Aggregation and Consequentialism

This paper discusses the "numbers problem," the problem of explaining why you should save more people rather than fewer when forced to choose. Existing non-consequentialist approaches to the problem appeal to fairness to explain why. I argue that this is a mistake and that we can give a more satisfying answer by appealing to requirements of charity or beneficence.

Is consequentialism consistent with common-sense morality? I argue for a negative answer to this question. In Sections 1-4, I develop and defend a definition for “consequentialism.” In Section 5, I attempt to show that, given this definition, consequentialism and common-sense morality cannot be reconciled. In Section 6, I argue that, on the definition of consequentialism I defend, consequentialism should be understood, not as a view about the relationship between the deontic and the evaluative (as many philosophers suppose), but as a (...) view about the relationship between the deontic and time. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty (...) about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

Derek Parfit argues that fission is prudentially better for you than ordinary death. But is having more fission products with good lives prudentially better for you than having just one? In this paper, we argue that it is. We argue that, if your brain is split and the halves are transplanted into two recipients, then it is prudentially better for you if both transplants succeed than if only one of them does. This upshot rules out, among other things, that the (...) prudential value of standing in the relation that matters in survival to multiple people is equal to their average well-being. (shrink)

According to Longtermism, our acts’ expected influence on the expected value of the world is mainly determined by their effects in the far future. There is, given total utilitarianism, a straightforward argument for Longtermism due to the enormous number of people that might exist in the future, but this argument does not work on person-affecting views. In this paper, we will argue that these views might also lead to Longtermism if Prudential Longtermism is true. Prudential Longtermism holds for a person (...) if and only if our acts’ overall influence on that person’s expected well-being is mainly determined by the acts’ effects in the far future. We argue that (due to a small chance of anti-ageing and uploading) there could be an enormous amount of prudential value for some contemporary person in the far future and that value may be so large that it dominates their overall expectation of lifetime well-being. (shrink)

Multidimensional concepts are everywhere, and they are important. Examples include moral value, welfare, scientific confirmation, democracy, and biodiversity. How, if at all, can we aggregate the underlying dimensions of a multidimensional concept F to yield verdicts about which things are Fer than which overall? Social choice theory can be used to model and investigate this aggregation problem. Here, we focus on a particularly thorny problem made salient by this social choice-theoretic framework: the underlying dimensions of a given concept might be (...) measurable on different types of scales—e.g., some ordinal and some cardinal. An underappreciated impossibility theorem due to Anna Khmelnitskaya shows that seemingly plausible constraints on aggregation across scale types are inconsistent. This impossibility threatens to render the notion of overall Fness incoherent. We attempt to defuse this threat, arguing that the impossibility depends on an overly restrictive conception of measurement and of how measurement constrains aggregation. Adopting a more flexible—and, we think, more perspicuous—conception of measurement opens an array of possibilities for aggregation across disparate scale types. (shrink)

After 50 years of debate, the ethics of aggregation has reached a curious stalemate, with both sides arguing that only their theory treats people as equals. I argue that, on the issue of equality, both sides are wrong. From the premise that “each counts for one,” we cannot derive the conclusion that “more count for more”—or its negation. The familiar arguments from equality to aggregation presuppose more than equality: the Kamm/Scanlon “Balancing Argument” rests on what social choice theorists call “(Positive) (...) Responsiveness,” Kamm’s “Aggregation Argument” assumes that “equal” lives are fungible, and Hsieh et al. have it that spreading goods broadly best approximates equality. In each case, the crucial premise is not equality itself but a further idea that Taurek, I argue, can safely reject. I conclude with a conjecture: there is no theory-neutral argument that settles the question of whether the numbers count. (shrink)

A person possesses value from various components of wellbeing, but they also have overall wellbeing from various instances of value taken together. Most ethicists assume that there is an objectively unique way that wellbeing from components aggregates into overall wellbeing. However, I argue that aggregation is subjective and varies depending on what sort of aggregation a person values. I end with some implications for the significance of death.

This paper presents a new puzzle for limited aggregation. Unlike other recent puzzles, this one arises independently of the issue of rational aversion to risk. Some possible responses are laid out and explored.

