kill any child who has
the corresponding ticket.

For each child, it is certain that choosing (1) will generate an ex post complaint based on
losing a hand, and there is a one-in-a-billion chance that choosing (2) will generate an ex post
56
complaint based on death. We have seen, from Villain 6, that an ex post complaint based on
losing a hand discounted by probability one is stronger than an ex post complaint based on
death discounted by probability one-in-a-billion. So ex post MC implies that, for each child,
you are morally required to choose (2). But choosing (2) rather than (1) for each child is
equivalent to choosing that the villain randomly select and kill one of the children rather than
cut one hand off each child. And that is the same choice that ex post MC condemned in
Villain 7. So ex post MC is inconsistent, in the sense that it has different implications across
cases that seem in all morally relevant respects equivalent.
The more general problem is this: ex post MC implies that we can be morally required
to make a choice A rather than a choice B, and yet be morally required to make a series of
choices C rather than a series of choices D, even when we know that making C rather than D
is in all morally relevant respects equivalent to making B rather than A. Put another way, ex
post MC violates the following principle of consistency: if a moral view condemns act X, it
should condemn any series of acts that is in all morally relevant respects equivalent to X.
48

It might seem that this objection can be avoided by adopting ex post PAMC. If we
hold that an ex post complaint based on losing a hand is sufficiently close in strength to an ex
post complaint based on death for PAMC to permit the aggregation of complaints in Villain
7, and we also hold that one billion ex post complaints based on losing a hand together
outweigh one ex post complaint based on death, then ex post PAMC implies that you are
morally required to choose (2) in Villain 7, which is consistent with the implication that you
are morally required to choose (2) for each child in Villain 8. However, we can block this
response by reducing the burden that the villain is threatening to impose on each child from
the loss of a hand to something much smaller, such as a broken finger, so that ex post PAMC

48
I am grateful to an anonymous editor for suggesting this way of putting the point.
57
no longer permits the aggregation of complaints in Villain 7. And if an ex post complaint
based on the reduced burden is weaker than an ex post complaint based on death discounted
by one-in-a-billion, we can just increase the number of children involved in these cases, so
that the probability of death for each child becomes negligible. These revisions would also
block a response to the objection that appeals to ex post MCweak.

5. Against Hybrid MC
I have now raised risk-based objections to both ex ante and ex post MC. It is natural to
wonder whether a hybrid of these views could avoid these objections.
49
According to the
simplest hybrid view, which we can call MChybrid, we have a pro tanto moral reason to act
in the way that minimizes the strongest ex ante complaint, and we also have a pro tanto moral
reason to act in the way that minimizes the expected strongest ex post complaint.
There are a number of problems with this hybrid view, but to save space, I will
mention just one. This view is vulnerable to the objection that I raised for ex ante MCweak.
Recall Villain 3.

Villain 3: A villain has kidnapped C1 and one billion other children. He will either (1)
break three of C1’s fingers, or (2) randomly select one of the other children and break
four of his fingers. You must choose which.

I take it that you are morally required to choose (1), imposing three broken fingers on C1 to
spare another child from four broken fingers. MChybrid implies otherwise. It implies that you
have a very strong ex ante complaints-based reason to choose (2), since a complaint against

49
James briefly considers a hybrid view in ‘Contractualism’s (Not So) Slippery Slope’, 273–274.
58
certainly having three fingers broken is much stronger than a complaint against a one-in-a-
billion chance of having four fingers broken. And though it also implies that you have an ex
post complaints-based reason to choose (1), this reason is much weaker, since an ex post
complaint against having four fingers broken is only slightly stronger than an ex post
complaint against having three fingers broken. Since the ex ante complaints-based reason to
choose (2) is much stronger than the ex post complaints-based reason to choose (1),
MChybrid implies that you are morally required to choose (2).
A proponent of MChybrid could avoid this objection by holding that ex post
complaints-based reasons are generally stronger than ex ante complaints-based reasons, but
this move, as well as seeming rather ad hoc, would leave the view vulnerable to a version of
the objection that I pressed against ex post MC. I conclude that MChybrid is not a promising
view.

6. Conclusion
That completes my critique of MC. I argued that we should reject ex ante MC, because it
implies that we are morally required to do what we know will be very bad for many people
rather than what we know will be much less bad for a few people whenever we have
sufficiently low credence about who the former people are. And I argued that we should
reject ex post MC, because it implies that we can be morally required to make a choice A
rather than a choice B, and yet be morally required to make a series of choices C rather than a
series of choices D, even when we know that making C rather than D is in all morally
relevant respects equivalent to making B rather than A.
I suspect that any plausible non-aggregative view would have to be structurally very
similar to MC. It might focus not on minimizing the strongest complaint, but instead on
minimizing the greatest loss, or on satisfying the strongest claim to be helped. But such
59
departures from MC would be largely cosmetic. If that is right, we can expect cases involving
risk to pose serious problems not just for MC, but also for non-aggregative views more
generally. We should therefore reconsider the prospects for aggregative views.

Appendix: Strengthening the Objection to Ex Ante MC and Ex Ante PAMC
In this appendix, I show that my objections to ex ante MC and ex ante PAMC can be greatly
strengthened.
My objection to ex ante MC focused on the following case.

Villain 2: A villain has kidnapped C1 and ten billion other children. He will either (1)
cut one hand off C1, or (2) randomly select and kill ten of the other children. You
must choose which.

Since a complaint against certainly losing a hand is much stronger than a complaint against a
one-in-a-billion chance of death, ex ante MC has the implausible implication that you are
morally required to choose (2). This objection can be strengthened in two ways.
First, we can reduce the cost that is to be imposed on C1. Suppose that in

Villain 2*: A villain has kidnapped C1 and N other children. He will either (1) give
C1 a headache, or (2) randomly select and kill ten of the other children. You must
choose which.

Presumably, there is some very tiny risk of death such that a complaint against this risk is
weaker than a complaint against a headache. (Most of us happily take aspirin despite the very
tiny risk that someone has switched our tablets for cyanide.) Let us say, being very
60
conservative, that this risk is one in a trillion. Then, so long as N, the number of kidnapped
children, is greater than ten trillion, ex ante MC still implies that you should choose (2). That
is, ex ante MC implies that you should sentence ten children to death in order to spare one
child from a headache.
Second, we can increase the number of children who are to be killed. Suppose that in

Villain 2**: A villain has kidnapped C1 and N other children. He will either (1) give
C1 a headache, or (2) randomly select and kill M of the other children. You must
choose which.

So long as N is a trillion times larger than M, no matter how large M is, ex ante MC implies
that you should choose (2), for (2) gives each of the M children only a one-in-a-trillion
chance of death. Thus, if N is 10
+18
, M could be one million, and ex ante MC would still
imply that you are morally required to choose (2). That is, ex ante MC would imply that you
are morally required to sentence one million children to death in order to spare one child
from a headache.
It is worth comparing this implication of ex ante MC with the counterintuitive
implications that aggregative views have in cases like Transmitter Room. In Transmitter
Room, aggregative views imply that you are morally required to save an enormous number of
people from missing the World Cup final rather than saving one person from a painful
electric shock. In Villain 2**, ex ante MC can imply that you are morally required to
sentence one million children to death in order to spare one child from a headache. Of these
two implications, the latter is clearly worse.
Next, notice that ex ante PAMC also implies that, so long as N is sufficiently larger
than M, you are morally required to choose (2), no matter how large M is. This is because, as
61
we increase the size of N relative to M, the complaints of each of the M children get weaker.
So even if M is one million, there is some very large number for N such that the M children
would have only a trivially weak complaint against (2). If we keep increasing N, this
complaint will become so much weaker than a complaint against a headache that PAMC will
no longer allow us to aggregate the complaints of the M children in a way that would
outweigh the complaint of C1. So ex ante PAMC can also imply that you are morally
required to sentence one million children to death in order to spare one child from a
headache. Again, this implication is clearly much worse than the implications that
aggregative views have in cases like Transmitter Room.

62
Chapter 3
Reconsidering Aggregation

1. Introduction
In Chapter 1, I described problems for the two most prominent partially aggregative views in
the literature, and then developed a new partially aggregative view, which I called Avoid
Inferior Claims (AIC). This new view avoids many of the standard problems with partially
aggregative views, and those that is does not avoid are not decisive.
In Chapter 2, I argued that, despite the appeal of AIC and partially aggregative views
more generally, we must reject all partially aggregative and non-aggregative views. I argued
that there is a problem with these views that has not been properly appreciated in the existing
literature: they have unacceptable implications in certain cases involving risk. I concluded
that we should reconsider the prospects for aggregative views. That is my task in this chapter.
The main objection to aggregative views is that they have counterintuitive
implications in cases in which we must choose between imposing large burdens on each of a
few people and imposing small burdens on each of many. Suppose that in

Death v Headaches: You can either save one person from death or save many people
from a headache.

Intuitively, you should save the one person from death, no matter how many people face
headaches. But aggregative views imply that, if enough people face headaches, you should
instead save them.
50

50
We might try to avoid these implications by arguing that the different burdens are incommensurable, but this
move leads to other problems. See note 28 in Chapter 2.
63
I here argue that, in the absence of a viable non-aggregative or partially aggregative
view, we should accept the counterintuitive implications that aggregative views have in cases
like Death v Headaches. In Section 2, I follow several proponents of aggregative views in
deploying what we can call the large numbers argument.
51
According to this argument, our
intuitions about cases like Death v Headaches are not reliable, because these cases require us
to imagine very large numbers of people and we cannot accurately imagine very large
quantities. In Section 3, I respond to an objection to my use of the large numbers argument.
According to this objection, appealing to the large numbers argument undermines my
objections to non-aggregative and partially aggregative views, for these objections also
appeal to our intuitions about cases involving very large numbers of people. I argue that this
objection is mistaken. In Section 4, I argue against two replies to the large numbers
argument. These replies have recently been offered by Alex Voorhoeve and Theron Pummer,
and both purport to show that we can trust our intuitions about cases involving very large
numbers of people even if, as the large numbers argument claims, we are unable to accurately
imagine these cases.
52
In Section 5, I briefly discuss three other arguments that, like the large
numbers argument, have been claimed to support the implications that aggregative views
have in cases like Death v Headaches. These arguments are not conclusive, but they
strengthen the case for aggregative views.

51
See Alastair Norcross, ‘Comparing Harms: Headaches and Human Lives’, Philosophy & Public Affairs 26
(1997): 135–167; Derek Parfit, ‘Justifiability to Each Person’, Ratio 16 (2003): 368–390, at 385–386; John
Broome, Weighing Lives (Oxford: Oxford University Press, 2004): at 56–57; Michael Huemer, ‘In Defence of
Repugnance’, Mind 117 (2008): 899–933, at 907–910; and John Halstead, ‘The Numbers Always Count’,
Ethics 126 (2016): 789–802, at 797.
52
See Alex Voorhoeve, ‘How Should We Aggregate Competing Claims?’, Ethics 125 (2014): 64–87, at 75–76;
and Theron Pummer, ‘Intuitions about Large Number Cases’, Analysis 74 (2013): 37–46.
64

2. The Large Numbers Argument
The large numbers argument has been articulated in several different ways and used to argue
for several different conclusions. Michael Huemer deploys the argument to argue that we
cannot trust our intuitions about Derek Parfit’s ‘Repugnant Conclusion’.
53
He writes,

We should be wary of intuitions whose reliability turns on our appreciating large
numbers. This is because, beyond a certain magnitude, all large quantities strike our
imagination much the same. … When we try to imagine a billion years, our mental
state is scarcely different, if at all, from what we have when we try to imagine a
million years. If promised a billion years of some pleasure, most of us would react
with little, if any, more enthusiasm than we would upon being promised a million
years of the same pleasure. Intellectually, we know that one is a thousand times more
pleasure than the other, but our emotions and felt desires will not reflect this.

And John Broome deploys the large number argument to argue that we cannot trust our
intuitions about Larry Temkin’s ‘Spectrum Arguments’.
54
He writes,

We are dealing with very large numbers of people, and we have no reason to trust
anyone’s intuitions about very large numbers, however excellent their philosophy.

53
Huemer, ‘In Defence of Repugnance’, at 908–909. For the Repugnant Conclusion, see Derek Parfit, Reasons
and Persons (Oxford: Oxford University Press, 1987): 381–390.
54
Broome, Weighing Lives, at 56–57. For the Spectrum Arguments, see Larry Temkin, ‘A Continuum
Argument for Intransitivity’, Philosophy & Public Affairs 23 (1996): 175–210; and Larry Temkin, Rethinking
the Good (Oxford: Oxford University Press, 2012): 23–66.
65
Even the best philosophers cannot get an intuitive grasp of, say, tens of billions of
people. That is no criticism; these numbers are beyond intuition. But these
philosophers ought not to think their intuition can tell them the truth about such large
numbers of people.

Put in the way that seems to me most forceful, and focusing on our intuitions about
cases like Death v Headaches, the large numbers argument goes as follows: There is an upper
limit on the number of people we can accurately imagine. When we get above this limit, the
image in our mind remains roughly the same. (To see this, try imagining a million people,
and then try imagining a billion.) Since there is an upper limit on the number of people we
can accurately imagine, there is an upper limit on the disvalue our intuitions place on large
numbers of people experiencing small burdens. But this limit reflects the limit on our
imaginations, not a genuine limit on the disvalue of large numbers of people experiencing
small burdens. If there were no such limit on our imaginations, our intuitions about cases like
Death v Headaches might be different. So we should place little or no weight on our
intuitions about these cases.
I confess that I used to be very sceptical of the large numbers argument. It seemed to
me so obvious that you should save one person from death rather than saving any number of
people from headaches that I was inclined to dismiss this argument without much thought.
But after seeing the problems that non-aggregative and partially aggregative have in cases
involving risk, I began to wonder whether I had previously dismissed the large numbers
argument too quickly. And on reflection, this argument seems to me quite powerful. It seems
right that there is an upper limit on the number of people that we can accurately imagine. And
it seems right that such a limit would make our intuitions about cases like Death v Headaches
unreliable. So I now think that we should take this argument seriously. Unless it can be
66
answered, our intuitions about cases like Death v Headaches do not give us decisive reason to
reject aggregative views.
55

In Section 4, I consider two recent attempts to answer the large numbers argument
and argue that both attempts fail. But first, I want to consider an objection that targets not the
large numbers argument itself, but rather my use of this argument.

3. Intuitions about My Villain Cases
It might seem that, in deploying the large numbers argument, I undermine the objections that
I pressed against non-aggregative and partially aggregative views in Chapter 2. This is
because these objections appeal to our intuitions about my villain cases, and my villain cases
also involve very large numbers of people. If the large numbers argument is right, and we
cannot be confident in our intuitions about cases involving very large numbers of people, it
seems that we cannot be confident in our intuitions about my villain cases. And so these cases
cannot provide a decisive objection to non-aggregative and partially aggregative views.
This is a natural reaction to my use of the large numbers argument, but it is
nevertheless mistaken. What the large numbers argument purports to show is not exactly that

55
Huemer offers a second reason to doubt our intuitions about cases involving very large numbers of people:
most of us make intuitive errors when compounding very small quantities. To illustrate the error, Huemer asks
us to imagine a very large piece of paper just one thousandth of an inch thick, and then imagine that this paper is
folded in half fifty times. Most people, he claims, would estimate that the folded paper would be less than a few
hundred feet thick, when in fact it would be around 18 million miles thick. See Huemer, ‘In Defence of
Repugnance’, at 909–910. However, I am sceptical that this error could explain our intuitions. Even if most
people would greatly underestimate the thickness of the paper, they would still recognize that folding the paper
an infinite number of times would make it infinitely thick. So while our inability to accurately compound very
small quantities could explain the intuition that even an enormous number of headaches is less bad than one
death, it could not by itself explain the intuition that any number of headaches is less bad than one death.
67
we cannot trust our intuitions about cases involving very large numbers of people, but rather
that we cannot trust our intuitions about cases that require us to imagine very large numbers
of people. And as I will now argue, though my villain cases involve very large numbers of
people, they require us to imagine at most only a very small number of these people.
Recall Villain 2, the case that I used to argue against ex ante MC and ex ante PAMC.

Villain 2: A villain has kidnapped C1 and ten billion other children. He will either (1)
cut one hand off C1, or (2) randomly select and kill ten of the other children. You
must choose which.

This case involves over a billion children. But to form an intuition about what you are
morally required to do in this case, we need not imagine all of these children. We need
imagine only an outcome in which C1 loses a hand and an outcome in which ten children die.
We can easily imagine these outcomes, and it is obvious which you should choose.
Next, recall Villain 7 and Villain 8, the cases that I used to argue against ex post MC
and ex post PAMC.

