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)

Why should a lottery be used in the allocation of an indivisible good to which participants in the lottery have an equally strong claim? Stone argues that when indeterminacy arises, in which it is impossible to satisfy the equality condition requiring like cases to be treated alike, the impartiality principle suggests that the agent responsible for the allocation task should not intend to favor one over another on the basis of invalid reasons. In this article, I argue that the impartiality (...) principle is neither sufficient nor necessary to explain the fairness of lotteries. Instead, the fairness of lotteries is explained by the sanitizing effect that lotteries generate to screen out the reactive attitudes of resentment and indignation that claimants might otherwise have if they do not obtain the good in question. (shrink)

Many goods are distributed by processes that involve randomness. In lotteries, randomness is used to promote fairness. When taking social risks, randomness is a feature of the process. The losers of such decisions ought to be given a reason why they should accept the outcome. Surprisingly, good reasons demand more than merely equalex antechances. What is also required is a true statement of the form: ‘the result could easily have gone the other way and you could have been the winner’. (...) This rules in standard lotteries but rules out many lotteries based on merely epistemic probability. (shrink)

According to a common view, in a case involving an indivisible good and several potential beneficiaries, who are equal in every relevant respect, there is a non-instrumental reason to allocate the benefit in a way that gives each an equal chance to receive the benefit. In this paper, I argue that this view is incompatible with several plausible and widely held assumptions. I emphasize especially the assumption that the distributive role of chances is secondary to that of benefits in an (...) important sense: the value of allocating chances is related to the ways in which it is possible to allocate the relevant benefits. Specifically, chances should be allocated only when it is impossible or too costly to allocate benefits in accordance with the relative importance of the reasons in favor of allocating the relevant benefit to each potential beneficiary. Given this assumption, I argue that the fact that there is no relation between the distributive concern for chances and other distributive concerns suggests that we should reject the view that chances have a distributive role that is not merely instrumental. (shrink)

According to the Competing Claims View we decide between alternatives by looking at the competing claims held by affected individuals. The strength of these claims is a function of two features: how much they stand to benefit by each alternative, and how badly off they would be in its absence. The view can be, and is, endorsed by both egalitarians and prioritarians. For the former the second condition will concern looking at how badly off the person is relative to others, (...) whereas for the latter it will be how badly off she is in absolute terms. In this paper I want to argue that neither should be endorsed. The egalitarian version of CCV breaks down when attempting to assess the competing claims of possible persons who may never exist. Also, the view, on at least one plausible interpretation, leads to intransitive judgements. The prioritarian version of CCV, in turn, is vulnerable to its own unique objection, namely delivering an anti-prioritarian and rather implausible verdict in certain Single Person Cases. (shrink)

In recent years, many non-consequentialists such as Frances Kamm and Thomas Scanlon have been puzzling over what has come to be known as the Number Problem, which is how to show that the greater number in a rescue situation should be saved without aggregating the claims of the many, a typical kind of consequentialist move that seems to violate the separateness of persons. In this article, I argue that these non-consequentialists may be making the task more difficult than necessary, because (...) allowing aggregation does not prevent one from being a non-consequentialist. I shall explain how a non-consequentialist can still respect the separateness of persons while allowing for aggregation. (shrink)

Suppose that you are trying to pursue a morally worthy goal, but cannot do so without incurring some moral costs. At the outset, you believed that achieving your goal was worth no more than a given moral cost. And suppose that, time having passed, you have wrought only harm and injustice, without advancing your cause. You can now reflect on whether to continue. Your goal is within reach. What's more, you believe you can achieve it by incurring—from this point forward—no (...) more cost than it warranted at the outset. If you now succeed, the total cost will exceed the upper bound marked at the beginning. But the additional cost from this point is below that upper bound. And the good you will achieve is undiminished. How do the moral costs you have already inflicted bear upon your decision now? (shrink)

John Broome argues that when all claims cannot be perfectly fairly satisfied in outcome, the contribution to fairness from entering claims into a lottery, and so providing them some surrogate satisfaction, ought to be weighed against, and can outweigh, what fairness can be achieved directly in outcome. I argue that this is a mistake. Instead, I suggest that any contribution to fairness from entering claims into a lottery is lexically posterior to fairness in outcome.

