We investigate the issue of aggregativity in fair division problems from the perspective of cooperative game theory and Broomean theories of fairness. Paseau and Saunders proved that no non-trivial theory of fairness can be aggregative and conclude that theories of fairness are therefore problematic, or at least incomplete. We observe that there are theories of fairness, particularly those that are based on cooperative game theory, that do not face the problem of non-aggregativity. We use this observation to argue that the (...) universal claim that no non-trivial theory of fairness can guarantee aggregativity is false. Paseau and Saunders’s mistaken assertion can be understood as arising from a neglect of the games approach to fair division. Our treatment has two further pay-offs: for one, we give an accessible introduction to the games approach to fair division, whose significance has hitherto not been appreciated by philosophers working on fairness. For another, our discussion explores the issue of aggregativity in fair division problems in a comprehensive fashion. (shrink)

In the article ‘How to be absolutely fair, Part I: the Fairness formula’, we presented the first theory of comparative and absolute fairness. Here, we relate the implications of our Fairness formula to economic theories of fair division. Our analysis makes contributions to both philosophy and economics: to the philosophical literature, we add an axiomatic discussion of proportionality and fairness. To the economic literature, we add an appealing normative theory of absolute and comparative fairness that can be used to evaluate (...) axioms and division rules. Also, we provide a novel definition and characterization of the absolute priority rule. (shrink)

We present the first comprehensive theory of fairness that conceives of fairness as having two dimensions: a comparative and an absolute one. The comparative dimension of fairness has traditionally been the main interest of Broomean fairness theories. It has been analysed as satisfying competing individual claims in proportion to their respective strengths. And yet, many key contributors to Broomean fairness agree that ‘absolute’ fairness is important as well. We make this concern precise by introducing the Fairness formula and the absolute (...) priority rule and analyse their implications for comparative fairness. (shrink)

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If deployed, aerosol geoengineering (AG) could involve unfairness to both present and future parties. I discuss three broad risks of unfairness that an AG deployment policy might carry: (1) causing disproportionate harm to those least responsible for climate change, (2) burdening future parties with the costs and risks of AG, and (3) excluding some interested parties from contributing to AG decision-making. Yet despite these risks, it may be too hasty to reject AG deployment as a potential climate change policy. I (...) argue that since it is very unlikely that a completely fair climate change policy will be pursued, we have ethical reason to prefer some “incompletely fair” policy. Given various facts about our world, it might be the case that some AG policy is ethically preferable to many other feasible climate change policies, even if AG carries deeply problematic risks of unfairness. (shrink)

Many philosophers think that we should use a lottery to decide who gets a good to which two persons have an equal claim but which only one person can get. Some philosophers think that we should save identified persons from harm even at the expense of saving a somewhat greater number of statistical persons from the same harm. I defend a principled way of justifying both judgements, namely, by appealing to the decreasing marginal moral value of survival chances. I identify (...) four desiderata that, I contend, any such justification should satisfy, and explain how my account meets these desiderata, unlike some previous accounts. (shrink)

In this article I am concerned with reasoning about matters of justice. There is no doubt that justice-reasoning is a significant mode of ethical reasoning and its importance is therefore generally accepted. But there is a considerable debate concerning the role formal justice can play in reasoning about justice. In this paper, I first provide an analysis of formal justice. I then show that the concept of formal justice is identical to one notion of fairness and I illustrate the function (...) of formal justice in reasoning about issues of fairness. In the third section, I argue that formal justice is an essential component of justice tout court and I demonstrate its value for understanding and assessing reasoning about matters of justice. The overall result of this investigation is that formal justice is an important notion that has a special function in moral thinking, which has not been sufficiently appreciated in the literature. (shrink)

John Broome has proposed a theory of fairness according to which fairness requires that agents’ claims to goods be satisfied in proportion to the relative strength of those claims. In the case of competing claims for a single indivisible good, Broome argues that what fairness requires is the use of a weighted lottery as a surrogate to satisfying the competing claims: the relative chance of each claimant's winning the lottery should be set to the relative strength of each claimant's claim. (...) In this journal, James Kirkpatrick and Nick Eastwood have objected that the use of weighted lotteries in the case of indivisible goods is unacceptable. In this article, I explain why Kirkpatrick and Eastwood's objection misses its mark. (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)