Villain 7: A villain has kidnapped one billion children. He will either (1) cut one hand
off each child, or (2) randomly select and kill one of the children. You must choose
which.

Villain 8: A villain has kidnapped one billion children. For each child, the villain will
either (1) cut one hand off this child, or (2) give this child a ticket for a lottery with
one billion unique tickets. You must choose between these options for each child in
turn. You know that, after you have chosen for all of the children, the villain will
68
randomly select one of the one billion lottery tickets and then kill any child who has
the corresponding ticket.

To form intuitions about what you should do in these cases, we would have to imagine an
outcome in which each of one billion children loses a hand. But my argument against ex post
MC and ex post PAMC did not rely on our intuitions about what you should do in these
cases. Instead, it relied on the judgment that these cases are in all morally relevant respects
equivalent. The problem for ex post MC and ex post PAMC is not that they conflict with our
intuitions about what you should do in these cases, but rather that they imply that you should
choose (1) in Villain 7 and yet choose (2) for each child in Villain 8.
In sum, though my villain cases involve very large numbers of people, my arguments
involving these cases require us to imagine at most only a very small number of these people.
So the large numbers argument does not undermine my objections to non-aggregative and
partially aggregative views.

4. Two Replies to the Large Numbers Argument
In this section, I argue against two replies to the large numbers argument. These replies have
recently been offered by Alex Voorhoeve and Theron Pummer, and both purport to show that
we can trust our intuitions about cases involving very large numbers of people even if, as the
large numbers argument claims, we are unable to accurately imagine these cases.

4.1. Voorhoeve’s Reply
Voorhoeve argues that our intuitions about cases like Death v Headaches are not the result of
our attempting to imagine and intuitively assess the disvalue of very large numbers of people
experiencing headaches or other small burdens. Instead, these intuitions are the result of our
69
intuitively grasping the following reasoning, which I discussed in Chapter 1: Each of the
people facing a headache should be more concerned about the one person avoiding death than
about herself avoiding a headache. Since they should be more concerned about the one
person avoiding death, they cannot reasonably press a claim to your help that competes with
the claim of the one person. Since they cannot reasonably press a claim to your help, you
should ignore their claims. So you should save the one person from death no matter how
many people face headaches.
56

If our intuitions about cases like Death v Headaches are indeed the result of our
intuitively grasping this kind of reasoning, the large numbers argument does nothing to
undermine these intuitions. But I am sceptical that most people intuitively grasp this
reasoning, and hence sceptical that this reasoning explains these intuitions. Philosophers have
been thinking about cases like Death v Headaches for some time now, and the above
reasoning was brought to bear on these cases only very recently, with the publication of
Voorhoeve’s paper. If most people intuitively grasped this reasoning, this reasoning would
have been brought to bear on these cases much earlier.
Furthermore, the claim that our intuitions about cases like Death v Headaches are the
result of our intuitively grasping this reasoning would vindicate these intuitions only if this
reasoning were sound. But, as we have seen, this reasoning leads to a partially aggregative
view that has unacceptable implications in certain cases involving risk. Since this reasoning
has unacceptable implications, we should reject it. And if our intuitions about cases like
Death v Headaches are the result of this reasoning, we should ignore these intuitions.
57

56
Voorhoeve, ‘How Should We Aggregate Competing Claims?’, at 75–76.
57
Does this response beg the question against Voorhoeve? I do not see how it could. The question is whether
our intuitions about cases like Death v Headaches are reliable. Voorhoeve claims that they are, because they are
70
So either our intuitions about cases like Death v Headaches are unreliable because
they are the result of our attempting to imagine and intuitively assess ever greater numbers of
people experiencing small burdens, or they are unreliable because they are the result of our
intuitively grasping Voorhoeve’s reasoning. Either way, we have good reason to doubt these
intuitions, and so they do not give us decisive reason to reject aggregative views.
At the end of the next subsection, I offer a further reason to doubt that our intuitions
about cases like Death v Headaches are the result of our intuitively grasping Voorhoeve’s
reasoning.

4.2. Pummer’s Reply
Pummer offers a different reply to the large numbers argument.
58
He focuses on defending
the intuition that no number of minute-long hangnail pains could be worse than two years of
excruciating torture, but he intends his argument to generalize, so we can here focus on the
intuition that you should save one person from death rather than saving any number of people
from headaches.
Pummer argues as follows. First, consider two competing hypotheses:

(A) If we could accurately imagine any number of people experiencing headaches, we
would have the intuition that there is no number of people such that you should save
this number from headaches rather than saving one person from death.

supported by a particular form of reasoning. I have argued that we should reject this reasoning. So, if this
reasoning is what supports these intuitions, these intuitions are unreliable.
58
Pummer, ‘Intuitions about Large Number Cases’, 37–46.
71
(B) If we could accurately imagine any number of people experiencing headaches, we
would have the intuition that there is some number of people such that you should
save this number from headaches rather than saving one person from death.

Next, consider the following claim:

The Variable Claim: You should save one person from death rather than saving X
number of people from headaches.

Using this claim, we can argue against (B), and in support of (A), as follows:

1. Our intuitions about cases involving small- and medium-sized numbers of people
are typically reliable.

2. If our intuitions about cases involving small- and medium-sized numbers of people
are typically reliable, then if (B) were true, we would become less confident in The
Variable Claim as we imagine X increasing from a small- to a medium-sized
number.
59
That is, we would become less confident in The Variable Claim as we
imagine X increasing from one to ten, even less confident as we imagine X increasing
to 100, and even less confident as we imagine X increasing to 1000.

59
Pummer does not explicitly include premise 1 or the first clause of premise 2 in the main presentation of his
argument, but he acknowledges the need for them at 41–42 and in footnote 5. If our intuitions about cases
involving small- and medium-sized numbers of people were not reliable, there would be no reason to think that,
if (B) were true, we would become less confident in The Variable Claim as we imagine X increasing from a
small- to a medium-sized number.
72

3. We do not become less confident in The Variable Claim as we imagine X
increasing from a small- to a medium-sized number.

Therefore,

4. (B) is false. And so (A) is true.
60

Pummer continues: Proponents of the large numbers argument do not deny that our moral
intuitions have justificatory force, nor do they deny that we can accurately imagine small-
and medium-sized sized quantities, so they should accept 1. 2 is intuitively plausible. And 3
is supported by our intuitions about cases in which small- and medium-sized numbers of
people experience headaches. Since, 1, 2, and 3 imply 4, we have reason to believe (A) rather
than (B). This reason is grounded in our intuitions about cases involving small- and medium-
sized numbers of people, together with the plausibility of 2, and it does not depend in any
way on our intuitions about cases that require us to imagine very large numbers of people.
Since we have reason to believe (A), we have reason to believe that there is no number of
people such that you should save this number from headaches rather than saving one person

60
This inference from the falsity of (B) to the truth of (A) is not valid. (A) and (B) could both be false, for it
could be that, even if we could accurately imagine any number of people experiencing headaches, we would
have no intuition whatsoever about whether there is some number of people such that you should save this
number from headaches rather than saving one person from death. For simplicity, I ignore this problem. In
Pummer’s original presentation of this argument, the (mistaken) assumption that (A) and (B) are jointly
exhaustive possibilities is implicit in the parenthetical clause of the first premise, rather than in the conclusion. I
think the parenthetical clause makes the first premise difficult to parse, hence my revised presentation.
73
from death. In short, even if we cannot trust our intuitions about cases that require us to
imagine very large numbers of people, we can still gain intuitive support for (A) over (B) by
extrapolating from our intuitions about cases involving small- to medium-size numbers of
people.
Pummer is probably right that proponents of the large numbers argument would
accept 1. But in order for his argument to provide intuitive support for (A) over (B), 2 and 3
must be more intuitively plausible than their denial. And it seems to me that they are not.
First, consider 3, the claim that we do not become less confident in The Variable
Claim as X increases. This claim seems to me clearly false. Compare the following two
claims: (i) you should save one person from death rather than saving one person from a
headache, and (ii) you should save one person from death rather than saving one thousand
people from a headache. These claims both seem clearly true. But (i) is clearly more
intuitively plausible than (ii). So our intuitions tell strongly against 3.
Second, consider 2, the claim that, if 1 and (B) were true, we would become less
confident in The Variable Claim as we imagine X increasing from a small- to a medium-sized
number. Suppose most people disagree with my argument against 3, agreeing with Pummer
that we do not become less confident in The Variable Claim as we imagine X increasing from
a small- to a medium-sized number. That may simply be because (i) X increasing from a
small- to a medium-sized number makes only a small difference to the wrongness of saving
X number of people from a headache rather than saving one person from death, and (ii) our
intuitions are not very sensitive to small differences in degrees of wrongness. (ii) could be
true even if, as 1 holds, our intuitions about cases involving small- and medium-sized
numbers of people are typically reliable.
61
This seems to me a perfectly plausible explanation

61
For some arguments that support (ii), see Mark Schroeder, ‘The Negative Reason Existential Fallacy’,
unpublished manuscript.
74
of any intuitions in support of 3. In which case, even if we do accept 3, Pummer’s argument
gives us no reason to accept (A), for it is still perfectly plausible for us to reject 2.
Since 3 is clearly false, and even if it were not, it would be perfectly plausible to
reject 2, Pummer’s argument provides no intuitive support for (A) over (B).
Pummer does anticipate that some people will become less confident in The Variable
Claim as they imagine X increasing from a small- to a medium-sized number.
62
He insists
that his argument still provides a way for people who do not become less confident to support
their intuitions about large number cases. I am sceptical that this includes many people. But
even if it does, the plausibility of my debunking explanation ensures that the support the
argument provides is at best very weak.
Pummer might now make a different argumentative move. In his paper, he twice
notes that proponents of the large numbers argument have provided ‘no reason whatsoever’
to believe (B).
63
He therefore seems to think that proponents of the large numbers argument
must do more than simply undermine his argument for (A): they must also defend (B).
There are two problems with this argumentative move. First, it is not incumbent on
proponents of the large numbers argument to defend (B). Their aim is to undermine
objections to aggregative views that depend on our intuitions about cases involving large
numbers of people. To do that, they need show only that there is no reliable intuitive support
for (A). Second, proponents of the large numbers argument actually can and have provided
positive intuitive support for (B). This positive intuitive support comes from the intuitive
plausibility of aggregative views themselves, together with the intuitively plausible
implications that aggregative views have in a wide range of cases.

62
Pummer, ‘Intuitions about Large Number Cases’, at 43.
63
Pummer, ‘Intuitions about Large Number Cases’, at 41 and 44.
75
Finally, it is worth noting that if our intuitions do tell against 3, as I think they clearly
do, we can turn Pummer’s argument around, using it to argue against (A):

1. Our intuitions about cases involving small- and medium-sized numbers of people
are typically reliable.

2*. If our intuitions about cases involving small- and medium-sized numbers of
people are typically reliable, then if (A) were true, we would not become less
confident in The Variable Claim as we imagine X increasing from a small- to a
medium-sized number.

3*. We do become less confident in The Variable Claim as we imagine X increasing
from a small- to a medium-sized number.

Therefore,

4*. (A) is false.

If (A) is false, our intuitions about cases like Death v Headaches give us no reason to reject
aggregative views.
I conclude that Pummer’s argument fails as a reply to the large numbers argument
and, surprisingly, a version of his argument gives us a powerful new way to support the
implications that aggregative views have in cases like Death v Headaches.
This extrapolation argument also provides a further response to Voorhoeve. If our
intuitions about cases like Death v Headaches were the result of our intuitively grasping
76
Voorhoeve’s reasoning (people facing headaches should withdraw their claims to your help
in the face of the stronger claim of the person facing death), presumably we would not
become less confident in The Variable Claim as we imagine X increasing from a small- to a
medium-sized number. But, as the extrapolation argument holds, we do become less
confident in The Variable Claim as we imagine X increasing from a small- to a medium-sized
number. So our intuitions about cases like Death v Headaches are not the result of our
intuitively grasping Voorhoeve’s reasoning.

5. Three More Arguments for Aggregation
I have argued that the large numbers argument is a plausible way to undermine our intuitions
about cases like Death v Headaches, that appealing to this argument does not undermine my
objections to non-aggregative and partially aggregative views, and that two recent replies to
this argument fail. In this section, I briefly discuss three other arguments that, like the large
numbers argument, have been claimed to support the implications that aggregative views
have in cases like Death v Headaches. These arguments are not conclusive, but they
strengthen the case for aggregative views.

5.1. The Common Practice Argument
Consider the claim that:

(C) You should save one person from death rather than saving any number of people
from a headache.

Broome suggests that intuitions supporting (C) might not be as strong or as wide-spread as
opponents of aggregative views often assume. He writes,
77

Hardly anyone in the world of practical health-care believes [(C)]. Take an example.
If you are in a hospital run by the UK National Health Service, and you get a
headache, you will be given an analgesic. The cost of the analgesics handed out this
way will in time add up to enough to cure a few people of severe illnesses. So the
health service, with its limited budget, is willing to leave a few people uncured of
their severe illnesses, for the sake of curing a very large number of headaches.
Anyone in the health service can work out that this is happening, but I have never
heard anyone objecting to this use of analgesics.
64

Alastair Norcross similarly suggests that ‘the attractiveness of [(C)] may be no more than
skin deep’.
65
He writes,

Most of us, consequentialists and nonconsequentialists alike, accept at least some
claims that [conflict with (C)]. … If there were a national speed limit of 50 mph, it is
overwhelmingly likely that many lives would be saved each year, as compared with
the current situation. One of the costs of the failure to impose such a speed limit is a
significant number of deaths. The benefits of higher speed limits are increased
convenience for many. Despite this, it is far from obvious that the failure to impose a

64
John Broome, ‘A Comment on Temkin’s Trade-Offs’, in Daniel Wikler and Christopher Murray (eds.),
“Goodness” and “Fairness”: Ethical Issues in Health Resource Allocation (Geneva: World Health
Organization): forthcoming.
65
Norcross, ‘Comparing Harms’, at 141.
78
50-mph speed limit is wrong. In fact, most people believe that … we are not morally
obligated to impose a national speed limit of 50 mph (or less).
66

Broome and Norcross are here deploying what we can call the common practice argument.
According to this argument, many current social policies are designed to save a large number
of people from a very small burden when they could instead be designed to save a few people
from a very large burden. It is not difficult to see that these policies are designed in this way,
and yet most of us believe that these policies are morally justified. So it is not clear that the
balance of our moral intuitions tells against the implications of aggregative views.
Furthermore, if our intuitions about cases like Death v Headaches lead us to abandon
aggregative views, we must also abandon these apparently aggregative social policies. But
few people would want to accept that the UK National Health Service should stop
distributing analgesics or that the speed limit should be reduced to 50 mph.
There are two main ways that opponents of aggregative views could respond to this
argument. First, they could simply insist that the relevant social policies are not morally
justified, that these social policies should be abandoned, and that people who think otherwise
are making a mistake. This response is difficult to swallow, and I doubt that many people will
be keen to embrace it. Second, opponents of aggregative views could argue that the relevant
social policies can be morally justified without appealing to aggregative considerations. This
response is obviously more attractive. But, as Norcross argues, finding a plausible non-
aggregative justification for these policies is not an easy task.
67

66
Norcross, ‘Comparing Harms’, at 159–160.
67
Norcross, ‘Comparing Harms’, at 160–167.
79
5.2. The Spectrum Argument
Larry Temkin has recently focused much philosophical attention on the following type of
argument, which he attributes to Stuart Rachels.
68
Let B1 be a burden that is just slightly less
bad than death, such as permanent quadriplegia. There is clearly some number N1 such that
one person dying is better than N1 people suffering B1. For example, it seems clear that one
person dying is better than twenty people suffering permanent quadriplegia. But now let B2
be a burden that is just slightly less bad than B1, such as losing the use of both legs. There is
clearly some larger number N2 such that N1 people suffering B1 is better than N2 people
suffering B2. For example, it seems clear that twenty people suffering permanent
quadriplegia is better than one thousand people losing the use of both legs. But now let B3 be
a burden that is just slightly less bad than B2, such as losing the use of only one leg. There is
clearly some larger number N3 such that N2 people suffering B2 is better than N3 people
suffering B3. It also seems clear that we will be able to continue this sequence until the
burdens that we are imagining are as small as headaches. That is, it seems clear that for any
number N and any burden B, there is some larger number N+ and some slightly lesser burden
B– such that N people suffering B is better than N+ people suffering B–. It therefore seems
clear that we can create a spectrum of the following form:

One person dying is better than
N1 people suffering B1, which is better than
N2 people suffering B2, which is better than
N3 people suffering B3, which is better than
…

68
See his ‘A Continuum Argument for Intransitivity’ and Rethinking the Good.
80
An enormous number of people suffering a headache.