This paper develops and explores a new framework for theorizing about the measurement and aggregation of well-being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen’s framework, a social or overall betterness ordering is assigned to each profile of real-valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal comparability of (...) well-being directly, without the use of invariance conditions, and to distinguish between real changes in well-being and merely representational changes in the unit of measurement. The qualitative framework is shown to have important implications for a range of issues in axiology and social choice theory, including the characterization of welfarism, axiomatic derivations of utilitarianism, the meaningfulness of prioritarianism, the informational requirements of variable-population ethics, the impossibility theorems of Arrow and others, and the metaphysics of value. (shrink)

Suppose we can save either a larger group of persons or a distinct, smaller group from some harm. Many people think that, all else equal, we ought to save the greater number. This article defends this view (with qualifications). But unlike earlier theories, it does not rely on the idea that several people's interests or claims receive greater aggregate weight. The argument starts from the idea that due to their stakes, the affected people have claims to have a say in (...) the rescue decision. As rescuers, our primary duty is to respect these procedural claims, which we must do by doing what these people would decide, in a process where each is given an equal vote on the matter. So in cases where each votes in their own self-interest, respect for their equal right to decide, or their autonomy, will lead us to save the greater number. The argument is explained in detail, with special attention to the questions of how, exactly, it avoids aggregation, and of why majority rule is superior to lottery procedures. The view has further advantages. Especially, it explains the “partial” relevance of numbers in cases involving unequal harms, and it does so in a way that dissolves the appearance of paradox that besets theories of “partial aggregation.”. (shrink)

Is well-being the kind of thing that can be summed across individuals? This paper takes a measurement-theoretic approach to answering this question. To make sense of adding well-being, we would need to identify some natural "concatenation" operation on the bearers of well-being that satisfies the axioms of extensive measurement and can therefore be represented by the arithmetic operation of addition. I explore various proposals along these lines, involving the concatenation of segments within lives over time, of entire lives led alongside (...) one another or in sequence, and of evaluatively basic propositions via conjunction. All of these proposals turn out to carry highly controversial commitments about the good. I do not claim that these commitments are unacceptable. But they suggest that we cannot simply take for granted, as many philosophers do, that there is any such thing as the sum of well-being. (shrink)

Scale-based models of weighing reasons face challenges concerning the context sensitivity of weight, the aggregation of weight, and the methodology for determining what the weights of reasons are. I resolve these challenges.

Many population axiologies avoid the Repugnant Conclusion by endorsing Superiority: some number of great lives is better than any number of mediocre lives. But as Nebel shows, RC follows from the Intrapersonal Repugnant Conclusion: a guaranteed mediocre life is better than a sufficiently small probability of a great life. This result is concerning because IRC is plausible. Recently, Kosonen has argued that IRC can be true while RC is false if small probabilities are discounted to zero. This article details the (...) unique problems created by combining Superiority with discounting. The resultant view, Superiority Discounting, avoids the Repugnant Conclusion only at the cost of the Preposterous Conclusion: near-certain hell for arbitrarily many people is better than near-certain heaven for arbitrarily many people. (shrink)

John Taurek argues that, in a choice between saving the many or the few, the numbers should not count. Some object that this view clashes with the transitivity of ‘better than’; others insist the clash can be avoided. I defend a middle ground: Taurek cannot have transitivity, but that doesn’t doom his view, given a suitable conception of value. I then formalize and explore two conceptions: one context-sensitive, one multidimensional.

This paper is about the role of interpersonal comparisons in Harsanyi's aggregation theorem. Harsanyi interpreted his theorem to show that a broadly utilitarian theory of distribution must be true even if there are no interpersonal comparisons of well-being. How is this possible? The orthodox view is that it is not. Some argue that the interpersonal comparability of well-being is hidden in Harsanyi's premises. Others argue that it is a surprising conclusion of Harsanyi's theorem, which is not presupposed by any one (...) of the premises. I argue instead that Harsanyi was right: his theorem and its weighted-utilitarian conclusion do not require interpersonal comparisons of well-being. The key to making sense of this possibility is to treat Harsanyi's weights as dimensional constants rather than dimensionless numbers. (shrink)

Ethics in the tradition of Derek Parfit’s Reasons and Persons is riddled with sorites-like arguments, which lead us by what seem innocent steps to seemingly false conclusions. Take, for example, spectrum arguments for the Repugnant Conclusion that appeal to slight differences in quality of life. Several authors have taken the view that, since spectrum arguments are structurally analogous to sorites arguments, the correct response to spectrum arguments is structurally analogous to the correct response to sorites arguments. This sorites analogy is (...) here argued against. There are potential structural disanalogies between spectrum arguments and sorites arguments. But even if these arguments are relevantly structurally analogous, they differ in their content in ways that show the sorites analogy to be implausible. Two content-based disanalogies are here explored—one is inspired by Parfit’s work on reductionism, and the other involves hypersensitivity. The chapter concludes with a methodological lesson. (shrink)

