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.

An allocation rule is ‘consistent’ if the recommendation it makes for each problem ‘agrees’ with the recommendation it makes for each associated reduced problem, obtained by imagining some agents leaving with their assignments. Some authors have described the consistency principle as a ‘fairness principle’. Others have written that it is not about fairness, that it should be seen as an ‘operational principle’. We dispute the particular fairness interpretations that have been offered for consistency, but develop a different and important fairness (...) foundation for the principle, arguing that it can be seen as the result of adding ‘some’ efficiency to a ‘post-application’ and efficiency-free expression of solidarity in response to population changes. We also challenge the interpretations of consistency as an operational principle that have been given, and here identify a sense in which such an interpretation can be supported. We review and assess the other interpretations of the principle, as ‘robustness’, ‘coherence’ and ‘reinforcement’. (shrink)

Perhaps the best-known theory of fairness is John Broome’s: that fairness is the proportional satisfaction of claims. In this article, I question whether claims are the appropriate focus for a theory of fairness, at least as Broome understands them in his current theory. If fairness is the proportionate satisfaction of claims, I argue, then the following would be true: fairness could not help determine the correct distribution of claims; fairness could not be used to evaluate the distribution of claims; fairness (...) could not guide us in distributing claims (or unowed goods); we could not have a claim to be treated fairly; and we would not be wronged when treated unfairly. These entailments mean that it is questionable that fairness is concerned with claims in the way Broome suggests. At the very least, the relationship between fairness and claims appears to be more complex than the picture painted by Broome. (shrink)

John Broome; V*—Fairness, Proceedings of the Aristotelian Society, Volume 91, Issue 1, 1 June 1991, Pages 87–102, https://doi.org/10.1093/aristotelian/91.1.87.

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)

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)

Counting QALYs (quality adjusted life years) has been proposed as a way of deciding how resources should be distributed in the health service: put resources where they will produce the most QALYs. This proposal has encountered strong opposition. There has been a disagreement between some economists favouring QALYs and some philosophers opposing them. But the argument has, I think, mostly been at cross-purposes. Those in favour of QALYs point out what they can do, and those against point out what they (...) can't. There need be no disagreement about this. What is needed is to sort out what is the proper domain of QALYs, and it may be possible to do this amicably. Then we may be able to get on with the more useful job of deciding how well QALYs perform within their domain. In this paper I shall try to accomplish the first task (sections II–IV), and make a start on the second (sections V–VIII). (shrink)

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)

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)

John Broome; V*—Fairness, Proceedings of the Aristotelian Society, Volume 91, Issue 1, 1 June 1991, Pages 87–102, https://doi.org/10.1093/aristotelian/91.1.87.

Sometimes, two unfair distributions cancel out in aggregate. Paradoxically, two distributions each of which is fair in isolation may give rise to aggregate unfairness. When assessing the fairness of distributions, it therefore matters whether we assess transactions piecemeal or focus only on the overall result. This piece illustrates these difficulties for two leading theories of fairness before offering a formal proof that no non-trivial theory guarantees aggregativity. This is not intended as a criticism of any particular theory, but as a (...) datum that must be taken into account in constructing a theory of fairness. (shrink)

This article offers a new theory about how using lotteries to distribute scarce benefits satisfies beneficiaries' claims. In the first section of the article I criticize John Broome's view and on the basis of these criticisms set out four desiderata for a philosophically adequate account of claim satisfaction by lottery. In section II I propose and defend a new view called the dual structure view, so called because it posits that claimants have two types of claims in the relevant scarce (...) benefit distribution cases under discussion. This view meets all the desiderata set out in section I. Section III draws out the practical implications of my view for a variety of temporally extended cases, including the distribution of corneas to patients who have suffered corneal degeneration. (shrink)

John Broome argues that fairness requires that claims are satisfied in proportion to their strength. Broome holds that, when distributing indivisible goods, fairness requires the use of weighted lotteries as a surrogate to satisfy proportionally each candidate's claims. In this article, we present two arguments against Broome's account of fairness. First, we argue that it is almost impossible to calculate the weights of the lotteries in accordance with the requirements of fairness. Second, we argue that Broome rules out those methods (...) whose use might provide some resolution to this problem. From these arguments, we conclude that, contra Broome, fairness does not require the proportional satisfaction of claims. (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)

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)

The main body of this paper assesses a leading recent theory of fairness, a theory put forward by John Broome. I discuss Broome's theory partly because of its prominence and partly because I think it points us in the right direction, even if it takes some missteps. In the course of discussing Broome's theory, I aim to cast light on the relation of fairness to consistency, equality, impartiality, desert, rights, and agreements. Indeed, before I start assessing Broome's theory, I discuss (...) two very popular conceptions of fairness that contrast with his. One of these very popular conceptions identifies fairness with the equal and impartial application of rules. The other identifies fairness with all-things-considered moral rightness. (shrink)

After providing a novel taxonomy of lottery procedures for fairly distributing scarce goods, I defend a new weighted lottery theory. This taxonomy is necessary because the debate between unweighted and weighted lottery theorists overlooks a range of cases, overlap cases, in which conducting an unweighted lottery is impossible or implausible. Therefore, to account for all such cases, lottery theorists must adopt a weighted lottery. However, while no extant weighted lottery is adequate in overlap cases, my new weighted lottery theory is. (...) I conclude by discussing my theory’s practical implications. (shrink)

The main body of this paper assesses a leading recent theory of fairness, a theory put forward by John Broome. I discuss Broome's theory partly because of its prominence and partly because I think it points us in the right direction, even if it takes some missteps. In the course of discussing Broome's theory, I aim to cast light on the relation of fairness to consistency, equality, impartiality, desert, rights, and agreements. Indeed, before I start assessing Broome's theory, I discuss (...) two very popular conceptions of fairness that contrast with his. One of these very popular conceptions identifies fairness with the equal and impartial application of rules. The other identifies fairness with all-things-considered moral rightness. (shrink)