Finally, notice that ‘better than’ is a transitive relation, meaning that if A is better than B, and
B is better than C, then A is better than C.
69
Since ‘better than’ is a transitive relation, our
spectrum implies that one person dying is better than an enormous number of people
suffering a headache. We can call this the spectrum argument.
Suppose that the spectrum argument succeeds. If we assume that it is always morally
permissible for you to choose the better of two outcomes, it follows that it is morally
permissible for you to choose that one person dies rather than that an enormous number of
people suffer a headache. We then have an independent argument for the implication that
aggregative views have in Death v Headaches.
70

Many philosophers reject the assumption that it is always morally permissible for you
to choose the better of two outcomes. But even these philosophers might find that the
spectrum argument weakens their intuitive resistance to the implications that aggregative
views have in cases like Death v Headaches. If we must anyway accept that one person dying
is better than an enormous number of people suffering headaches, it might seem less
counterintuitive to accept that you should save an enormous number of people from a
headache rather than saving one person from death.
Can we reject the spectrum argument? This argument makes only two assumptions.
First, it assumes that for any number N and any burden B, there is some larger number N+
and some slightly lesser burden B– such that N people suffering B is better than N+ people
suffering B–. Second, it assumes that ‘better than’ is a transitive relation. It seems to me that
giving up either of these premises is less plausible than accepting the conclusion that one

69
Or at least ‘all-things-considered better than’ is a transitive relation.
70
Norcross uses this argument to defend aggregative views. See his ‘Comparing Harms’, at 138–139.
81
person dying is better than an enormous number of people suffering headaches—especially
given that the large numbers argument casts doubt on our intuitive reaction to this
conclusion.
71

5.3. The Heuristic Argument
Broome and Victor Tadros suggest a final argument that casts doubt on the reliability of our
intuitions about cases that require us to imagine very large numbers of people. Broome
gestures at this argument when he writes,

Our moral intuitions are formed and polished in our homely interactions with the few
people we have to deal with in ordinary life. But nowadays the scale of our societies
and the power of our technologies raise moral problems that involve huge numbers of
people. … We cannot expect our intuitions to cope successfully with such big
problems. No doubt our homely intuitive morality gives us a starting point, but we
have to project our morality beyond the homely to the vast new arenas.
72

Victor Tadros makes the point more explicit. He writes,

71
Temkin argues that it might be more plausible to reject the assumption that ‘better than’ is a transitive
relation. See his ‘A Continuum Argument for Intransitivity’ and Rethinking the Good. Alex Voorhoeve, Theron
Pummer, and Jacob Nebel argue that it might be more plausible to reject the assumption that, for any number N
and any burden B, there is some larger number N+ and some slightly lesser burden B– such that N people
suffering B is better than N+ people suffering B–. See Alex Voorhoeve, ‘Heuristics and Biases in a Purported
Counterexample to the Acyclicity of ‘Better Than’’, Politics, Philosophy & Economics 7 (2008): 285–299;
Theron Pummer, ‘Spectrum Arguments and Hypersensitivity’, Philosophical Studies (forthcoming); and Jacob
Nebel, ‘The Good, the Bad, and the Transitivity of Better Than’, Noûs (forthcoming).
72
Broome, Weighing Lives, at 57.
82

Our anti-aggregationist intuitions might be explained by the fact that ignoring minor
harms leads to better and more efficient decision making—when faced with the
opportunity to save a person from being killed, it is often safe to ignore minor harms
to others on the grounds that it is normally impossible to establish that enough people
will be saved from minor harms to justify refraining from saving a person’s life given
epistemic and time constraints on decision-making. Our intuitions that minor harms
are irrelevant might be explained by the fact that this heuristic device for determining
what to do tends to lead to good decisions given that we are fallible decision-makers
even if, in principle, interpersonal aggregation is always warranted in determining
what to do.
73

Broome and Tadros are here deploying what we can call the heuristic argument. According
to this argument, our intuitions about cases like Death v Headaches are a result not of
sensitivity to the moral facts, but rather of a reasoning heuristic that directs us to ignore very
small benefits and burdens whenever they compete with much larger benefits and burdens.
We have learned to employ this heuristic because in many cases it strikes an optimal balance
between efficient moral decision making and correct moral decision making. This heuristic is
particularly reliable when making moral decisions within small social groups, where the
number of people across whom benefits and burdens can be spread is relatively small.
However, in larger social groups, and when thinking about cases involving very large
numbers of people, this heuristic is likely to lead us astray. Since our intuitions about cases

73
Victor Tadros, ‘Localised Restricted Aggregation’, Oxford Studies in Political Philosophy: forthcoming.
83
like Death v Headaches are a result of this heuristic, and this heuristic is not reliable when
thinking about cases like Death v Headaches, these intuitions are not reliable.
I do not want to put too much weight on this argument. Many people who have spent
a great deal of time reflecting on cases like Death v Headaches retain the strong intuition that
you should save the one person from death rather than saving any number of people from
headaches, and it seems presumptuous to insist that these people are simply being led astray
by a heuristic. Still, the heuristic argument clearly has some plausibility, and so it at least
strengthens the case for embracing aggregation.

6. Conclusion
In Section 2, I presented the large numbers argument and explained why, unless this
argument can be answered, cases like Death v Headaches do not give us decisive reason to
reject aggregative views. In Section 3, I argued that, despite appearances, the large numbers
argument does not undermine my objections to non-aggregative and partially aggregative
views. In Section 4, I argued that two recent replies to the large numbers argument fail, one
from Voorhoeve and one from Pummer. I also argued that Pummer’s reply can be turned into
a powerful new argument against our intuitions about cases like Death v Headaches. I called
this the extrapolation argument. In Section 5, I briefly discussed three other arguments that
support the implications that aggregative views have in cases like Death v Headaches: the
common practice argument, the spectrum argument, and the heuristic argument.
I do not deny that the implications that aggregative views have in cases like Death v
Headaches are counterintuitive. But the large numbers argument casts sufficient doubt on the
reliability of our intuitions about these implications that these intuitions do not give us a
decisive reason to reject aggregative views. The extrapolation argument, the common
practice argument, the spectrum argument, and the heuristic argument strengthen the case for
84
embracing these implications. And if my earlier arguments against non-aggregative and
partially aggregative views were sound, we really have no choice but to embrace these
implications, and to embrace aggregation.

85
Chapter 4
Count Complaints, Not Happiness

1. Introduction
In Chapters 1–3, I considered whether and to what extent our moral view should permit
aggregation. I argued that we should reject non-aggregative and partially aggregative views
and embrace a fully aggregative view. In this chapter, I turn from the question of whether our
moral view should be aggregative to the question of what it should aggregate.
I have so far defined aggregative views rather loosely as views on which, when other
things are equal, we are morally required to maximize the sum of benefits minus burdens. On
the most influential kind of aggregative view, a benefit is just any increase in happiness or
well-being and a burden is just any loss in happiness or well-being. So aggregative views
typically require us, when other things are equal, to do whatever maximizes the total amount
of happiness or well-being in the world.
There is, then, more than one important difference between traditional aggregative
views and traditional non-aggregative and partially aggregative views. The most obvious
difference is that traditional aggregative views are fully aggregative while traditional non-
aggregative and partially aggregative views are not. But another important difference is that
traditional aggregative views focus on the sum of happiness or well-being, while traditional
non-aggregative and partially aggregative views focus on individual complaints. Given this
second difference, it might seem that if we are to reject non-aggregative and partially
aggregative views and embrace aggregation, we should forget about complaints and focus on
happiness or well-being. In this chapter, I argue that we should not. Though aggregative
views have traditionally focused on the sum of happiness or well-being, they can also focus
on the sum of complaints. I argue that we should prefer those that do.
86
It will be useful to introduce some new labels. If an aggregative view requires us to
maximize the sum of happiness or well-being, we can call it traditional. If an aggregative
view requires us to minimize the sum of complaints, we can call it complaints-based. I will
be arguing that we should prefer complaints-based aggregative views to traditional
aggregative views.
In Section 2, I present two reasons to prefer complaints-based aggregative views to
traditional aggregative views. These reasons are not decisive, for we might be able to modify
traditional aggregative views to capture the intuitions that drive these reasons. But it seems to
me that complaints-based aggregative views not only capture the relevant intuitions but also
capture them in what is intuitively the correct way. So I think that these intuitions tell
strongly in favour of complaints-based aggregative views.
In Section 3, I argue that complaints-based aggregative views are grounded in a
contractualist picture of the moral landscape that is more attractive than the teleological
picture in which traditional aggregative views are grounded.
In Section 4, I develop a fourth reason to prefer complaints-based aggregative views.
By extending an argument from Michael Otsuka and Alex Voorhoeve, I show that traditional
aggregative views face a dilemma: they can respect either but not both of two morally
important facts: the separateness of persons and the unity of the individual.
74
In contrast,
complaints-based aggregative views are able to respect both of these facts.
In developing this fourth reason to prefer complaints-based aggregative views, I also
answer an important question about these views. As with complaints-based non-aggregative
and partially aggregative views, complaints-based aggregative views can focus on either ex

74
Michael Otsuka and Alex Voorhoeve, ‘Why It Matters that Some Are Worse Off Than Others: An Argument
against the Priority View’, Philosophy & Public Affairs 37 (2009): 171–99. I owe the phrase ‘the unity of the
individual’ to Thomas Porter, ‘In Defence of the Priority View’, Utilitas 24 (2012): 349–64.
87
ante complaints or ex post complaints. So the question is: which should they focus on? I
argue that they should focus on ex ante complaints, for only ex ante complaints-based views
can respect both the separateness of persons and the unity of the individual.
In Section 5, I respond to an objection that Jacob Ross has pressed (in
correspondence) against the argument that I develop in Section 4. According to this
objection, my argument has the very counterintuitive implication that we should sometimes
actively avoid acquiring information that we know bears decisively on what we are morally
required to do. My response to this objection is to bite the bullet, accepting the
counterintuitive implication. But to make this response more plausible, I point out that
several other philosophers have bitten the same bullet for different reasons.
Derek Parfit has developed another important and very influential challenge to
complaints-based views.
75
It is known as The Non-Identity Problem. This challenge requires
a detailed response, so I save discussion of it for the next chapter.

2. Two Reasons to Prefer Complaints-Based Aggregative Views
In this section, I present two reasons to prefer complaints-based aggregative views to
traditional aggregative views. These reasons are not decisive, for there might be ways to
modify traditional aggregative views to capture the intuitions that drive these reasons. But it
seems to me that complaints-based aggregative views not only capture the relevant intuitions
but also capture them in what is intuitively the correct way. So I think that these two
intuitions tell strongly in favour of complaints-based aggregative views.

75
Derek Parfit, Reasons and Persons (Oxford: Oxford University Press, 1987): Chapter 16.
88
2.1. The Permissibility of Self-Denial and Self-Harm
According to traditional aggregative views, when other things are equal, we are morally
required to maximize the sum of happiness or well-being. These views have the very
counterintuitive implication that self-denial is wrong. That is, they imply that it is morally
wrong for us to deny ourselves happiness or to do what would make ourselves worse off,
even when our doing so is not worse for anyone else.
To illustrate this problem, suppose that you are deciding whether to go on holiday.
You know that going will make you happier than, and increase your long-term well-being
relative to, staying at home. You also know that going will not make anyone else worse off.
Nevertheless, you decide to stay at home. Clearly, you are irrational. But it is very difficult to
believe that, as traditional aggregative views imply, your decision is morally wrong.
Similarly, traditional aggregative views have the counterintuitive implication that
self-harm is morally wrong. That is, they imply that it is morally wrong for us to inflict harm
on ourselves, even when our doing so is not worse for anyone else. Though it is more
plausible that self-harm is morally wrong than that self-denial is morally wrong, that might be
because self-harm more often makes other people worse off, by causing them distress. When
self-harm would really make no one else worse off, it is difficult to believe that it is morally
wrong.
Unlike traditional aggregative views, complaints-based aggregative views do not
imply that self-denial or self-harm is morally wrong. According to complaints-based
aggregative views, when other things are equal, we are morally required to act in the way that
minimizes the sum of complaints. If you decide to deny yourself some amount of happiness
or well-being, clearly you are not in a position to complain about being denied this happiness
or well-being. So, if no one else is affected by your self-denial, your self-denial does not
bring about any additional complaints. Similarly, if you decide to inflict harm on yourself,
89
clearly you are not in a position to complain about this harm. So, if no one else is affected by
your self-harm, your self-harm does not bring about any additional complaints.
Can we modify traditional aggregative views to capture the intuition that self-denial
and self-harm are morally permissible? We could defend a view on which, when other things
are equal, we are morally required to maximize the sum of other people’s well-being.
76
Since
we can modify traditional aggregative views in this way, our intuitions about the
permissibility of self-denial and self-harm do not give us a decisive reason to prefer
complaints-based aggregative views. But modifying traditional aggregative views in this way
does come at a significant theoretical cost. Proponents of traditional aggregative views
standardly justify their view by claiming that happiness or well-being is good, and that
because it is good, we are morally required to promote it. If the reason we are morally
required to promote happiness or well-being is that it is good, then presumably we are
morally required to promote our own happiness or well-being too. So it seems that
proponents of traditional aggregative views can capture the intuition that self-denial and self-
harm are morally permissible only by giving up the standard justification for their view. And
without a plausible alternative justification, the modified view will be ad hoc.
77

76
For a defence of this kind of view, see Theodore Sider, ‘Asymmetry and Self-Sacrifice’, Philosophical
Studies 70 (1993): 117–132; Douglas W. Portmore, ‘Dual-Ranking Act Consequentialism’, Philosophical
Studies 138 (2008): 409–427; and Douglas W. Portmore, Commonsense Consequentialism: Wherein Morality
Meets Rationality (Oxford: Oxford University Press, 2011).
77
It might be suggested that the modified view could be justified in something like the way that Samuel
Scheffler justifies agent-centred prerogatives. See his The Rejection of Consequentialism (Oxford: Oxford
University Press, 1982): Chapter 3. Scheffler argues that we each have a unique, personal perspective on the
world, and morality recognises the importance of this perspective by permitting us to grant more moral weight
to our own interests than we are required to grant to the interests of others. However, while it is perhaps
plausible that the importance of our personal perspective is a reason for us to grant more moral weight to our
90
Furthermore, a key reason philosophers have been attracted to traditional aggregative
views is their considerable theoretical simplicity. Even if a justification can be found for
modifying these views in the way proposed, this justification is likely to render these views
less theoretically simple than many complaints-based aggregative views. So anyone drawn to
theoretical simplicity should prefer to accommodate the permissibility of self-denial and self-
harm by accepting a complaints-based aggregative view.
Finally, it seems to me that complaints-based aggregative views not only capture the
intuition that self-denial and self-harm are morally permissible but also capture this intuition
in what is intuitively the correct way. It seems very plausible that the reason you are
permitted to deny yourself happiness or well-being is that you can have no complaint against
your own acts. So I think that the permissibility of self-denial and self-harm gives us a strong
reason to prefer complaints-based aggregative views to traditional aggregative views.

2.2. The Permissibility of Not Having Children
Traditional aggregative views face another important problem. They have the very
counterintuitive implication that you are morally required to have children, so long as (i) your
children would be happy, (ii) their happiness would not be offset by a corresponding loss in
happiness to anyone else, and (iii) having them would not be too burdensome for you. In fact,
traditional aggregative views imply that you are morally required to keep having children
until, for whatever reason, the happiness of another child would be offset by a corresponding
loss in happiness to others. While there are possible circumstances in which it is plausible
that it would be wrong not to have children, such as if humans were on the verge of

own interests, it is difficult to see how it could also be a reason for us to grant less moral weight to our own
interests, which is what would be required to justify the view under consideration here.
91
extinction, it is very difficult to believe that, as traditional aggregative views imply, everyone
is morally required to keep having children until the planet reaches its optimum capacity.
Unlike traditional aggregative views, complaints-based aggregative views do not
imply that you are morally required to have children. Since your potential children do not yet
exist, they cannot have any complaint against you choosing not to have them. If you choose
not to have them, they will continue to not exist, and so they will continue to not have any
complaint. So, as long as no one else is negatively affected by your not having children, your
not having children will not bring about any additional complaints.
78

Again, we might be able to modify traditional aggregative views to accommodate the
intuition that it is morally permissible for you to not have children. We could defend a view
on which, when other things are equal, we are morally required to maximize the sum of
presently-existing people’s well-being.
79
However, as before, modifying traditional
aggregative views in this way would mean giving up the standard justification for these
views. If happiness or well-being is good, and it is to be promoted because it is good, then
presumably we are morally required not only to make presently-existing people happy, but
also to produce more happy people. And even if a justification can be found for modifying
traditional aggregative views in this way, this justification is likely to render these views
considerably less theoretically simple than many complaints-based aggregative views.