To your left, three strangers are drowning. To your right, one other stranger is drowning. You can effortlessly save the three by throwing a lifebuoy to your left. Alternatively, you can save the one by throwing the lifebuoy to your right. You cannot save all four. What should you do? It’s wrong to do nothing, but is it wrong to save just the one stranger? Are you morally required to save the three? Many claim that, when those you can help (...) are innocent strangers with similar interests at stake, you’re required to save the greater number. Is this claim justified? This essay reviews some doubts. (shrink)

Is an outcome where many people are saved and one person dies better than an outcome where the one is saved and the many die? According to the standard utilitarian justification, the former is better because it has a greater sum total of well-being. This justification involves a controversial form of moral aggregation, because it is based on a comparison between aggregates of different people's well-being. Still, an alternative justification—the Argument for Best Outcomes—does not involve moral aggregation. I extend the (...) Argument for Best Outcomes to show that any utilitarian evaluation can be justified without moral aggregation. (shrink)

How should governments balance saving people from very large individual disease burdens (such as an early death) against saving them from middling burdens (such as erectile dysfunction) and minor burdens (such as nail fungus)? This chapter considers this question through an analysis of a priority-setting proposal in the Netherlands, on which avoiding a multitude of middling burdens takes priority over saving one person from early death, but no number of very small burdens can take priority over avoiding one death. It (...) argues that there is some, albeit imperfect, evidence of substantial public support for such a policy. Furthermore, it provides a principled rationale for it in terms of respect for the person who faces the largest burden. (shrink)

This chapter presents arguments for two slightly different versions of the thesis that the value of persons is incomparable. Both arguments allege an incompatibility between the demands of a certain kind of practical reasoning and the presuppositions of value comparisons. The significance of these claims is assessed in the context of the “Numbers problem”—the question of whether one morally ought to benefit one group of potential aid recipients rather than another simply because they are greater in number. It is argued (...) that many of the popular approaches to this problem—even ones that avoid the aggregation of personal value—are imperiled by the incomparability theses. -/- . (shrink)

There is a well-known moral quandary concerning how to account for the rightness or wrongness of acts that clearly contribute to some morally significant outcome – but which each seem too small, individually, to make any meaningful difference. One consequentialist-friendly response to this problem is to deny that there could ever be a case of this type. This paper pursues this general strategy, but in an unusual way. Existing arguments for the consequentialist-friendly position are sorites-style arguments. Such arguments imagine varying (...) a subject’s predicament bit by bit until it is clear that a relevant difference has been achieved. The arguments offered in this paper are structurally different, and do not rely on any sorites series. For this reason, they are not vulnerable to objections that have been leveled against the sorites-style arguments. (shrink)

Many of us believe (1) Saving a life is more important than averting any number of headaches. But what about risky cases? Surely: (2) In a single choice, if the risk of death is low enough, and the number of headaches at stake high enough, one should avert the headaches rather than avert the risk of death. And yet, if we will face enough iterations of cases like that in (2), in the long run some of those small risks of (...) serious harms will surely eventuate. And yet: (3) Isn't it still permissible for us to run these repeated risks, despite that knowledge? After all, if it were not, then many of the risky activities that we standardly think permissible would in fact be impermissible. Nobody has yet offered a principle that can accommodate all of 1-3. In this paper, I show that we can accommodate all of these judgements, by taking into account both ex ante and ex post perspectives. In doing so, I clear aside an important obstacle to a viable deontological decision theory. (shrink)

Larry Temkin famously argues that what he calls spectrum arguments yield strong reason to reject Transitivity, according to which the ‘all-things-considered better than’ relation is transitive. Spectrum arguments do reveal that the conjunctions of independently plausible claims are inconsistent with Transitivity. But I argue that there is very strong independent reason to reject such conjunctions of claims, and thus that the fact that they are inconsistent with Transitivity does not yield strong reason to reject Transitivity.