The paper considers a hierarchical theory that combines concern for two values: individual well-being – as a fundamental, first-order value – and (distributive) fairness – as a high-order value that its exclusive function is to complete the value of individual well-being by resolving internal clashes within it that occur in interpersonal conflicts. The argument for this unique conception of high-order fairness is that fairness is morally significant in itself only regarding what matters – individual well-being – and when it matters (...) – in interpersonal conflicts in which constitutive aspects of individual well-being clash. Consequently, the proposed theory is not exposed to claim that fairness comes at the expense of welfare. This theory is considered within a consequential framework, based on the standard version and, alternatively, on a novel interpretation of consequentialism. Thus, it refutes the claim that consequentialism does not take the distinction between persons seriously. (shrink)

Fairness is a central, but under-theorized, notion in moral and political philosophy. This paper makes two contributions. Firstly, it criticizes Broome’s seminal account of fairness in Proc Aristotelian Soc 91:87–101, showing that there are problems with restricting fairness to a matter of relative satisfaction and holding that it does not itself require the satisfaction of the claims in question. Secondly, it considers the justification of lotteries to resolve cases of ties between competing claims, which Broome claims as support for his (...) theory, and contrasts random procedures to contests of skill, which may also be considered lotteries in a broader sense. I offer no alternative account of fairness of my own, but hope to point the way for future research on the nature of fairness. (shrink)

The three most common responses to Taurek’s ‘numbers problem’ are saving the greater number, equal chance lotteries and weighted lotteries. Weighted lotteries have perhaps received the least support, having been criticized by Scanlon What We Owe to Each Other ( 1998 ) and Hirose ‘Fairness in Life and Death Cases’ ( 2007 ). This article considers these objections in turn, and argues that they do not succeed in refuting the fairness of a weighted lottery, which remains a potential solution to (...) cases of conflict. Moreover, it shows how these responses actually lead to a new argument for weighted lotteries, appealing to fairness and Pareto-optimality. (shrink)

Penicillin is a serendipitous discovery par excellence. But, what does this say about Alexander Fleming’s praiseworthiness? Clearly, Fleming would not have received the Nobel Prize, had not a mould accidently entered his laboratory. This seems paradoxical, since it was beyond his control. The present article will first discuss Fleming’s discovery of Penicillin as an example of moral luck in science and technology and critically assess some common responses to this problem. Second, the Control Principle that says that people are not (...) responsible for things beyond their control will be defended. An implication of this principle is that Alexander Fleming’s desert, which is based on his epistemic skills, remains untouched by luck. Third, by distinguishing different notions of praiseworthiness, a way to resolve the paradox of moral luck will be elaborated. Desert provides only a pro tanto reason to determine whether someone is an appropriate addressee of reward. Here, luck can make a difference. Forth, it will be argued that stimulating the quest for socially beneficial science provides a compelling reason to treat scientists with equal desert differently. Penicillin provides striking evidence for the importance of this quest and showcasing it incentivizes the making of socially beneficial science. Ultimately, it will be justified why Fleming deserved the Nobel Prize in at least one sense of the concept. (shrink)

One rationale policy-makers sometimes give for declining to fund a service or intervention is on the grounds that it would be ‘unaffordable’, which is to say, that the total cost of providing the service or intervention for all eligible recipients would exceed the budget limit. But does the mere fact that a service or intervention is unaffordable present a reason not to fund it? Thus far, the philosophical literature has remained largely silent on this issue. However, in this article, we (...) consider this kind of thinking in depth. Albeit with certain important caveats, we argue that the use of affordability criteria in matters of public financing commits what Parfit might have called a ‘mistake in moral mathematics’. First, it fails to abide by what we term a principle of ‘non-perfectionism’ in moral action: the mere fact that it is practically impossible for you to do all the good that you have reason to do does not present a reason not to do whatever good you can do. And second, when used as a means of arbitrating between which services to fund, affordability criteria can lead to a kind of ‘numerical discrimination’. Various attendant issues around fairness and lotteries are also discussed. (shrink)

When faced with multiple claims to a particular good, what does distributive justice require? To answer this question, we need a substantive moral theory that will enable us assign relative moral weights to the parties' claims. But this is not all we need. Once we have assessed the moral weight of each party's claim, we still need to decide what method of distribution to employ, for there are two methods open to us. We could take the winner-take-all approach, and award (...) the good to the party with the strongest claim. On the other hand, we could divide the good proportionally, according to the relative strength of each party's claim. Because the choice between these two methods of distribution can have a dramatic impact on the resulting pattern of distribution, the choice presents a question of justice. But this is a question of justice that is often overlooked. As a result, we currently employ the principle of proportionality far less often than justice actually requires. If we focus on the question of distributive method, however, we are not only better able to understand how certain reasons enter into our all-things-considered moral judgments, we are also able to explain some perplexing but common aspects of our moral beliefs: how rights can be said to have peremptory force, yet still be balanced against other important interests; how justice can sometimes require compromise, yet sometimes require victory; and how a moral theory can avoid being too demanding while still being demanding enough. Key Words: autonomy • equality • indivisibility • inviolability • weighted lotteries • rights. (shrink)