78
This attractive feature of complaints-based views is also what makes these views vulnerable to the Non-
Identity Problem, which I discuss in the next chapter.
79
John Harsanyi defends this kind of view on the grounds that it would be rational for everyone to agree to it
from behind a Rawlsian ‘veil of ignorance’. See Harsanyi, ‘Morality and the Theory of Rational Behaviour’, in
Amartya Sen and Bernard Williams (eds.), Utilitarianism and Beyond (Cambridge: Cambridge University Press,
1982): 39–62. However, given Harsanyi’s assumptions, it is not obvious that it would be more rational for
people behind a veil of ignorance to choose this kind of view than for them to choose a traditional aggregative
view. Also see Richard Yetter Chappell, ‘Value Receptacles’, Nous 49 (2015): 322–332.
92
Finally, again, it seems to me that complaints-based aggregative views not only
capture the intuition that it is permissible for you not to have children, but also capture this
intuition in what is intuitively the correct way. It seems very plausible that the reason you are
permitted to not have children is that merely possible children have no complaint against not
being brought into existence. So I think that the permissibility of not having children also
gives us a strong reason to prefer complaints-based aggregative views to traditional
aggregative views.

3. Contractualism v Teleology
I have just presented two reasons to prefer complaints-based aggregative views to traditional
aggregative views. I now want to suggest a third, more fundamental reason: complaints-based
aggregative views are grounded in a more attractive picture of the moral landscape.
As I have said, proponents of traditional aggregative views standardly justify their
views by holding that happiness or well-being is good, and that it is to be promoted because it
is good. As critics of traditional aggregative views have pointed out, this teleological moral
picture is not particularly attractive. On this picture, people seem to be regarded as mere
‘receptacles’ into which the good of happiness or well-being is poured.
80
It does not matter
whether a receptacle gets emptied or broken, so long as another receptacle is sufficiently
filled. It is unsurprising that a view grounded in this kind of moral picture is unable to
account for the intuitive permissibility of self-denial and self-harm and of not having
children.

80
For discussion of this kind of objection, see Jan Narveson, ‘Moral Problems of Population’, The Monist 57
(1973): 62–86; Peter Singer, Practical Ethics (New York: Cambridge University Press, 1993): at 121; and
Yetter Chappell, ‘Value Receptacles’, 322–332.
93
In contrast, complaints-based aggregative views are grounded in a contractualist
moral picture. On this picture, we are not mere value receptacles. Instead, we are moral
agents with the standing to demand justification for the way that other moral agents act. If I
act in a way that harms you, or in a way that fails to benefit you, you have the moral standing
to complain, and to demand a justification. The more I harm you, or the more I fail to benefit
you, the stronger your complaint will be, and the harder it will be for me to meet the demand
for justification. One important way that I can meet the demand is by showing that every
alternative act would have given rise to an even greater sum of complaints.
81
This
contractualist moral picture seems to me more attractive than its teleological rival. And it
offers a natural and compelling explanation of why we have a pro tanto moral duty to make
other people happy but no similar duty to make ourselves happy or to bring new happy
people into existence.

4. Respecting the Separateness of Persons and the Unity of the Individual
I have just presented three reasons to prefer complaints-based aggregative views to traditional
aggregative views: (i) complaints-based aggregative views can much more easily explain the
permissibility of self-denial and self-harm, (ii) complaints-based aggregative views can much
more easily explain the permissibility of not having children, and (iii) complaints-based
aggregative views are grounded in a contractualist picture of the moral landscape that is more
attractive than the teleological picture in which traditional aggregative views are grounded. In
this section, I present a fourth reason to prefer complaints-based aggregative views to
traditional aggregative views. I show that traditional aggregative views face a dilemma: they
can respect either but not both of two morally important facts: the separateness of persons

81
I leave open whether you could meet the demand for justification in other ways, such as by appealing to a
right to act in the relevant way or by showing that your act brought many new happy people into existence.
94
and the unity of the individual. In contrast, complaints-based aggregative views are able to
respect both of these facts.
In developing this fourth reason to prefer complaints-based aggregative views, I also
answer an important question about these views. As with complaints-based non-aggregative
and partially aggregative views, complaints-based aggregative views can focus on either ex
ante complaints or ex post complaints. So the question is: which should they focus on? I
argue that they should focus on ex ante complaints, for only ex ante complaints-based views
can respect both the separateness of persons and the unity of the individual.

4.1. A Dilemma for Traditional Aggregative Views
I will now present a dilemma for traditional aggregative views. In doing so, I build on an
argument originally presented by Otsuka and Voorhoeve.
82

Suppose that in

Treatment 1: C1 and C2 are aged ten. They have a terrible disease that requires
immediate treatment. If you do (1), they will both live to exactly twenty-five. If you
do (2), either C1 will live to exactly twenty-five and C2 will live to exactly twenty, or
C1 will live to exactly twenty-five and C2 will live to exactly thirty-one, with an
equal chance of each.
83

Since C1 will live to twenty-five regardless of whether you do (1) or (2), we can ignore him
for the moment. If you choose (1), C2 will live to twenty-five. If you choose (2), C2 will live

82
Otsuka and Voorhoeve, ‘Why It Matters that Some Are Worse Off Than Others’.
83
Treatment 1 and Treatment 2 are adapted from cases used by Derek Parfit, which are adapted from cases used
by Otsuka and Voorhoeve. See Parfit, ‘Another Defence of the Priority View’, Utilitas 24 (2012): 399–440.
95
to either twenty or thirty-one, with an equal chance of each. Suppose, for the sake of
argument, that each year of life is a roughly equal benefit. Given this supposition, (2) gives
C2 a slightly greater expected benefit than (1), for it gives him an expected 15.5 years of life
as opposed to fifteen. Given standard assumptions about rationality, because (2) gives C2 a
slightly greater expected benefit than (1), it would be rational for C2 to choose that you do
(2). And very plausibly, because it would be rational for C2 to choose that you do (2), and
because no one else has any stake in your decision, it is at least morally permissible for you
to do (2).
Suppose next that in

Treatment 2: C1 and C2 are aged ten. They have a terrible disease that requires
immediate treatment. If you do (1), they will both live to exactly twenty-five. If you
do (2), either C1 will live to exactly twenty and C2 will live to exactly twenty-five, or
C1 will live to exactly twenty-five and C2 will live to exactly thirty-one, with an
equal chance of each.

In this case, doing (2) rather than (1) is significantly better for C2, since it gives him a 0.5
chance of living to thirty-one rather than twenty-five without any prospect of a loss.
However, doing (2) rather than (1) is significantly worse for C1, since it gives him a 0.5
chance of living to twenty rather than twenty-five without any prospect of a gain. I take it that
giving the larger benefit to C2 does not justify giving the smaller benefit to C1, so you are
morally required to do (1).
If we agree that it is morally permissible for you to do (2) in Treatment 1 and that you
are morally required to do (1) in Treatment 2, we must reject traditional aggregative views.
To see why, consider the following four outcomes.
96

A. C1 lives to twenty-five C2 lives to twenty-five
B. C1 lives to twenty-five C2 lives to twenty
C. C1 lives to twenty-five C2 lives to thirty-one
D. C1 lives to twenty C2 lives to twenty-five

In Treatment 1, (1) will bring about A, and (2) will bring about either B or C, with an equal
chance of each. In Treatment 2, (1) will bring about A, and (2) will bring about either C or D,
with an equal chance of each. So traditional aggregative views can capture our judgment
about the difference between these cases only if we hold that the distribution of benefits and
burdens in B is somehow morally better than the distribution in D. And that would be very
implausible, for it would imply that benefits and burdens to C1 have greater moral
importance than benefits and burdens to C2.
To avoid this objection, proponents of traditional aggregative views could deny that it
is morally permissible for you to choose (2) in Treatment 1. And to defend this denial, they
could plausibly claim that C2 living to twenty-five rather than twenty is of greater moral
importance than him living to thirty-one rather than twenty-five.
84
However, this response
comes at a significant intuitive cost, for it implies that it is morally wrong for you to do what
it would be rational for C2 to choose that you do, even though no one else has any stake in
your decision.
85

84
This claim is supported by Prioritarianism. See Parfit, ‘Equality and Priority’, at 212–214.
85
It might be argued that the claim that it is wrong for you to do what it would be rational for C2 to choose that
you do is supported by The Doctrine of Doing and Allowing, or DDA. According to the DDA, it is morally
worse to do harm than to merely allow harm. If the only permissible alternative to (2) is (1), then it might seem
that (2) risks doing harm to C2, for it risks leaving her worse off than if you had chosen (1). This argument fails
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So traditional aggregative views face a dilemma. Either they imply that it is morally
permissible for you to do (2) in Treatment 1, in which case they have the very
counterintuitive implication that it is morally permissible for you to do (2) in Treatment 2, or
they imply that you are morally required to do (1) in Treatment 2, in which case they have the
very counterintuitive implication that you are morally required to do (1) in Treatment 1.
The more general dilemma is this: either traditional aggregative views imply that we
are morally required to distribute benefits and burdens across different people in a way that
seems appropriate only when distributing benefits and burdens within a single life, or they
imply that we are morally required to distribute benefits and burdens within a single life in a
way that seems appropriate only when distributing benefits and burdens across different
people. If a view falls on the first horn of this dilemma, we can say that it fails to respect the
separateness of persons—it wrongly implies that whenever giving someone a prospect of a
gain G is intuitively sufficient to justify exposing the same person to a risk R, giving
someone G is sufficient to justify exposing someone else to R. If a view falls on the second
horn of this dilemma, we can say that it fails to respect the unity of the individual—it
wrongly implies that giving someone a prospect of a gain G is sufficient to justify exposing
the same person to a risk R only when giving someone G is intuitively sufficient to justify
exposing someone else to R.
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for two reasons. First, it is very doubtful that giving someone the lesser of two benefits constitutes doing harm
rather than merely allowing harm. Second, if this did constitute doing harm, then choosing (1) would also risk
doing harm, for it would make C2 worse off than she might have been if you had chosen (2).
86
As John Rawls argues, Utilitarianism fails to respect the separateness of persons. See Rawls, A Theory of
Justice (Cambridge, Mass.: Harvard University Press, 1999): at 19–24. Prioritarianism fails to respect the unity
of the individual. See Otsuka and Voorhoeve, ‘Why It Matters That Some Are Worse Off Than Others’, at 171–
178.
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4.2. How Ex Ante Complaints-Based Views Can Avoid the Dilemma
As with complaints-based non-aggregative and partially aggregative views, complaints-based
aggregative views can focus on either ex ante complaints, which are determined by the
prospects that an act gives to people, or ex post complaints, which are determined by the
actual results that an act has for people. I will now argue that ex ante complaints-based views,
whether aggregative or nonaggregative, can simultaneously respect both the unity of the
individual and the separateness of persons.
Recall Treatment 1.

Treatment 1: C1 and C2 are aged ten. They have a terrible disease that requires
immediate treatment. If you do (1), they will both live to exactly twenty-five. If you
do (2), either C1 will live to exactly twenty-five and C2 will live to exactly twenty, or
C1 will live to exactly twenty-five and C2 will live to exactly thirty-one, with an
equal chance of each.

Since (2) gives C2 a slightly greater expected benefit than (1), C2 has an ex ante complaint
against (1) and no ex ante complaint against (2). Since C1 will live to twenty-five regardless
of whether you do (1) or (2), there is no opposing ex ante complaint to consider. So ex ante
complaints-based views imply that you are morally required to do (2).
More generally, in cases in which only one person is affected by what we do, the only
possible ex ante complaints are against acts that go against the ex ante interest of the one
person. So in these cases, ex ante complaints-based views always imply that we are morally
required to act in the way that gives the one person the greatest expected benefit, which is
also what it would be rational for the one person to choose that we do.
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Next, recall Treatment 2.

Treatment 2: C1 and C2 are aged ten. They have a terrible disease that requires
immediate treatment. If you do (1), they will both live to exactly twenty-five. If you
do (2), either C1 will live to exactly twenty and C2 will live to exactly twenty-five, or
C1 will live to exactly twenty-five and C2 will live to exactly thirty-one, with an
equal chance of each.

Again, C2 has an ex ante complaint against (1), since (2) gives him a 0.5 chance of living to
thirty-one rather than twenty-five without any prospect of a loss. But now C1 has an
opposing ex ante complaint, since (2) gives him a 0.5 chance of living to twenty rather than
twenty-five without any prospect of a gain. So to determine what ex ante complaints-based
views imply about this case, we must decide which of these opposing complaints is stronger.
Plausibly, the strength of a person’s complaint against an act is determined in part by
the difference between how well off she can expect to be given this act and how well off she
can expect to be given the act that would be best for her, with the strength of the complaint
increasing as this difference increases.
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If this difference were the sole determinant of the

87
This way of determining complaints is vulnerable to the following objection. Suppose that Albert is already
reasonably well off, while everyone else is very badly off. You can either make everyone else reasonably well
off, or give Albert a super-human level of well-being. If the amount of well-being that you could give Albert is
large enough, his complaint will swamp the aggregated complaints of everyone else. It will follow,
counterintuitively, that you should give Albert a super-human level of well-being. This objection is powerful,
and one that proponents of complaints-based aggregative views must either confront or make their peace with.
But it is not an objection that needs to be addressed here, for traditional aggregative views are vulnerable to a
parallel objection, and the goal of this chapter is only to show that complaints-based aggregative views are
preferable to traditional aggregative views.
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strength of a complaint, C2 would have a stronger complaint against (1) than C1 has against
(2), since the difference for C2 is three years while the difference for C1 is only 2.5 years.
However, as proponents of MC have argued, this difference should not be the sole
determinant of the strength of a complaint. Plausibly, the strength of a person’s complaint
against an act is also determined by how well off she can expect to be given this act, with the
strength of the complaint increasing the worse off she can expect to be. Since C2 can expect
to live to twenty-five given (1) while C1 can expect to live to only 22.5 given (2), this second
consideration strengthens the complaint of C1 relative to the complaint of C2.
When determining the strength of a complaint, we can plausibly give this second
consideration significant weight. We can then conclude that, on the whole, C1 has a stronger
complaint against (2) than C2 has against (1). So ex ante complaints-based views are
compatible with the claim that you are morally required to do (1) in Treatment 2. And more
importantly, they are compatible with this claim even though they also imply that you are
morally permitted to do (2) in Treatment 1.
More generally, in cases in which more than one person is affected by what we do,
there can be opposing ex ante complaints, and the strongest complaint can be against the act
that would give the greatest expected benefit. So ex ante complaints-based views are
compatible with the claim that, in these cases, what we are morally required to do is not
always what would maximize the greatest expected benefit. So these views are compatible
with the claim that the appropriate way to distribute benefits and burdens across different
people is different from the appropriate way to distribute benefits and burdens within a single
life.
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In other words, ex ante complaints-based views can simultaneously respect both the
unity of the individual and the separateness of persons.
88
That gives us a strong reason to
favor ex ante complaints-based aggregative views over traditional aggregative views.

4.3. Why Ex Post Complaints-Based Views Cannot Respect the Unity of the Individual
Unlike ex ante complaints-based views, ex post complaints-based views cannot respect the
unity of the individual. I will now explain why.
Recall Treatment 1.

Treatment 1: C1 and C2 are aged ten. They have a terrible disease that requires
immediate treatment. If you do (1), they will both live to exactly twenty-five. If you
do (2), either C1 will live to exactly twenty-five and C2 will live to exactly twenty, or
C1 will live to exactly twenty-five and C2 will live to exactly thirty-one, with an
equal chance of each.