Epistemic consequentialism has been charged with ignoring the epistemic separateness of propositions and with (thereby) allowing trade-offs between propositions. Here, I do two things. First, I investigate the metaphor of the epistemic separateness of propositions. I argue that either (i) the metaphor is meaningfully unpacked in a way that is modeled on the moral separateness of persons, in which case it doesn’t support a ban on trade-offs or (ii) it isn’t meaningfully unpacked, in which case it really doesn’t support a (...) ban on trade-offs. Second, I consider the strategy of arguing against the trade-off permitting conception of epistemic rationality that is central to epistemic consequentialism on the basis of our intuitive verdicts about the permissibility of trade-offs in cases. I argue the execution of this strategy suffers a methodological mistake that, once corrected, vitiates the probative value of those intuitive verdicts. Hence the conclusion: the separateness of propositions provides no support for a ban on trade-offs, and an influential independent argument for such a ban is flawed. (shrink)

Common principles for resource allocation in health care can prioritize the alleviation of small health burdens over lifesaving treatment. I argue that there is some evidence that these principles are at odds with a sizable share of public opinion, which holds that saving a life should take priority over any number of cures for minor ailments. I propose two possible explanations for this opinion, one debunking and one vindicatory. I also outline how well-designed surveys and moral inquiry could help decide (...) between them. Finally, I consider how priority-setting principles could be adjusted if the view that saving a life always trumps alleviating small burdens were vindicated. (shrink)

When one faces competing claims of varying strength on public resources for health, which claims count? This paper proposes the following answer. One should count, or aggregate, a person’s claim just in case one could sympathize with her desire to prioritize her own claim over the strongest competing claim. It argues that this principle yields appealing case judgments and has a plausible grounding in both sympathetic identification with each person, taken separately, and respect for the person for whom most is (...) at stake. It also defends this principle against several heretofore unanswered objections. (shrink)

Utilitarianism is often rejected on the grounds that it fails to respect the separateness of persons, instead treating people as mere “receptacles of value”. I develop several different versions of this objection, and argue that, despite their prima facie plausibility, they are all mistaken. Although there are crude forms of utilitarianism that run afoul of these objections, I advance a new form of the view—‘token-pluralistic utilitarianism’—that does not.

When do claims to be saved of a small or moderate harm aggregate against a competing claim to be saved from an early death? In this short response to Kamm's Bioethical Prescriptions, I argue for the following answer: aggregation of weaker claims against a life is permitted just in case, in a one-to-one contest, a person with a weaker claim would have a personal prerogative to prioritize her claim over a stranger’s competing claim to life.

In this paper, I set out and defend a new theory of value, whole-life welfarism. According to this theory, something is good only if it makes somebody better off in some way in his life considered as a whole. By focusing on lifetime, rather than momentary, well-being, a welfarist can solve two of the most vexing puzzles in value theory, The Badness of Death and The Problem of Additive Aggregation.

Interpersonal aggregation involves the combining and weighing of benefits and losses to multiple individuals in the course of determining what ought to be done. Most consequentialists embrace thoroughgoing interpersonal aggregation, the view that any large benefit to each of a few people can be morally outweighed by allocating any smaller benefit to each of many others, so long as this second group is sufficiently large. This would permit letting one person die in order to cure some number of mild headaches (...) instead. Most non-consequentialists reject thoroughgoing interpersonal aggregation despite also believing it is permissible to let one person die in order to prevent many cases of paraplegia instead. Non-consequentialists defend this asymmetry largely on the basis of intuition, and some rely on the notion of relevance to formalize the grounding intuitions. This article seeks to clarify and strengthen the non-consequentialist notion of relevance by engaging with three objections to it. (shrink)

Moral duties concerning climate change mitigation are – for good reasons – conventionally construed as duties of institutional agents, usually states. Yet, in both scholarly debate and political discourse, it has occasionally been argued that the moral duties lie not only with states and institutional agents, but also with individual citizens. This argument has been made with regard to mitigation efforts, especially those reducing greenhouse gases. This paper focuses on the question of whether individuals in industrialized countries have duties to (...) reduce their individual carbon footprint. To this end it will examine three kinds of arguments that have been brought forward against individuals having such duties: the view that individual emissions cause no harm; the view that individual mitigation efforts would have no morally significant effect; and the view that lifestyle changes would be overly-demanding. The paper shows how all three arguments fail to convince. While collective endeavours may be most efficient and effective in bringing about significant changes, there are still good reasons to contribute individually to reducing emission. After all, for most people the choice is between reducing one’s individual emissions and not doing anything. The author hopes this paper shows that one should not opt for the latter. (shrink)

Many believe that we ought to save a large number from being permanently bedridden rather than save one from death. Many also believe that we ought to save one from death rather than a multitude from a very minor harm, no matter how large this multitude. I argue that a principle I call “Aggregate Relevant Claims” satisfactorily explains these judgments. I offer a rationale for this principle and defend it against objections.