Waiting time is widely used in health and social policy to make resource allocation decisions, yet no general account of the moral significance of waiting time exists. We provide such an account. We argue that waiting time is not intrinsically morally significant, and that the first person in a queue for a resource does not ipso facto have a right to receive that resource first. However, waiting time can and sometimes should play a role in justifying allocation decisions. First, there (...) is a duty of fairness prohibiting line-cutting where a sufficiently just queue exists. Second, waiting time has several morally attractive features that can justify its incorporation into allocation schemes. Where candidates are in relevantly similar circumstances, allocating by waiting time is relatively efficient, maximizes distribution equality relative to other Pareto efficient distributions, and treats candidates fairly. The claim that allocation using waiting time is fair is controversial. Some have claimed that formal lotteries are a fairer way to select among equal beneficiaries. We argue that lotteries are no fairer than allocation based on waiting time when it is equiprobable how a prospective queue will be ordered. In practice, lotteries share many of the disadvantages of queues; which is fairer will depend on contingent features of the allocation scenario. The upshot is that first-come, first-served is in fact a just way to allocate resources in many of the cases where it seems pre-theoretically compelling, and waiting time has unique normative properties which frequently justify its incorporation into resource allocation schemes. (shrink)

Fair priority setting is based on morally sound criteria. Still, there will be cases when these criteria, our primary considerations, are tied and therefore do not help us in choosing one allocation over another. It is sometimes suggested that such cases can be handled by tiebreakers. In this paper, we discuss two versions of tiebreakers suggested in the literature. One version is to preserve fairness or impartiality by holding a lottery. The other version is to allow secondary considerations, considerations that (...) are not part of our primary priority setting criteria, to be decisive. We argue that the argument for preserving impartiality by holding a lottery is sound, while the argument for using tiebreakers as secondary considerations is not. Finally, we argue that the instances where a tiebreaker seems necessary are precisely the situations where we have strong reasons for preferring a lottery. We conclude that factors that we consider valuable should all be included among the primary considerations, while ties should be settled by lotteries. (shrink)

Luck egalitarians claim that disadvantage is worse when it emerges from an unchosen risk than when it emerges from a chosen risk. I argue that disadvantage is also worse when it emerges from an unchosen risk that the disadvantaged agent would have declined to take, had he or she been able to do so, than when it emerges from an unchosen risk that the disadvantaged agent would not have declined to take. Such a view is significant because it allows both (...) luck egalitarians and prioritarians to respond to Voorhoeve and Fleurbaey's charge that they fail to accommodate intuitions about the moral relevance of interpersonal boundaries – the so-called separateness of persons objection. I argue that the view is plausible independently of its ability to answer the separateness of persons objection, and is a natural extension of the luck egalitarian concern with the impact of unchosen circumstance. (shrink)

I defend a weak version of the Pigou-Dalton principle for chances. The principle says that it is better to increase the survival chance of a person who is more likely to die rather than a person who is less likely to die, assuming that the two people do not differ in any other morally relevant respect. The principle justifies plausible moral judgements that standard ex post views, such as prioritarianism and rank-dependent egalitarianism, cannot accommodate. However, the principle can be justified (...) by the same reasoning that has recently been used to defend the core axiom of ex post prioritarianism and egalitarianism, namely, Pigou-Dalton for well-being. The arguably biggest challenge for proponents of Pigou-Dalton for chances is that it violates State Dominance for social prospects. However, I argue that we have independent reason for rejecting State Dominance for social prospects, since it prevents a social planner from properly respecting people's preferences. (shrink)

With the increasing use of algorithms in high-stakes areas such as criminal justice and health has come a significant concern about the fairness of prediction-based decision procedures. In this article I argue that a prominent class of mathematically incompatible performance parity criteria can all be understood as applications of John Broome’s account of fairness as the proportional satisfaction of claims. On this interpretation these criteria do not disagree on what it means for an algorithm to be _fair_. Rather they express (...) different understandings of what grounds a claim to a good being allocated by an algorithmic decision procedure. I then argue that an important implication of the Broomean interpretation is that it strengthens the case for outcome-based criteria. Finally, I consider how a version of the levelling-down objection to performance parity criteria arises within the Broomean account. (shrink)

The move from open outcry to electronic trading added another responsibility to futures exchanges—that of matching orders between buyers and sellers. Matching systems can affect the level and speed of price discovery, the distribution of revenue, as well as the level of price efficiency of a given market. Whether the matching system is procedurally fair is another important consideration. I argue that while FIFO (First In First Out) is a fair procedure in principle and is perceived as the default matching (...) system, it is not a fair procedure in practice. Likewise, while pro rata is a fair procedure in principle, it is not so in practice. Nevertheless, both FIFO and pro rata are relics of an open outcry system. Instead, I propose an alternative approach to matching systems that builds on the strengths of electronic trading—the ability to randomize in real time. I introduce random selection for service (RSS) as a matching system that is procedurally fair both in principle and in practice. (shrink)

Many authors in ethics, economics, and political science endorse the Lottery Requirement, that is, the following thesis: where different parties have equal moral claims to one indivisible good, it is morally obligatory to let a fair lottery decide which party is to receive the good. This article defends skepticism about the Lottery Requirement. It distinguishes three broad strategies of defending such a requirement: the surrogate satisfaction account, the procedural account, and the ideal consent account, and argues that none of these (...) strategies succeed. The article then discusses and discharges some remaining grounds for resistance to these skeptical conclusions, as well as the possibility of defending a weaker version of a normative lottery principle. The conclusion is that we have no reason to believe that where equal claims conflict, we are morally required to hold a lottery, as opposed to simply picking one of the parties on more subjective grounds or out of pure whim. In addition to the practical consequences of this skeptical view, the article sketches some theoretical implications for debates about saving the greater number and about axiomatic utilitarianism. (shrink)