88
It might be objected that ex ante complaints-based aggregative views do not fully respect the separateness of
persons, because a view fully respects the separateness of persons only if it implies that a large harm to one
person cannot be morally outweighed by a very small harm to each of very many people. But I see no reason to
accept that respecting the separateness of persons requires this implication. If the separateness of persons is
compatible with the implication that a large harm to one person can be morally outweighed by a moderate harm
to each of many people, why is it not compatible with the implication that a large harm to one person cannot be
morally outweighed by a very small harm to each of very many people? If it is claimed that the separateness of
persons is not compatible with the former implication, then the separateness of persons is not something that a
moral view should respect, for this implication is undeniable. For similar remarks, see David Brink, ‘The
Separateness of Persons, Distributive Norms, and Moral Theory’, in C. Morris and R. Frey (eds.), Value,
Welfare, and Morality (Cambridge: Cambridge University Press, 1993): 252–289.
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It is not obvious what ex post complaints-based views imply about this case. If you do (2),
there is a one-in-two chance that C2 will live to twenty, in which case he will have an ex post
complaint based on living to twenty rather than twenty-five. If you do (1), C2 will live to
twenty-five, but we do not know how long he would have lived for otherwise, so it is not
obvious what ex post complaint he will have.
I suggest that we determine the ex post complaint that C2 will have given (1) by
comparing how well off he will be given (1) with how well off he can expect to be given (2).
If you do (2), he will live to either twenty or thirty-one, with an equal chance of each. So his
life expectancy given (2) is 25.5. So, on this way of determining ex post complaints, doing
(1) will give C2 an ex post complaint against living to twenty-five rather than 25.5.
So to determine what ex post complaints-based views imply about this case, we must
compare a complaint against living to twenty rather than twenty-five discounted by one in
two with a complaint against living to twenty-five rather than 25.5. Presumably, a complaint
against living to twenty rather than twenty-five discounted by one in two is roughly
equivalent to a complaint against living to twenty rather than 22.5. Since that complaint is
stronger than a complaint against living to twenty-five rather than 25.5, ex post complaints-
based views imply that you are morally required to do (1). They thereby conflict with our
judgment that you are at least morally permitted to do (2).
Of course, this argument relies on my suggested way of determining the ex post
complaint that C2 will have given (1). But I cannot see a plausible alternative to this
suggestion. And really it should be unsurprising that ex post complaints-based views fail to
respect the rational preferences of C2, for his rational preferences are determined by his ex
ante perspective, and ex post complaints-based views ignore that perspective.
More generally, in cases in which only one person is affected by what we do, ex post
complaints-based views sometimes imply that we are morally required to act against the
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rational preferences of the one person. They thereby fail to respect the unity of the individual.
That gives us a strong reason to favor ex ante complaints-based aggregative views over ex
post complaints-based aggregative views. (It also gives us another reason to reject ex post
MC and ex post PAMC.)

5. Avoiding Important Information
In this section, I respond to an objection that Jacob Ross has pressed against the argument
that I developed in Section 4. According to this objection, my argument has the very
counterintuitive implication that we should sometimes actively avoid acquiring information
that we know bears decisively on what we are morally required to do. My response is to bite
the bullet, accepting the counterintuitive implication. But to make this response more
plausible, I point out that several other philosophers have bitten the same bullet for different
reasons.

5.1. Ross’s Challenge
Suppose that you must choose between outcome (1) and a gamble that will bring about either
outcome (2) or outcome (3) with an equal chance of each.

(1) C1 and C2 both live to exactly 25
(2) C1 lives to exactly 20 and C2 lives to exactly 31
(3) C1 lives to exactly 31 and C2 lives to exactly 20

If my argument in Section 4 was sound, you are morally required to choose the gamble, for
the gamble is in the ex ante interest of both C1 and C2. However, if you knew in advance
what the outcome of the gamble would be, you would be morally required to choose (1), for
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then the gamble would be against the ex ante interest of one of the children, and that child
would have a stronger ex ante complaint against the gamble than the other child would have
against (1).
Why is that a problem? Suppose that the outcome of the gamble is determined by the
toss of a coin. Suppose also that the coin is tossed before you choose between (1) and the
gamble, and the tossed coin is now lying in your closed fist. If my argument in Section 4 is
sound, then it is in the ex ante interest of both C1 and C2 that you keep your fist closed until
you have chosen between (1) and the gamble. If you open your fist and see the coin, it will no
longer be in the ex ante interest of both children that you gamble, and you will then be
morally required to choose (1). But before you open your fist, it is in the ex ante interest of
both children that you gamble, so both children have an ex ante complaint against you
opening your fist, even though the result of the coin toss bears decisively on what you are
morally required to do. In fact, if the stakes for C1 and C2 were high enough, you might be
morally required to pay a small amount of money to avoid seeing the coin inside your closed
fist, for your complaint against paying this money could be significantly weaker than the
complaint that C1 and C2 have against you seeing the result of the coin toss. Ross thinks that
this implication—that you are morally required to actively avoid information that you know
bears decisively on what you are morally required to do—is very counterintuitive. He
therefore thinks that we should reject my argument in Section 4.

5.2. A Response to Ross
Unlike Ross, I do not find it very counterintuitive that you are morally required to avoid
seeing the coin in the case just described, especially in light of the rationale for this
implication that I presented in Section 4. My response to the objection is therefore to bite the
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bullet, accepting what I concede is a somewhat counterintuitive conclusion. As I will now
explain, several other philosophers have bitten the same bullet for different reasons.
First, consider again the ex ante, complaints-based, non-aggregative and partially
aggregative views that I discussed in Chapters 1 and 2. As we have seen, these views are
endorsed by several philosophers.
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And, as some of these philosophers recognize, these
views sometimes imply that you are morally required to actively avoid information that you
know bears decisively on what you are morally required to do. Suppose that in

Ignorance: Each of a huge number of people is suffering from a mild health
impairment. You can either (1) give all of these people a medication that will cure
them, or (2) give none of these people this medication. Everyone knows that one of
these people is fatally allergic to the medication, but no one knows who.

If the number of people is large enough, it will be in the ex ante interest of each person that
you choose (1), giving everyone the medication, for it will be worth accepting the very tiny
chance of death to be cured of the mild health impairment. Since it will be in the ex ante
interest of each person that you give her the medication, none of these people will have an ex
ante complaint against being given the medication, and each will have an ex ante complaint
against not being given the medication. So all ex ante complaints-based views will imply that
you should choose (1). However, ex ante complaints-based non-aggregative and partially
aggregative views also imply that, if you were to find out which person is fatally allergic to

89
Aaron James, ‘Contractualism’s (Not So) Slippery Slope’, Legal Theory 18 (2012): 263–292; Rahul Kumar,
‘Risking and Wronging’, Philosophy & Public Affairs 43 (2015): 27–51; and Johann Frick, ‘Contractualism and
Social Risk’, Philosophy & Public Affairs 43 (2015): 175–223. T. M. Scanlon has also recently switched from
an ex post to an ex ante complaints-based view. He credits Frick’s paper with changing his mind.
106
the medication, it would then be true that you should choose (2), giving no one rather than
everyone the medication. For if you were to find out which person is fatally allergic to the
medication, that person would have a much stronger complaint against being given the
medication than everyone else has against not being given the medication. And because the
complaint of the one person would be much larger than the complaints of everyone else, non-
aggregative and partially aggregative views would not allow the complaints of the many to be
aggregated in a way that would outweigh the complaint of the one. Finally, let us imagine
that you have the option of opening an envelope that will tell you which person is fatally
allergic to the medication. Ex ante complaints-based non-aggregative and partially
aggregative views imply that you should refuse to open this envelope, and should even pay a
small amount of money to avoid opening it, despite the contents of the envelop bearing
decisively on what you are morally required to do. They have this implication because if you
open the envelope, you will be morally required to choose (2), but everyone currently has an
ex ante complaint against that option.
As I have argued, we should reject non-aggregative and partially aggregative views.
But is it a decisive objection to these views that they imply that you are sometimes morally
required to actively avoid information that you know bears decisively on what you are
morally required to do? Proponents of these views do not think so. They hold that the
rationale for their views is plausible enough to render this somewhat counterintuitive
implication acceptable.
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I share this judgment. And I hold that, similarly, this implication is
not a decisive reason to reject the argument that I offered in Section 4.
It might seem odd for me to respond to Ross’s objection by pointing out that other
views that I reject are vulnerable to the same objection. But my point is not that these other

90
Johann Frick has made this claim in a recent online discussion of his paper, and Caspar Hare makes the same
claim in ‘Should We Wish Well to All?’, Philosophical Review 124 (2016): 451–472, at 456–457.
107
views give us independent reason to embrace the problematic implication. Rather, my point is
that I am not alone in thinking that this implication is acceptable on reflection.

6. Summary
Aggregative views typically focus on the sum of happiness or well-being. Non-aggregative
and partially aggregative views typically focus on complaints. It might therefore seem that, if
we are to reject non-aggregative and partially aggregative views and embrace aggregation,
we should forget about complaints and focus on the sum of happiness or well-being. In this
chapter, I have argued that we should not. Though aggregative views have traditionally
focused on the sum of happiness or well-being, they can also focus on the sum of complaints.
And we should prefer those that do, for four main reasons. First, unlike traditional
aggregative views, complaints-based aggregative can easily explain the intuitive
permissibility of self-denial and self-harm. Second, unlike traditional aggregative views,
complaints-based aggregative views can easily explain the intuitive permissibility of not
having children. Third, complaints-based aggregative views are grounded in a contractualist
picture of the moral landscape that is more attractive than the teleological picture in which
traditional aggregative views are grounded. Fourth, unlike traditional aggregative views,
complaints-based aggregative views can, by focusing on ex ante rather than ex post
complaints, respect both the separateness of persons and the unity of the individual.
As I said in the introduction, there is an important and influential challenge to
complaints-based views that I have not discussed in this chapter. This challenge is Derek
Parfit’s Non-Identity Problem. We can now turn to consider this challenge.

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Chapter 5
The Non-Identity Problem

1. Introduction
In Chapters 1–3, I considered whether and to what extent our moral view should permit
aggregation. I argued that we should reject non-aggregative and partially aggregative views
and embrace a fully aggregative view. In Chapter 4, I turned from the question of whether
our moral view should be aggregative to the question of what it should aggregate. I presented
several reasons to prefer ex ante complaints-based aggregative views, which direct us to
minimize the sum of ex ante complaints, to traditional aggregative views, which direct us to
maximize the sum of happiness or well-being. In this fifth and final chapter, I respond to an
important and very influential challenge to complaints-based views. This challenge is
originally due to Derek Parfit, and it is known as The Non-Identity Problem.
91

In Section 2, I consider Parfit’s initial version of The Non-Identity Problem, which
focuses on a case that I call Mary’s Choice. I argue that our intuitions about this case are
distorted in various ways, and that when we consider a purified version of the case, our
intuitions change, and the problem promptly disappears.
92

In Section 3, I consider Parfit’s second and seemingly more powerful version of The
Non-Identity Problem, which focuses on a case that I call Future Catastrophe. I again argue

91
Derek Parfit, Reasons and Persons (Oxford: Oxford University Press, 1987): Chapter 16.
92
I do not discuss other potential solutions to The Non-Identity Problem in this chapter. For an excellent and
comprehensive overview of other potential solutions and the problems that they face, see David Boonin, The
Non-Identity Problem & the Ethics of Future People (Oxford: Oxford University Press, 2014). Also see Parfit,
Reasons and Persons, Chapter 16.
109
that our intuitions about this case are distorted in various ways, and that when we consider a
purified version of the case, our intuitions change, and the problem promptly disappears.
In Section 4, I consider a revenge version of The Non-Identity Problem suggested to
me in conversation by Jacob Ross.
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This version presents a genuine problem for simple
complaints-based views. However, by modifying complaints-based views in plausible ways,
we can avoid even this version of the problem.

2. The Non-Identity Problem: Mary’s Choice
In this section, I respond to Parfit’s initial version of The Non-Identity Problem. This version
focuses on a case that I call Mary’s Choice.
94
I argue that our intuitions about this case are
distorted in various ways, and that when we consider a purified version of the case, our
intuitions change, and the problem promptly disappears.

2.1. Mary’s Choice
According to what we can call

The Weak Time-Dependence Thesis: If any person had not been conceived within a
month of the time when she was in fact conceived, she would never have existed.

This claim is clearly true. We each grew from a particular ovum and spermatozoon. If your
mother had conceived even a few seconds earlier or later than when she conceived you, her

93
Ross presented this version of the problem to me in conversation, but he discusses several similar versions in
his ‘Rethinking the Person-Affecting Principle’, Journal of Moral Philosophy 12 (2015): 428–461.
94
Parfit, Reasons and Persons: 357–361. Parfit calls his case ‘The 14-Year-Old Girl’. My case differs
somewhat from his, but only in ways that make the important features of the case clearer.
110
child would almost certainly have grown from a different spermatozoon, and so her child
would almost certainly not have been you. If she had conceived a month earlier or later than
when she conceived you, her child would have grown from a different ovum as well as a
different spermatozoon, and so her child would certainly not have been you.
Suppose that in

Mary’s Choice: Mary is sick. If she conceives a child now, it will have moderate
health impairments throughout its life, though it will still have a life worth living. If
she waits a month, she will get better. She could then conceive a healthy child.

Suppose also that

It makes no difference to Mary or any other presently-existing person whether Mary
conceives now or in a month.

Many people judge that Mary is morally required to wait. This judgment, combined with The
Weak Time-Dependence Thesis, poses a problem for complaints-based views. If Mary
conceives now, her child will have moderate health impairments throughout its life. But it
will still have a life worth living. If she waits, she will not have this child. She will conceive
some other, genetically distinct child. So by conceiving now, she will not be harming, or
making worse off, the-child-she-will-have. Since this child will not be worse off, it will have
no complaint. Since no one else is affected by whether Mary conceives now or in a month, no
one else has any complaint against her conceiving now. Since neither the-child-she-will-have
nor anyone else has any complaint against her conceiving now, complaints-based views are
unable to capture the judgment that Mary is morally required to wait.
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2.2. Let Mary Choose
Complaints-based views imply that it is morally permissible for Mary to conceive now. Is
that a decisive problem? I do not think so. When I keep in mind that Mary conceiving now
will not be worse for the-child-she-will-have, and that it will not be worse for her or anyone
else, I no longer find it counterintuitive that it is morally permissible for her to conceive now.
I suggest that any lingering intuitions to the contrary can be explained away. First, we might
find it hard to keep in mind the rather fantastical stipulation that whether Mary conceives
now or in a month makes no difference to her or anyone else. In the real world, conceiving a
child with significant health impairments would make life much more difficult for Mary and
anyone else responsible for the child, and it would be unsurprising if this fact were distorting
our intuitions. Second, we might find it hard to keep in mind the distinction between the truth
that Mary’s child will be worse off if she conceives now, where ‘Mary’s child’ refers to
whatever child Mary actually has, and the falsity that Mary’s child will be worse off if she
conceives now, where ‘Mary’s child’ refers to the child that she will have if she conceives
now. Third, we might find it hard to keep in mind that the child that Mary will have if she
conceives now would, despite having significant health impairments, have a life worth living.
This child, we should try to remember, would be on-the-whole happy to have been born.
Fourth, we might be caught in the grip of traditional aggregative views, on which we are
morally required to maximize the sum of happiness or well-being in the world. These views
straightforwardly imply that Mary is morally required to wait. If we were already inclined to
accept these views before considering the case, that might have biased our reaction.
I think we can test my suggestion that the common intuitive reaction to Mary’s
Choice is the result of one or more of the four mistakes just described. Suppose that there is a
button on the table in front of you. If you press this button, a new person, Amy, will pop into
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existence on a far-away, otherwise uninhabited planet. Amy will have a healthy and happy
life, but she will never know about our world, and no one in our world will ever know about
her—after pressing the button, your memory of pressing it would be permanently erased. Are
you morally required to press the button? Keep in mind that Amy does not yet exist, and so
not pressing the button would not be worse for her or anyone else. Most people to whom I
have put this case judge that the answer is ‘no’. They judge that, though it is morally
permissible to press the button, there is also nothing wrong with not pressing it.
Suppose next that you have a different button on the table in front of you. If you press
this button, a new person, Bobby, will pop into existence on a far-away, otherwise
uninhabited planet. Bobby will have significant health impairments, but his life will still be
worth living. He will be on-the-whole happy to have come into existence. Bobby will never
know about our world, and no one in our world will ever know about him—after pressing the
button, your memory of pressing it would be permanently erased. Would it be morally wrong
for you to press the button? Keep in mind that Bobby would have a life worth living and
would be on-the-whole happy to have come into existence. Most people to whom I have put
this case judge that the answer is ‘no’. They judge that, though there is nothing wrong with
not pressing the button, there is also nothing wrong with pressing it.
Suppose finally that you have both the Amy button and the Bobby button on the table
in front of you. You can press one of these buttons or neither, but not both. Would it now be
morally wrong for you to press the Bobby button? I cannot see how it could be. If you are not
morally required to press the Amy button when that is your only option, and it is not morally
wrong for you to press the Bobby button when that is your only option, why would the
availability of the Amy button make pressing the Bobby button morally wrong?
When I have presented these three ‘button’ cases to people, in this order, they have
almost unanimously shared my judgment that it is permissible for you to press the Bobby
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button even when the Amy button is also available. But your choice between the Amy button
and the Bobby button is analogous, in all morally relevant respects, to Mary’s Choice. This
strongly suggests that the judgment that Mary is morally required to wait before conceiving is
distorted by one of the four factors that I earlier identified. When we consider the first button
case, in which only the Amy button is available, and we judge that you are not morally
required to press the button, this frees us from the grip of traditional aggregative views, on
which we are morally required to maximize the sum of happiness or well-being. When we
consider the second button case, in which only the Bobby button is available, the most
important features of the case are that Bobby would have a life worth living and that his
existence would affect no one else, so it is easier for us to keep these features in mind. And
because the case is so abstract, it is easy for us to avoid unduly importing assumptions from
similar, real-world cases. When we finally consider the third button case, in which both the
Amy button and the Bobby button are available, we are free from the grip of traditional
aggregative views, we recognise that Bobby would have a life worth living, we recognise that
Bobby’s existence would affect no one else, and we have been primed to think of Amy and
Bobby as distinct possible people. We are therefore free from the four factors that potentially
distort our judgment when we consider Mary’s Choice. It seems reasonable to infer that the
apparent discrepancy between the judgment that Mary is morally required to wait and the
judgment that it is morally permissible for you to press the Bobby button even when the Amy
button is available is explained by the former judgment being distorted by these four factors.
I conclude that the common intuitive reaction to Mary’s Choice is a mistake, and hence it is
no objection that complaints-based views are unable to capture this intuition.
I should pause here to address a potential misunderstanding. I have said that, if it is
permissible for you to refrain from pressing the Amy button when only the Amy button is
available, and it is permissible for you to press the Bobby button when only the Bobby button
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is available, then we should conclude that it is permissible for you to press the Bobby button
when both the Amy button and the Bobby button are available. It might seem that I am here
appealing to the following ‘transitivity principle’: if it is permissible for you to do nothing
given the option set {do nothing, do X}, and it is permissible for you to do Y given the option
set {do nothing, do Y}, then it is permissible for you to do Y given the option set {do X, do
Y}. David Boonin has appealed to precisely this transitivity principle to argue that the
common intuitive reaction to Mary’s Choice is mistaken.
95
But I do not intend to be
appealing to this transitivity principle here. I am instead appealing directly to the judgment
that adding the Amy button makes no difference to the permissibility of pressing the Bobby
button.
Why not appeal to the transitivity principle? I think that this principle is vulnerable to
decisive counterexamples. For example, it is permissible for you to do nothing given the
option set {do nothing, sacrifice your life to save person A and person B}, and it is
permissible for you to sacrifice your life to save only person A given the option set {do
nothing, sacrifice your life to save only person A}, but it is still wrong for you to sacrifice
your life to save only person A given the option set {sacrifice your life to save only person A,
sacrifice your life to save person A and person B}.
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Boonin is aware that the transitivity principle is vulnerable to counterexamples, but he
thinks that a weakened version of this principle still gives us reason to reject the common
intuitive reaction to Mary’s Choice. According to the ‘weaker transitivity principle’, if it is
permissible for you to do nothing given the option set {do nothing, do X}, and it is
permissible for you to do Y given the option set {do nothing, do Y}, and the change from
choosing between {do nothing, do X} and choosing between {do nothing, do Y} to choosing