I argue that a crucial point has been overlooked in the debate over the “numbers problem.” The initial arrangement of parties in the problem can be thought of as chancy, and whatever considerations of fairness recommend the reliance on something like a coin toss in approaching this problem equally recommend treating the initial distribution as a kind of lottery. This fact, I suggest, undermines one of the principal arguments against saving the greater number.

Is there some large number of very mild hangnail pains, each experienced by a separate person, which would be worse than two years of excruciating torture, experienced by a single person? Many people have the intuition that the answer to this question is No. However, a host of philosophers have argued that, because we have no intuitive grasp of very large numbers, we should not trust such intuitions. I argue that there is decent intuitive support for the No answer, which (...) does not depend on our intuitively grasping or imagining very large numbers. (shrink)

With the rapidly growing amounts of information, visualization is becoming increasingly important, as it allows users to easily explore and understand large amounts of information. However the field of information visualiza- tion currently lacks sufficient theoretical foundations. This article addresses foundational questions connecting information visualization with computing and philosophy studies. The idea of multiscale information granula- tion is described based on two fundamental concepts: information (structure) and computation (process). A new information processing paradigm of Granular Computing enables stepwise increase of (...) granulation/aggregation of information on different levels of resolution, which makes possible dynamical viewing of data. Information produced by Google Earth is an illustration of visualization based on clustering (granulation) of information on a succession of layers. Depending on level, specific emergent properties become visible as a result of different ways of aggregation of data/information. As information visualization ultimately aims at amplifying cognition, we discuss the process of simulation and emulation in relation to cognition, and in particular visual cognition. (shrink)

The aim of this paper is to discuss the plausibility of a certain position in the philosophical literature within which the Repugnant Conclusion is treated, not as repugnant, but as an acceptable implication of the total welfare principle. I will confine myself to focus primarily on Törbjörn Tännsjö’s presentation. First, I reconstruct Tännsjö’s view concerning the repugnance of the RC in two arguments. The first argument is criticized for (a) addressing the wrong comparison, (b) relying on the controversial claim that (...) the privileged people in our actual world only have lives barely worth living and (c) that Tännsjö’s identification between Z-lives and privileged lives is restricted to certain versions of the notion ‘barely worth living’ – a restriction that weakens the force of the argument. The second argument is criticized because some of it premises entailed (b) and (d) for its implausible claim that non-imaginable outcomes cannot be compared. (shrink)

How many people should there be? Can there be overpopulation: too many people living? I shall present a puzzling argument about these questions, show how this argument can be strengthened, then sketch a possible reply.

Abstract Tom Dougherty observes that challenges to counting the numbers often cite John Taurek’s 1977 article, “Should the Numbers Count.” Dougherty, though sympathetic to Taurek’s (and others) critique of consequentialism’s aggregating good across individuals, defends a non-consequentialist principle for addition he calls “the Ends Principle. Take the case (he labels “Drug”) when an agent, possessing a dose of a lifesaving drug, can save one person with the entire dose, or two people, each of whom only need half the dose. Dougherty (...) argues that a rational agent, summing her altruistic goals (three), but unable to save all three, will save two. I give two criticisms of Dougherty’s paper. (1) He hasn’t ruled out, though acknowledging, the equal chance principle as deontological grounds for deciding Drug. (2) An agent using the Ends Principle in Drug, as he formulates it, will not have the requisite aims to make use of the Principle. I also consider an issue, little discussed, the conditions for aggregation in general. (shrink)

This article applies the tools of experimental philosophy to the ongoing debate about both the theoretical viability and the practical import of partially aggregative moral theories in distributive ethics. We conduct a series of three experiments (N=383): First, we document the widespread occurrence of the intuitions that motivate this position. Our study then moves beyond establishing the existence of partially aggregative intuitions in two dimensions: First, we extend experimental work in such a way as to ascertain which amongst existing versions (...) of partial aggregation (localised vs. global) chimes more fully with moral common sense. Specifically, we document how, in tie-breaking cases, ‘irrelevant goods’ judgments (Kamm) are just as robust as the original aggregative/non-aggregative pair of judgments that constitute partial aggregation. Second, by pairing laypeople’s moral judgments in standard cases with their intuitions about the limits of permissible self-prioritisation, we investigate whether one prominent explanation of why irrelevant claims may not be aggregated (Voorhoeve’s ‘personal prerogative’ argument) can be said to underpin people’s intuitions about the (ir)relevance relation of claims in conflict cases. We close with a discussion of our findings’ practical and theoretical import and highlight avenues for future research. (shrink)