This paper argues that close personal relationships play an important role in our judgments about what is fair. I start with an explanation of leading theories of fairness, highlighting the potential for further work on the grounds of fairness. Next, I offer an account of close personal relationships as having the ability to generate legitimate and reasonable expectations of one or other party to a judgment about fairness, or both. I show how and when close personal relationships can ground fairness.

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)

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)

We confront the philosophical literature on fair division problems with axiomatic and game-theoretic work in economics. Firstly, we show that the proportionality method advocated in Curtis is not implied by a general principle of fairness, and that the proportional rule cannot be explicated axiomatically from that very principle. Secondly, we suggest that Broome’s notion of claims is too restrictive and that game-theoretic approaches can rectify this shortcoming. More generally, we argue that axiomatic and game-theoretic work in economics is an indispensable (...) ingredient of any theorizing about fair division problems and allocative justice. (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)

The application of machine-learning technologies to medical practice promises to enhance the capabilities of healthcare professionals in the assessment, diagnosis, and treatment, of medical conditions. However, there is growing concern that algorithmic bias may perpetuate or exacerbate existing health inequalities. Hence, it matters that we make precise the different respects in which algorithmic bias can arise in medicine, and also make clear the normative relevance of these different kinds of algorithmic bias for broader questions about justice and fairness in healthcare. (...) In this paper, we provide the building blocks for an account of algorithmic bias and its normative relevance in medicine. (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)

In this article I present a theory of what it is to be fair. I take my cue from Broome’s well known 1990 account of fairness. Broome’s basic thesis is that fairness is the proportional satisfaction of claims, and with this I am in at least partial agreement. But neither Broome nor anyone else (so far as I know) has laid down a theory of precisely what one must do in order to be fair. The theory offered here does just (...) this. (shrink)

A number of findings in the field of machine learning have given rise to questions about what it means for automated scoring- or decisionmaking systems to be fair. One center of gravity in this discussion is whether such systems ought to satisfy classification parity (which requires parity in accuracy across groups, defined by protected attributes) or calibration (which requires similar predictions to have similar meanings across groups, defined by protected attributes). Central to this discussion are impossibility results, owed to Kleinberg (...) et al. (2016), Chouldechova (2017), and Corbett-Davies et al. (2017), which show that classification parity and calibration are often incompatible. This paper aims to argue that classification parity, calibration, and a newer, interesting measure called counterfactual fairness are unsatisfactory measures of fairness, offer a general diagnosis of the failure of these measures, and sketch an alternative approach to understanding fairness in machine learning. (shrink)

In this paper I criticize the standard argument for deontological egalitarianism, understood as the thesis that there is a moral claim to have an equal share of well-being or whatever other good counts. That argument is based on the idea that equals should be treated equally. I connect the debate over egalitarianism with that over comparative justice. A common theme is a general skepticism against comparative claims. I argue (i) that there can be no claim to equality based simply on (...) the fact of equal worth as that fact itself does not have any value for the supposed claim holder; and (ii) intuitions that suggest otherwise can be explained away without appealing to comparative claims. (shrink)

In this thesis, I discuss the aggregation problem for T. M. Scanlon’s “contractualism”. I argue that Scanlonian contractualists have the following two options when it comes to the aggregation problem. First, they can choose to limit aggregation directly via a specific version of the Relevance View, “Sequential Claims-Matching”. Second, Scanlonian contractualists can adopt a so-called “mixed solution” of which I propose a specific version. My mixed solution does not limit aggregation. Rather, it either avoids some of the counterintuitive results in (...) certain cases, or at least makes these same results look a lot less counterintuitive by putting them into perspective thanks to a plausible plurality of precisely specified values. The stakes between these two options are as follows. The first option justifies Scanlon’s intuition in one vs. many cases of which his “World Cup Case” is one example, but it comes at the cost of a seemingly quite limited range of application: any version of the Relevance View only works in cases in which we have no more than two groups of competing claimants. The second option has the exact opposite implications: my mixed solution cannot justify Scanlon’s intuition in one vs. many cases, but it could be applied to any case with any number of groups of competing claimants. In this choice between pre-theoretical intuition and feasibility, I would urge Scanlonian contractualists to choose feasibility. (shrink)