95
Boonin, The Non-Identity Problem & the Ethics of Future People, at 198–205.
96
I discuss a similar example in ‘The All or Nothing Problem’, The Journal of Philosophy 114 (2017): 94–104.
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between {do X, do Y} makes no difference in terms of the morally relevant properties of
either X or Y, then it is permissible for you to do Y given the option set {do X, do Y}.
97
The
problem with appealing to this weaker transitivity principle is that this principle is trivial. It
amounts to the claim that, if X is permissible, and adding option Y does not change whether
X is permissible, then X will remain permissible even after adding Y. Since this principle is
trivial, it cannot give us reason to reject the common intuitive reaction to Mary’s Choice.
But, as I say, the argument that I have presented in this section is not intended to
appeal to either the transitivity principle or the weaker transitivity principle. So these
problems with Boonin’s argument are not problems with mine.
98
In order for my argument to
have been successful, I do not need to have shown that adding the Amy button could not
make a difference to the permissibility of pressing the Bobby button. I need to have shown
only that it is plausible that adding the Amy button does not make a difference to the
permissibility of pressing the Bobby button. If that is plausible, then it is plausible that the
common intuitive reaction to Mary’s Child is unreliable, and so this intuition does not
provide a strong reason to reject complaints-based views.

3. The Non-Identity Problem: Future Catastrophe
I have just argued that Parfit’s initial version of The Non-Identity Problem is not really a
problem, and hence it is not a problem for complaints-based views. In this section, I consider
Parfit’s second and seemingly more powerful version of The Non-Identity Problem. This

97
Boonin, The Non-Identity Problem & the Ethics of Future People, at 202.
98
Boonin presents several other arguments designed to put pressure on the common intuitive reaction to Mary’s
Choice. See his The Non-Identity Problem & the Ethics of Future People, Chapter 7. These arguments all appeal
to partial analogies with other cases. I am sympathetic to these other arguments, but they seem to me less
persuasive than the more direct argument that I have presented here.
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version focuses on a case that I call Future Catastrophe.
99
I again argue that our intuitions
about this case are distorted in various ways, and that when we consider a purified version of
the case, our intuitions change, and the problem promptly disappears.

3.1. Future Catastrophe
Suppose that in

Future Catastrophe: We are deciding whether to build a nuclear reactor to supply our
energy. We know that, if we build the reactor, then in around four hundred years, the
reactor will melt down, instantaneously killing tens of thousands of people.

Suppose also that

If we build the reactor, that will be no worse for anyone who is presently living. But it
will have significant effects on the details of their lives. These effects will grow and
spread, like ripples in a pond. They will result in different people meeting, different
relationships being formed, and different children being conceived. Within four
hundred years, the people who will exist will be entirely different from the people
who would have existed had the reactor not been built.

It seems obvious that it would be morally wrong to build the reactor. But if we build the
reactor, that will not be worse for anyone. It is true that, in around four hundred years, the
reactor will melt down, and tens of thousands of people will be killed. But if we do not build

99
Parfit, Reasons and Persons: 371–377. Parfit calls his case ‘The Risky Policy’. Again, my case differs
somewhat from his, but only in ways that make the important features of the case clearer.
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the reactor, these people will never live at all. So as long as these people have a life worth
living, it is not worse for them if we build the reactor, for a premature death after a life worth
living is not worse than no life at all. Since our building the reactor is not worse for these
people, they have no complaint against our building it. Since no one else is made worse off
by our building the reactor, no one has any complaint against our building it. Since no one
has any complaint against our building the reactor, complaints-based views are unable to
capture the judgment that it would be morally wrong for us to build the reactor.

3.2. Catastrophe for Whom?
Complaints-based views imply that it is morally permissible for us to build the reactor. Is that
a decisive problem? This version of The Non-Identity Problem seems to me considerably
more powerful than the previous version. Even when I try to keep in mind that building the
reactor will not be worse for anyone, I cannot shake the intuition that it would be morally
wrong to build it. But perhaps that is unsurprising. The same factors that distorted our
intuitive reaction to Mary’s Choice are present here, and they are present to a much greater
degree. First, given that building the reactor will result in the premature death of tens of
thousands of our descendants, it is very hard to hold fixed the fantastical stipulation that
building the reactor would not be worse for anyone who is alive now. In the real world, most
people would be distraught at the prospect of a future in which their descendants die
prematurely.
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Furthermore, it would almost always be true that building a reactor would

100
Samuel Scheffler has argued that most people are even more invested in ensuring the survival of future
generations that they realise. See his Death and the Afterlife (New York: Oxford University Press, 2013). He
argues that many of the things that give meaning to our lives would fail to give meaning if we knew that people
would not survive long after our deaths. For example, campaigns for social reform; long-term medical,
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impose other costs, or at least other risks, on presently-existing people. Second, this case
presents us with the very difficult task of imagining not simply that our choice will affect the
identity of one person who exists in the future, but rather that it will affect the identity of
everyone who exists in the future. That seems a very hard thing to imagine. Third, imagining
the horror of thousands of people being killed by the reactor melting down makes it very
difficult to also keep in mind that all of these people had lives worth living, and that it was
better for them to have lived and then died prematurely than never to have lived at all. Fourth,
we might again be caught in the grip of traditional aggregative views, which
straightforwardly imply that building the reactor would be very seriously morally wrong.
Again, I think we can test my suggestion that the common intuitive reaction to Future
Catastrophe is the result of one or more of the four mistakes just described. Suppose that
there is a button on the table in front of you. If you press this button, tens of thousands of new
people, ‘The Newbies’, will pop into existence on a far-away, otherwise uninhabited planet.
The Newbies will have long and happy lives, but they will never know about our world, and
no one in our world will ever know about them—after pressing the button, your memory of
pressing it will be permanently erased. Are you morally required to press the button? Keep in
mind that The Newbies do not yet exist, and so not pressing the button would not be worse
for them or anyone else. Most people to whom I have put this case judge that the answer is
‘no’. They judge that, though it is morally permissible to press the button, there is also
nothing wrong with not pressing it.
Suppose next that you have a different button on the table in front of you. If you press
this button, tens of thousands of other new people, ‘The Others’, will pop into existence on a
far-away, otherwise uninhabited planet. The Others will have happy lives until around the age

scientific, and technological research; the advancement of human understanding; and the protection of cultures
and traditions would all seem pointless if we knew that humanity would soon disappear.
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of forty, at which point they will instantaneously drop dead. They will never know about our
world, and no one in our world will ever know about them—after pressing the button, your
memory of pressing it would be permanently erased. Would it be morally wrong for you to
press the button? Keep in mind that The Others would have lives worth living and would be
on-the-whole happy to have come into existence. Most people to whom I have put this case
judge that the answer is ‘no’. They judge that, though there is nothing wrong with not
pressing the button, there is also nothing wrong with pressing it.
Suppose finally that you have both the Newbies button and the Others button on the
table in front of you. You can press one of these buttons or neither, but not both. Would it
now be morally wrong for you to press the Others button? I cannot see how it could be. If
you are not morally required to press the Newbies button when that is your only option, and it
is not morally wrong for you to press the Others button when that is your only option, why
would the availability of the Newbies button make pressing the Others button morally
wrong?
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When I have presented these three ‘button’ cases to people, in this order, they have
almost unanimously shared my judgment that it is permissible for you to press the Others
button even when the Newbies button is also available. But your choice between the Newbies
button and the Others button is analogous, in all morally relevant respects, to Future
Catastrophe. This strongly suggests that the judgment that it is morally wrong to build the
reactor is distorted by one of the four factors that I earlier identified. When we consider the
first button case, in which only the Newbies button is available, and we judge that you are not
morally required to press the button, this frees us from the grip of traditional aggregative

101
Again, I am not appealing to Boonin’s transitivity principle, or to his weaker transitivity principle. I am
instead appealing directly to the judgment that adding the Newbies button makes no difference to the
permissibility of pressing the Others button.
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views, on which we are morally required to maximize the sum of happiness or well-being.
When we consider the second button case, in which only the Others button is available, the
most important features of the case are that The Others would have lives worth living and
that their existence would affect no one else, so it is easier for us to keep these features in
mind. And because the case is so abstract, it is easy for us to avoid unduly importing
assumptions from similar, real-world cases. When we finally consider the third button case,
in which both the Newbies button and the Others button are available, we are free from the
grip of traditional aggregative views, we recognise that The Others would have lives worth
living, we recognise that the existence of The Others would affect no one else, and we have
been primed to think of The Newbies and The Others as distinct possible people. We are
therefore free from the four factors that potentially distort our judgment when we consider
Future Catastrophe. It seems reasonable to infer that the apparent discrepancy between the
judgment that it is morally wrong to build the reactor and the judgment that it is morally
permissible for you to press the Others button even when the Newbies button is available is
explained by the former judgment being distorted by one or more of these four factors. I
conclude that the common intuitive reaction to Future Catastrophe is a mistake, and hence it
is no objection that complaints-based views are unable to capture this intuition.

3.3. Human Extinction
Suppose that we accept my arguments thus far. We accept that it is permissible for Mary to
conceive now, even though her child would have significant health impairments, and we
accept that it is permissible for us to build the reactor, even though it will eventually melt
down, killing tens of thousands of people. We might still be worried about a yet more
extreme version of The Non-Identity Problem. In this version, we can choose to do
something that would both change the identities of all future generations and, within a few
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hundred years, lead to the total extinction of humanity. If we accept a complaints-based view,
are we committed to accepting that this act would also be morally permissible? This
conclusion might seem unacceptable.
I am not sure that this conclusion is unacceptable. If each person alive now decided to
take her own life, thereby bringing about human extinction, that would be a tragedy, but I do
not think that anyone would have done anything morally wrong, at least so long as each
person knew that she would not be leaving behind any dependents. So it does not seem to me
implausible that it could be permissible for us to bring about human extinction more slowly,
if we could do so in a way that would genuinely be no worse for anyone who ever lives.
But even if we do find this conclusion unacceptable, that does not force us to reject
complaints-based views. We could plausibly hold that, though there is no moral reason to
maximize the number of happy people in the world, there is moral reason to preserve
humanity itself. We would then believe that humanity has what Christine Korsgaard calls
‘final value’.
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A thing has final value when there is reason to preserve it, even though there
is no reason to maximize the amount of it that exists. Plausible examples include great works
of art, beautiful landscapes, species of animal and plant, languages, and cultures. It seems no
less plausible to hold that humanity should be regarded in this way. If humanity has final
value, there is moral reason to avoid acting in ways that could lead to human extinction, even
when acting in these ways would not be worse for anyone who ever lives.

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Christine M. Korsgaard, Creating the Kingdom of Ends (Cambridge: Cambridge University Press, 1996):
Chapter 9. Johann Frick also appeals to Korsgaard’s notion of ‘final value’ to explain why it would be wrong to
allow humanity to become extinct. See his ‘Making People Happy, Not Making Happy People’, unpublished
manuscript, Chapter 3.
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4. Revenge of The Non-Identity Problem
I have so far considered both Parfit’s initial version of The Non-Identity Problem, which
focuses on Mary’s Choice, and his second and seemingly more powerful version of The Non-
Identity Problem, which focuses on Future Catastrophe. I have argued that our intuitions
about these cases are distorted in various ways, and that when we consider purified versions
of these cases, our intuitions change, and the problem promptly disappears. Thus, these
versions of The Non-Identity Problem do not threaten complaints-based views.
In this section, I consider a revenge version of The Non-Identity Problem suggested to
me in conversation by Jacob Ross. This version presents a genuine problem for simple
complaints-based views. However, by modifying complaints-based views in plausible ways,
we can avoid even this version of the problem.

4.1. Ross’s Challenge
Here is Ross’s version of The Non-Identity Problem.
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Suppose that you must choose
between the following three outcomes.

(1) Amy is the only person who ever lives, and she has a life that is only just worth
living.
(2) Bobby is the only person who ever lives, and he has a good life.
(3) Bobby and one thousand other people are the only people who ever live. Bobby
has a fantastic life, but the others have lives of constant, agonising pain.

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Ross discusses several similar cases in ‘Rethinking the Person-Affecting Principle’.
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It would clearly be morally wrong for you to choose (3), and Bobby has a much better life in
(2) than Amy does in (1), so it is extremely plausible that it is at least morally permissible for
you to choose (2). It follows from my previous arguments that it is also morally permissible
for you to choose (1), but that is not important here. The problem for complaints-based views
is that they seem to imply that it is morally wrong for you to choose (2). The reason is this. If
you choose (2), you will bring into existence Bobby, and Bobby will have a complaint
against how you acted, for you could instead have chosen (3), which would have made
Bobby significantly better off. Of course, you should not choose (3), for that would bring into
existence a thousand people with lives of constant agonising pain, and these people would
then have very strong complaints against how you acted. But if you instead choose (1), no
one will have any complaint, for Amy will be the only person who ever lives, she will have a
life worth living, and you could not have made her any better off. Since choosing either (2) or
(3) will generate complaints, whereas choosing (1) will not generate any complaints,
complaints-based views seem to imply that you are morally required to choose (1). They then
have the very implausible implication that it is morally wrong for you to choose (2).