Philosophical theories of fairness propose to divide a good that several individuals have a claim to in proportion to the strength of their respective claims. We suggest that currently, these theories face a dilemma when dealing with a good that is indivisible. On the one hand, theories of fairness that use weighted lotteries are either of limited applicability or fall prey to an objection by Brad Hooker. On the other hand, accounts that do without weighted lotteries fall prey to three (...) fairness paradoxes. We demonstrate that division methods from apportionment theory, which has hitherto been ignored by philosophical theories of fairness, can be used to provide fair division for indivisible goods without weighted lotteries and without fairness paradoxes. (shrink)

In the recent literature across philosophy, medicine and public health policy, many influential arguments have been put forward to support the use of randomization procedures to allocate scarce life-saving resources. In this paper, I provide a systematic categorization and a critical evaluation of these arguments. I shall argue that those arguments justify using RAND to allocate SLSR in fewer cases than their proponents maintain and that the relevant decision-makers should typically allocate SLSR directly to the individuals with the strongest claims (...) to these resources rather than use RAND to allocate such resources. (shrink)

The difference between the unity of the individual and the separateness of persons requires that there be a shift in the moral weight that we accord to changes in utility when we move from making intrapersonal tradeoffs to making interpersonal tradeoffs. We examine which forms of egalitarianism can, and which cannot, account for this shift. We argue that a form of egalitarianism which is concerned only with the extent of outcome inequality cannot account for this shift. We also argue that (...) a view which is concerned with both outcome inequality and with the unfairness of inequality in individuals‘ expected utilities can account for this shift. Finally, we limn an alternative view, on.. (shrink)

Many oppose the use of profile evidence against defendants at trial, even when the statistical correlations are reliable and the jury is free from prejudice. The literature has struggled to justify this opposition. We argue that admitting profile evidence is objectionable because it violates what we call “equal protection”—that is, a right of innocent defendants not to be exposed to higher ex ante risks of mistaken conviction compared to other innocent defendants facing similar charges. We also show why admitting other (...) forms of evidence, such as eyewitness, trace, and motive evidence, does not violate equal protection. (shrink)

When there are equally strong claimants for a scarce good, lotteries are often argued to be a fair method of allocation. This paper reproduces four of the views on the fairness of lotteries that have been presented in the literature: the distributive view; the preference view; the actual consent view; and the expressive view. It argues that these four views cannot offer plausible explanations for the fairness of lotteries. The distributive view is argued to be inadequate because, even though receiving (...) expectations to a good is of value to the participants, this value cannot plausibly make a contribution to the satisfaction of a participant’s claim. Both the preference and actual consent views are argued to be implausible because they lead to accepting procedures as legitimate that fail to correspond with what a claim is. Finally, it is contended that the expressive view identifies a value that is relevant to respecting equal claimants, but that cannot plausibly be related to a procedure’s fairness. The paper concludes by maintaining that an equal treatment view can accept all the valid insights from these four views without needing to accept their untenable implications. (shrink)

This thesis is about the moral reasons we have to do less than best. It consists of six chapters. Part I of the thesis proposes, extends, and defends reasons to do less than best. In Chapter One (“The Conditional Obligation”) I outline and reject two recent arguments from Joe Horton and Theron Pummer for the claim that we have a conditional obligation to bring about the most good. In Chapter Two (“Agglomeration and Agent-Relative Costs”) I argue that agent-relative costs can (...) justify permissions to less than best in a far greater range of decisions contexts than we currently believe. In Chapter Three (“Risk and Aggregation”) I discuss how anti-aggregative moral theories deal with risk, whilst proposing an argument in favour of ex-post moral theories. -/- In Part II of the thesis, I discuss longtermism, presenting a series of reasons to believe we have both significant permissions and obligations to prioritise those in the short-term. In Chapter Four (“Listening to Future People”) I criticise a recent argument presented by Andreas Mogensen for the claim we cannot have obligations grounded in the wellbeing of future people. I then show that, even permitting the existence of obligations to future people, we still have significant reasons to resist longtermism on the grounds of partiality. In Chapter Five (“The Complaints of Future People”) I argue that scepticism about aggregation is inconsistent with an obligation, or indeed even a permission, to help far future people. In Chapter Six (“Leaving the Present Behind”) I explore the moral significance of “dooming”, whilst arguing that we have a pro tanto reason of fairness to prioritise aiding those currently in existence. (shrink)

A very short, exegetical paper about Taurek's "Should the Numbers Count?," arguing against the view that Taurek requires giving chances.