4.2. A Response to Ross
It is clear that Bobby’s potential complaint does not give you any reason to choose (1) rather
than (2). But that does not show that we should reject complaints-based views. It shows only
that complaints-based views cannot take their simplest form, in which they require us to
minimize the sum of complaints. They can instead take a more complicated form.
We want a complaints-based view that captures the fact that Bobby’s potential
complaint is a complaint against you choosing (2) rather than (3), but not a complaint against
you choosing (2) rather than (1). Here is a first attempt at formulating such a view:

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View 1
1. A person has a complaint against our choosing option X rather than option Y if
and only if our choosing X rather than Y is worse for her.
2. It is wrong to choose an option X if and only if there is an option Y such that the
sum of complaints against our choosing X rather than Y is greater than the sum of
complaints against our choosing Y rather than X.

This view avoids Ross’s version of The Non-Identity Problem. Bobby has a complaint
against you choosing (2) rather than (3). But each of the one thousand other people has a
much stronger complaint against you choosing (3) rather than (2). So View 1 implies that it is
wrong for you to choose (3). Since choosing (2) rather than (1) is not worse for anyone, no
one has any complaint against you choosing (2) rather than (1), and so View 1 also implies
that it is permissible for you to choose (2). View 1 also implies that it is permissible for you
to choose (1), but I have already argued that we should accept that result.
However, View 1 faces a new problem. Suppose that you must choose between the
following three outcomes, in which only the mentioned people ever exist.

(1) Amy has a life that is only just worth living. Bobby has a better life.
(2) Bobby has a life that is only just worth living. Carly has a better life.
(3) Carly has a life that is only just worth living. Amy has a better life.

Bobby has a complaint against you choosing (2) rather than (1), and no one has any
complaint against you choosing (1) rather than (2), so View 1 implies that it is wrong for you
to choose (2). Carly has a complaint against you choosing (3) rather than (2), and no one has
any complaint against you choosing (2) rather than (3), so View 1 implies that it is wrong for
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you to choose (3). Amy has a complaint against you choosing (1) rather than (3), and no one
has any complaint against you choosing (3) rather than (1), so View 1 implies that it is wrong
for you to choose (1). View 1 therefore implies that every option is wrong.
This problem with View 1 parallels the no permissible options problem for partially
aggregative views, which I discussed in Chapter 1. We can avoid this problem in the same
way. Let us say that an option X defeats an option Y, and Y is defeated by X, if and only if
the sum of complaints against our choosing Y rather than X is greater than the sum of
complaints against our choosing X rather than Y. It follows that (1) is defeated by (3), (2) is
defeated by (1), and (3) is defeated by (2). If we assume that it is wrong to choose a defeated
option, we get the no permissible options problem. But we can plausibly reject this
assumption. Even if one option is defeated by another, these options might be morally on a
par, for the latter might be defeated by some other option. If every option is defeated by
exactly one other option, we can hold that every option is morally on a par. And if every
option is morally on a par, it is permissible for you to choose any option.
We might now conclude that, when every option is defeated by another option, it is
permissible for you to choose any option. But this conclusion needs to be qualified. Suppose
that in addition to (1), (2), and (3), you could choose (1*).

(1*) As in (1) except that Bobby has a slightly worse life.

It would clearly be wrong for you to choose (1*), given that you could choose (1) instead. I
suggest the reason is that (1*) is not only defeated by also dominated. It is dominated in the
sense that there is another option, (1), that defeats it and defeats every other option that it
defeats. If an option is not only defeated but also dominated, it is morally inferior to every
non-dominated option.
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We have now arrived at the following view.

View 2
1. A person has a complaint against our choosing option X rather than option Y if
and only if our choosing X rather than Y is worse for her.
2. X defeats Y if and only if the sum of complaints against our choosing Y rather
than X is greater than the sum of complaints against our choosing X rather than Y.
3. X dominates Y if and only if X both defeats Y and defeats every option that Y
defeats.
4. Other things equal, you should choose a non-defeated option, unless every option
is defeated, in which case you should choose a non-dominated option.

This view avoids Ross’s version of The Non-Identity Problem and also avoids the no
permissible options problem.
It might now be objected that, like the partially aggregative views that I discussed in
Chapter 1, View 2 is vulnerable to the option dependence problem. Suppose again that you
must choose between (1), (2), and (3). View 2 implies that, because each option is defeated,
and no option is dominated, it is permissible for you to choose any option. Suppose that you
initially decide to choose (1), but just as you are about to make this choice, option (2) is taken
away. With (2) gone, (3) is no longer defeated. So View 2 now implies that you should
choose (3). View 2 therefore implies that whether it is permissible for you to choose (1)
rather than (3) depends on whether option (2) is available.
I think that we should defend View 2 against this problem in the same way that I
defended the partially aggregative views discussed in Chapter 1. We should simply point out
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that, when the rationale for View 2 is kept in mind, option dependence does not seem so
counterintuitive.
I conclude that while Ross’s version of The Non-Identity Problem presents a genuine
problem for simple complaints-based views, it is not a problem for somewhat more
complicated complaints-based views, such as View 2.

5. Dissertation Summary
That completes my defence of a fully aggregative, ex ante, complaints-based moral view. Let
me summarise the discussion.
In Chapter 1, I described problems for the two most prominent partially aggregative
views in the literature, and then developed a new partially aggregative view, which I called
Avoid Inferior Claims (AIC). This new view avoids many of the standard problems with
partially aggregative views, and those that is does not avoid are not decisive.
In Chapter 2, I argued that, despite the appeal of AIC and partially aggregative views
more generally, we must reject all partially aggregative and non-aggregative views. I argued
that there is a problem with these views that has not been properly appreciated in the existing
literature: they have unacceptable implications in certain cases involving risk. I concluded
that we should reconsider the prospects for aggregative views.
The main objection to aggregative views is that they have counterintuitive
implications in cases like Death v Headaches. In Chapter 3, I argued that we should accept
these counterintuitive implications. I followed several proponents of aggregative views in
deploying the large numbers argument. According to this argument, our intuitions about
cases like Death v Headaches are not reliable, because these cases require us to imagine very
large numbers of people and we cannot accurately imagine very large quantities. I also
defended this argument against some recent objections.
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In Chapter 4, I turned from the question of whether our moral view should be
aggregative to the question of what it should aggregate. I presented several reasons to prefer
ex ante complaints-based aggregative views, which direct us to minimize the sum of ex ante
complaints, to traditional aggregative views, which direct us to maximize the sum of
happiness or well-being.
In this fifth and final chapter, I responded to an important and very influential
challenge to complaints-based views, known as The Non-Identity Problem. I considered both
Parfit’s initial version of The Non-Identity Problem, which focuses on Mary’s Choice, and
his second and seemingly more powerful version of The Non-Identity Problem, which
focuses on Future Catastrophe. I argued that our intuitions about these cases are distorted in
various ways, and that when we consider purified versions of these cases, our intuitions
change, and the problem promptly disappears. I then considered a revenge version of The
Non-Identity Problem suggested to me in conversation by Ross. I argued that while this
version presents a genuine problem for simple complaints-based views, it is not a problem for
somewhat more complicated complaints-based views, such as View 2.

In the following addendum, I discuss two recent developments in the literature on
aggregation, which are due to Patrick Tomlin and Victor Tadros.

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Addendum
Recent Developments

1. Introduction
In this addendum, I discuss two recent developments in the literature on aggregation. Patrick
Tomlin has argued that partially aggregative views have implausible implications in cases in
which there are additions or subtractions to the groups of people that we can save.
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His
argument complements the risk-based argument that I developed in Chapter 2. In Section 2, I
summarise his argument. Victor Tadros has subsequently responded to both Tomlin’s
argument and my risk-based argument.
105
In Section 3, I summarise and argue against his
response to Tomlin. In Section 4, I summarise and argue against his response to me.

2. Tomlin’s Argument
According to standard versions of partially aggregative views, at least when other things are
equal, we should minimize the sum of strength-weighted, relevant complaints.
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When is a

This chapter began as comments on a draft of Victor Tadros’s paper ‘Localised Restricted Aggregation’, which
I gave at the University of St Andrews Centre for Ethics, Philosophy, and Public Affairs in October 2017. I am
very grateful to Theron Pummer for inviting me to give those comments, and to Victor, Theron, and everyone in
attendance for a helpful discussion. For helpful feedback on earlier drafts of this paper, I am very grateful to
Abelard Podgorski, Jonathan Quong, Alexander Sarch, and an audience at the University College London
philosophy department symposium.
104
Patrick Tomlin, ‘On Limited Aggregation’, Philosophy & Public Affairs 45 (2017): 232–260.
105
Victor Tadros, ‘Localised Restricted Aggregation’, Oxford Studies in Political Philosophy: forthcoming.
106
I am here formulating these views in terms of ‘complaints’ rather than ‘claims’. Though the latter
terminology is more common in the literature, the former is more intuitive when applying these views to risk, as
I do in Section 4. For more on this terminological issue, see the first few paragraphs of Chapter 2.
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complaint relevant? Tomlin identifies two possible answers.
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According to Competitive
Relevance, a complaint is relevant if and only if it is sufficiently strong relative to the
strongest complaint with which it competes. According to Global Relevance, a complaint is
relevant if and only if it is sufficiently strong relative to the strongest complaint in the
competition.
Let me illustrate this distinction. Suppose that a complaint against a lost finger is
sufficiently strong relative to a complaint against a lost arm, and a complaint against a lost
arm is sufficiently strong relative to a complaint against death, but a complaint against a lost
finger is not sufficiently strong relative to a complaint against death. Now consider the
following two cases.

Case 1: You can save either group A, which contains 1 person facing death and 1
person facing a lost finger, or group B, which contains 1 person facing a lost arm.

Case 2: You can save either group A, which contains 1 person facing death, or group
B, which contains 1 person facing a lost arm and 1 person facing a lost finger.

Focus on the potential complaint of the person facing a lost finger. On Competitive
Relevance, this complaint is relevant in Case 1, for it is sufficiently strong relative to a
complaint against a lost arm, which is the strongest complaint with which it competes, but it
is not relevant in Case 2, for it is not sufficiently strong relative to a complaint against death,
which is the strongest complaint with which it competes. On Global Relevance, this

107
Tomlin refers to these answers respectively as ‘Anchor by Competition’ and ‘Anchor by Strength’. See ‘On
Limited Aggregation’, at 239.
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complaint is not relevant in either case, for it is not sufficiently strong relative to a complaint
against death, which is the strongest complaint in both competitions.
Tomlin argues that, regardless of which view about relevance we adopt, partially
aggregative views have implausible implications in certain cases in which there are additions
or subtractions to the groups of people that we can save.
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Suppose that 10 complaints
against a lost arm equals 1 complaint against death (that is, the combined moral weight of the
former is equal to the moral weight of the latter). Now consider Case 3, which has two
stages.

Stage 1: You can save either group A, which contains 1 person facing death, or group
B, which contains 10 people facing a lost arm.

Stage 2: 1 person facing a lost finger is added to group A, and 1,000,000 people
facing a lost finger are added to group B.

Partially aggregative views imply that it is permissible to save either group at Stage 1. If it is
permissible to save either group at Stage 1, it must be at least permissible to save B at Stage
2. But on Competitive Relevance, partially aggregative views imply otherwise. Since the
1,000,000 complaints against a lost finger added to B are in competition with a complaint
against death, they are not relevant. But the 1 complaint against a lost finger added to A is
relevant, for it is in competition only with a complaint against a lost arm. This complaint
must tip the balance. So partially aggregative views imply that you should save A.

108
Tomlin, ‘On Limited Aggregation’, at 240–247.
132
We can avoid this problem by adopting Global Relevance. On this view, none of the
complaints added at Stage 2 are relevant, for they are not sufficiently strong relative to the
strongest complaint in the competition, which is a complaint against death. So partially
aggregative views imply that Stage 2 makes no moral difference.
But, as Tomlin argues, Global Relevance faces an even worse problem. Suppose that
5,000 complaints against a lost finger outweigh 20 complaints against a lost arm, and 20
complaints against a lost arm outweigh 1 complaint against death. Now consider Case 4,
which has two stages.

Stage 1: You can save either group A, which contains 5,000 people facing a lost
finger, or group B, which contains 20 people facing a lost arm.

Stage 2: 1 person facing death is added to group A.

Partially aggregative views imply that you should save A at Stage 1. If you should save A at
Stage 1, you should clearly save A at Stage 2. But on Global Relevance, partially aggregative
views imply otherwise. At Stage 2, the 5,000 complaints against a lost finger in A become
irrelevant, for they are not sufficiently strong relative to the strongest complaint in the
competition, which is now a complaint against death. Since the only relevant complaints are
the 1 complaint against death and the 20 complaints against a lost arm, and the latter
outweighs the former, partially aggregative views imply that you should save B.
Can partially aggregative views avoid these problems? That depends on whether we
can find a plausible alternative to Competitive Relevance and Global Relevance. Tomlin
133
considers a few alternatives and shows that they run into similar problems.
109
I suggested
another alternative in Chapter 1, but this alternative is complicated, and it ultimately fails to
help, so I will not discuss it here. Instead, I will discuss a more promising alternative
proposed by Tadros.

3. Tadros’s Response to Tomlin
In this section, I summarise Tadros’s response to Tomlin and then develop two problems for
this response. The second problem extends Tomlin’s argument in a way that, I believe,
presents a decisive dilemma for all partially aggregative views.

3.1. Local Relevance
Tadros argues that we should respond to Tomlin by accepting a new kind of partially
aggregative view that he calls Local Relevance.
110
He does not formulate this view precisely,
but the basic idea is this: if a complaint C1 is not sufficiently strong relative to a competing
complaint C2, C1 cannot contribute to counterbalancing C2, but C1 can still contribute to
counterbalancing other competing complaints relative to which it is sufficiently strong.
Recall Case 3.

Stage 1: You can save either group A, which contains 1 person facing death, or group
B, which contains 10 people facing a lost arm.

Stage 2: 1 person facing a lost finger is added to group A, and 1,000,000 people
facing a lost finger are added to group B.

109
Tomlin, ‘On Limited Aggregation’, at 247–251.
110
Tadros, ‘Localised Restricted Aggregation’.
134

On Competitive Relevance, partially aggregative views have the implausible implication that,
though it is permissible to save either group at Stage 1, you should save A at Stage 2. On
Local Relevance, partially aggregative views still imply that it is permissible to save either
group at Stage 1, but they need not imply that you should save A at Stage 2. Though the
complaints against a lost finger added to B cannot contribute to counterbalancing the
complaint against death in A, they can still contribute to counterbalancing the complaint
against a lost finger added to A. Since they more than counterbalance this complaint, this
complaint cannot tip the balance in favour of A. So Stage 2 makes no difference.
Recall Case 4.

Stage 1: You can save either group A, which contains 5,000 people facing a lost
finger, or group B, which contains 20 people facing a lost arm.

Stage 2: 1 person facing death is added to group A.

On Global Relevance, partially aggregative views have the implausible implication that,
though you should save A at Stage 1, you should save B at Stage 2. On Local Relevance,
partially aggregative views still imply that you should save A at Stage 1, but they need not
imply that you should save B at Stage 2, for the complaints against a lost finger in A can
always contribute to counterbalancing the complaints against a lost arm in B.

3.2. A Path Dependence Problem
Local Relevance seems more promising than Competitive Relevance and Global Relevance.
But it faces a path dependence problem. Suppose that 2,000 complaints against a lost finger
135
equal 20 complaints against a lost arm, and 20 complaints against a lost arm outweigh 1
complaint against death. Now consider Case 5, which has two stages.

Stage 1: You can save either group A, which contains 1 person facing death, or group
B, which contains 20 people facing a lost arm.

Stage 2: 2,000 people facing a lost finger are added to each group.

Partially aggregative views imply that you should save B at Stage 1. If you should save B at
Stage 1, it must be at least permissible to save B at Stage 2. Local Relevance can capture this
judgment if we apply it as follows.

Group A Group B
1 person facing death 20 people facing a lost arm
2,000 people facing a lost finger 2,000 people facing a lost finger

Here, we allow the complaints added to each group to counterbalance each other, so that
Stage 2 makes no difference. However, we could instead apply Local Relevance as follows.

Group A Group B
1 person facing death 20 people facing a lost arm
2,000 people facing a lost finger 2,000 people facing a lost finger

Here, we allow the complaints added to A to counterbalance the complaints against a lost arm
in B. If we apply Local Relevance in this way, it has the implausible implication that, though
136
you should save B at Stage 1, you should save A at Stage 2. Tadros give us no reason to
apply Local Relevance in the former way rather than the latter.

3.3. A Dilemma
Perhaps Tadros can give us a reason to apply Local Relevance in the former way rather than
the latter. As I will now show, Local Relevance would then face a different problem.
We begin with a second illustration of the path dependence problem. Consider Case
6, which has two stages.

Stage 1: You can save either group A, which contains 1 person facing death, or group
B, which contains 4,000 people facing a lost finger.

Stage 2: 20 people facing a lost arm are added to each group.

Partially aggregative views imply that you should save A at Stage 1. If you should save A at
Stage 1, it must be at least permissible to save A at Stage 2. Local Relevance can capture this
judgment if we apply it as follows.

Group A Group B
1 person facing death 4,000 people facing a lost finger
20 people facing a lost arm 20 people facing a lost arm

However, we could instead apply Local Relevance as follows.

137
Group A Group B
1 person facing death 2,000 people facing a lost finger
20 people facing a lost arm 2,000 people facing a lost finger
20 people facing a lost arm

If we apply Local Relevance in this second way, it has the implausible implication that,
though you should save A at Stage 1, you should save B at Stage 2, for the 20 complaints
against a lost arm added to B outweigh the 1 complaint against death in A.
Suppose that Tadros gives us a reason to apply Local Relevance in the former way
rather than the latter. Now consider three more cases, each of which has only one stage.

Case 7: You can save either group C, which contains 1 person facing death, or group
D, which contains 20 people facing a lost arm.

Case 8: You can save either group E, which contains 20 people facing a lost arm, or
group F, which contains 4,000 people facing a lost finger.

Case 9: You can save either group C + E or group D + F.

Since 20 complaints against a lost arm outweigh 1 complaint against death, you should save
D in Case 7. Since 4,000 complaints against a lost finger outweigh 20 complaints against a
lost arm, you should save F in Case 8. Since you should save D rather than C in Case 7, and F
rather than E in Case 8, it seems clear that you should save D + F in Case 9. Local Relevance
can capture this judgment only if we apply it in the latter of the following two ways.

138
Group C + E Group D + F
1 person facing death 4,000 people facing a lost finger
20 people facing a lost arm 20 people facing a lost arm

Group C + E Group D + F
1 person facing death 2,000 people facing a lost finger
20 people facing a lost arm 2,000 people facing a lost finger
20 people facing a lost arm

But C + E is equivalent to A in Case 6, and D + F is equivalent to B in Case 6. So it would be
inconsistent to apply Local Relevance in the former way in Case 6 and the latter way in Case
9. So Local Relevance must have an implausible implication in one of these cases.
This dilemma for Local Relevance is really a dilemma for all partially aggregative
views. In order to avoid an implausible implication in Case 6, a partially aggregative view
must balance claims in the former way. In order to avoid an implausible implication in Case
9, a partially aggregative view must balance claims in the latter way. But it is inconsistent to
balance claims in the former way in Case 6 and the latter way in Case 9. So all partially
aggregative views must have an implausible implication in one of these cases.

3.4. Sharpening the Horns
Some people might be tempted to embrace a horn of my dilemma, accepting one of the
problematic implications. Let me stress why that would be a mistake.
How bad would it be to embrace the first horn? Consider a modified version of Case
6.

139
Stage 1: You can save either group A, which contains 1 person facing death, or group
B, which contains a ginormous number of people facing a lost finger.

Stage 2: 1,000,000 people facing a lost arm are added to group A, and 20 people
facing a lost arm are added to group B.

Partially aggregative views imply that you should save A at Stage 1. If you should save A at
Stage 1, it is clear that you should save A at Stage 2. Since the number of people facing a lost
arm added to A is vastly greater than the number added to B, this is even clearer than in the
original case. If we embrace the first horn of my dilemma, however, we must allow the
1,000,000 complaints against a lost arm added to A to be neutralized by the complaints
against a lost finger in group B, and that leaves the 20 complaints against a lost arm added to
B free to outweigh the 1 complaint against death in A. We must then accept the bizarre
implication that, though you should save A at Stage 1, you should save B at Stage 2.
Could reflecting on possible justifications for partially aggregative views make this
implication easier to accept? These views are typically justified by appeal to respect. Here is
a respect-based justification for the implication that we are considering: It is disrespectful to
press a complaint against a harm when this complaint is intended to compete with a
complaint against a much stronger harm, but it is not disrespectful to press a complaint
against a harm when this complaint is intended to compete only with a complaint against a
harm that is sufficiently close in size. Thus, at Stage 1, the people facing a lost finger cannot
press a relevant complaint, for their complaints would be intended to compete with the
complaint against death, and that would be disrespectful. At Stage 2, however, the people
facing a lost finger can press a relevant complaint, for their complaints can be intended to
compete only with the complaints against a lost arm added to A. The complaints against a
140
lost finger in B defeat the complaints of the people facing a lost arm in A, and that leaves the
complaints against a lost arm added to B free to defeat the complaint against death in A.
If this respect-based justification helps, it does not help enough. It remains bizarre to
hold that you should save A at Stage 1 and then, after we add complaints of equal strength to
both groups with the numbers heavily in favour of A, you should save B at Stage 2.
Furthermore, respect-based justifications for the opposite result are easy to find, making it
dubious to place much weight on any of these justifications. We could reason as follows: It is
disrespectful to press a complaint against a harm whenever doing so would result in someone
not being saved from a much stronger harm. At Stage 1, the people facing a lost finger cannot
press a relevant complaint, for doing so would result in someone not being saved from death,
and so would be disrespectful. At Stage 2, the people facing a lost finger still cannot press a
relevant complaint, for doing so would still result in someone not being saved from death.
Since there is nothing to defeat the complaints against a lost arm added to A, and these
complaints defeat the complaints against a lost arm added to B, we have a respect-based
justification for holding that you should save A at both Stage 1 and Stage 2.
111

How bad would it be to embrace the second horn? We would then accept that, though
you should save D rather than C in Case 7, and F rather than E in Case 8, you should save C
+ E rather than D + F in Case 9. To reveal how bizarre this implication is, we can combine
the cases and make things more vivid. Suppose that on your left are two buttons marked C

111
This alternative justification could be used to support the bizarre implication that Competitive Relevance has
in Case 3: the 1,000,000 people facing a lost finger added to B cannot make a relevant complaint, for doing so
would result in someone not being saved from death, and so would be disrespectful, whereas the person facing a
lost finger added to A can make a relevant complaint, for doing so would not result in anyone not being saved
from death. Thus, Tomlin is wrong when he says that there is ‘no respect-based rationale’ for the bizarre
implication that Competitive Relevance has in Case 3. See Tomlin, ‘On Limited Aggregation’, 244.
141
and D, and on your right are two buttons marked E and F. If you press a button, that will save
the corresponding group. But you can press only one button in each pair. Suppose next that
your arm span is just slightly too short for you to reach both pairs of buttons simultaneously.
It follows, on the view that we are considering, that you should press button D on your left
and then button F on your right, even though, had your arm span been just slightly longer, it
would have been permissible for you to simultaneously press buttons C and E.
We could again provide a respect-based justification for this bizarre implication, by
appealing to the latter justification described above. But that would not be enough to make
the implication plausible. And the former justification yields the opposite result, making
appeal to either justification very dubious.

4. Tadros’s Response to Me
In this section, I briefly recap my risk-based argument against partially aggregative views,
summarise Tadros’s response to this argument, and then argue that his response fails.

4.1. Recap: The Argument from Risk
In cases involving risk, we can apply partially aggregative views either ex ante or ex post. In
Chapter 2, I argued that they have implausible implications either way.
Consider the following case.

Villain A: A villain has kidnapped X and ten billion other people. He will either (1)
cut one finger off X, or (2) randomly select and kill ten of the other people. You must
choose which.

142
Clearly, you should choose (1), imposing the loss of a finger on X to spare ten other people
from death. When partially aggregative views are applied ex ante, they imply otherwise. X
has an ex ante complaint against (1) based on losing a finger, and each of the other people has
an ex ante complaint against (2) based on a one-in-a-billion chance of death. Since a
complaint against losing a finger is much stronger than a complaint against a one-in-a-billion
chance of death, partially aggregative views cannot allow us to aggregate the complaints
against (2). So, when applied ex ante, these views imply that you should choose (2).
We can avoid this problem by applying partially aggregative views ex post. When
partially aggregative views are applied ex post, they hold that, at least when other things are
equal, we should minimize the expected strongest ex post complaint. (1) will result in an ex
post complaint against a lost finger, and (2) will result in ten ex post complaints against
death. Since the complaints against death are much stronger than the complaint against a lost
finger, when applied ex post, partially aggregative views imply that you should choose (1).
But when applied ex post, partially aggregative views face a different problem.
Consider the following pair of cases.

Villain B: A villain has kidnapped one billion people. He will either (1) cut one finger
off each person, or (2) randomly select and kill one person. You must choose which.

Villain C: A villain has kidnapped one billion people. For each person, the villain will
either (1) cut one finger off this person, or (2) give this person a ticket for a lottery
with one billion tickets. You must choose between these options for each person in
turn. You know that, after you have finished choosing, the villain will randomly select
one of the lottery tickets and kill anyone who has the corresponding ticket.

143
Focus on Villain B. (1) will result in one billion ex post complaints against a lost finger, and
(2) will result in one ex post complaint against death. Since a complaint against death is much
stronger than a complaint against a lost finger, partially aggregative views cannot allow us to
aggregate the ex post complaints against (1). So, when applied ex post, these views imply
that you should choose (1). Focus next on Villain C. For each person, it is certain that (1) will
result in an ex post complaint against a lost finger, and there is a one-in-a-billion chance that
(2) will result in an ex post complaint against death. Since a complaint against a lost finger is
stronger than a complaint against death discounted by one-in-a-billion, when applied ex post,
partially aggregative views imply that you should choose (2) for each person. So, when
applied ex post, partially aggregative views imply that you should choose (1) in Villain B and
yet choose (2) for each person in Villain C. Since choosing (2) for each person in Villain C
seems morally equivalent to choosing (2) in Villain B, this result is bizarre.

4.2. Evaluating Sets of Acts
Tadros suggests that we respond to my risk-based argument by holding that partially
aggregative views apply to sets of acts rather than individual acts.
112
If we do, we can apply
partially aggregative views ex post without them implying that you should give each person a
lottery ticket in Villain C. To see this, suppose that your only options are performing the set
of acts that consists of giving a lottery ticket to each person and performing the set of acts
that consists of choosing for each person to lose a finger. The former set is certain to generate
an ex post complaint against death, and the latter set is certain to generate a billion ex post
complaints against a lost finger. Since a complaint against death is much stronger than a
complaint against a lost finger, partially aggregative views cannot allow us to aggregate the

112
Tadros, ‘Localised Restricted Aggregation’.
144
complaints against a lost finger. So, when these views are applied ex post and to sets of acts,
they imply that you should choose for each person to lose a finger rather than for each person
to have a lottery ticket. And that is consistent with what these views imply in Villain B.
Of course, these two sets of acts are not your only options. You could also perform a
set of acts that consists of giving some limited number of people lottery tickets and then
choosing for everyone else to lose a finger. If we apply partially aggregative views ex post
and to sets of acts, they imply that you should perform some such set of acts. More
specifically, they imply that you should stop giving lottery tickets to people once the
probability of someone being killed is such that a complaint against death discounted by this
probability is equal in strength to a complaint against losing a finger.
As Tadros recognises, this implication faces the following, powerful challenge.

Argument 1: You should not stop giving tickets after the first person, for giving a
ticket to the second person increases the chance that someone will die by only a tiny
amount. You should not stop giving tickets after the second person, for giving a ticket
to the third person increases the chance that someone will die by only a tiny amount.
… You should not stop giving tickets after the 999,999,999
th
person, for giving a
ticket to the billionth person increases the chance that someone will die by only a tiny
amount.

However, Tadros argues that, even if we cannot identify where Argument 1 goes wrong, we
can safely reject it. He asks us to consider the following case.

Killing the Harmless Torturers: Each of one million torturers is about to flip a switch
on a torture machine. Each switch will cause the same million victims to each
145
experience an imperceptible pain, but the combined effect on the victims will be
agony. You can kill any number of the torturers one by one, thereby relieving some or
all the pain of the victims.

Plausibly, it is permissible for you to kill at least some of the torturers. But this claim faces
the following, powerful challenge.

Argument 2: You should not kill all the torturers, for killing the millionth would make
almost no difference to the victims. You should not kill 999,999 torturers, for killing
the 999,999
th
would make almost no difference to the victims. … You should not kill
one torturer, for killing one would make almost no difference to the victims.

Tadros reasons as follows: It is clearly permissible to kill some number of the torturers. So
there is clearly something wrong with Argument 2. Since Argument 1 seems to parallel
Argument 2, we can safely assume that there is something wrong with Argument 1.
Tadros concludes that, since we can safely assume that there is something wrong with
Argument 1, we can plausibly hold that you should give lottery tickets to some but not all the
people in Villain C, so we can plausibly respond to my risk-based argument by applying
partially aggregative views ex post and to sets of acts.

4.3. A Reply to Tadros
Tadros’s argument is attractive. I am not sure what to think about Killing the Harmless
Torturers, or about the idea that Argument 1 parallels Argument 2. Nevertheless, I am still
sure that there is no point at which you should stop giving out lottery tickets in Villain C, for
two main reasons.
146
First, suppose for reductio that there is some number N such that you should stop
giving out lottery tickets after N people. Now imagine trying to explain to person N+1 why
you are choosing for him to lose a finger rather than receive a lottery ticket.
Second, if there is a point at which you should stop giving out lottery tickets in Villain
C, there must be a number of risky operations after which surgeons should quit their jobs, for
enough risky operations are certain to result in an accidental death. This implication is
absurd.

5. Summing Up (Pun Intended)
Fully aggregative views have counterintuitive implications in large number cases. They
imply, for example, that you should save an enormous number of people from headaches
rather than saving one person from death. We have seen that partially aggregative views have
counterintuitive implications both in certain cases in which there are additions or subtractions
to the groups of people that we can save and in certain cases involving risk. To my mind,
even considered individually, the counterintuitive implications of partially aggregative views
are far more counterintuitive than the counterintuitive implications of aggregative views. But
we should not consider these counterintuitive implications individually. When it comes to
counterintuitive implications, we should always aggregate.
113

113
The case for accepting a fully aggregative view rather than a partially aggregative view is even stronger
when we take into account the option dependence problem (see Chapter 1) and the various reasons to be
sceptical of our intuitions about large number cases (see Chapter 3).
147
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Abstract (if available)

Abstract Is there any number of people you should save from a moderately large burden, such as paralysis, rather than saving one person from a very large burden, such as death? Is there any number of people you should save from a very small burden, such as a headache, rather than saving one person from a very large burden, such as death? If we answer ‘no’ and ‘no’, we accept a non-aggregative moral view—a view on which benefits and burdens cannot be interpersonally aggregated. If we answer ‘yes’ and ‘no’, we accept a partially aggregative moral view—a view on which benefits and burdens can sometimes be interpersonally aggregated. If we answer ‘yes’ and ‘yes’, we accept a fully aggregative moral view—a view on which benefits and burdens can always be interpersonally aggregated. ❧ Most people accept a partially aggregative moral view. In Chapters 1–3, I argue that we should reject partially aggregative and non-aggregative views and accept a fully aggregative view. In Chapters 4–5, I turn from the question of whether our moral view should be aggregative to the question of what is should aggregate. I argue that, although our view should be fully aggregative, it should not focus on well-being, as fully aggregative views typically do. Instead, it should focus on complaints, as non-aggregative and partially aggregative views typically do. I argue that complaints-based views have some important advantages, and I defend them against Derek Parfit’s ‘Non-Identity Problem’.

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Asset Metadata

Creator Horton, Joe Peter (author)

Core Title Aggregating complaints

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Philosophy

Publication Date 09/12/2019

Defense Date 02/13/2018

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

Tag aggregation,Complaints,contractualism,OAI-PMH Harvest,the non-identity problem

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Quong, Jonathan (committee chair), Ross, Jacob (committee member), Schroeder, Mark (committee member), Wedgwood, Ralph (committee member)

Creator Email joe.horton@ucl.ac.uk,joepeteh@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-483453

Unique identifier UC11266920

Identifier etd-HortonJoeP-6103.pdf (filename),usctheses-c40-483453 (legacy record id)

Legacy Identifier etd-HortonJoeP-6103.pdf

Dmrecord 483453

Document Type Dissertation

Rights Horton, Joe Peter

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