How to be fairer

Abstract

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 (in Analysis 74:417-57, 2014) 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 (in Proc Aristot Soc 91:87-101, 1990) 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.

Dividing the indivisible

“…Hence, calling the structures of Definition 1 claims problems is convenient as it makes explicit that Curtis’ philosophical theory of fairness applies to problems that have been studied extensively in the economic literature. Actually, the results obtained in this literature have bearing on Curtis’ arguments as to why fairness requires us to adopt method P and L , as we argue in Heilmann and Wintein (2015). 4…”

Theories of Fairness and Aggregation

“…What should a ''Broomean fairness theorist'', who is sympathetic to the slogan that fairness consists of the proportional satisfaction of claims, do in such a context? See Wintein and Heilmann (2018) for an elaborate answer to that question.. 14 See Proposition 4 of Heilmann and Wintein (2017) 15 See Heilmann and Wintein (2017) for a detailed discussion of the relation between fairness and proportionality on the games approach Theorem 2 testifies that the Shapley value is aggregative. Hence Paseau and Saunders's assertion of NAT-there are no aggregative theories of fairness-is false.…”

“…2.3, that the games approach has a scope that is at least as broad as the claims approach: any fair division problem that can be analysed as a claims problem can also be analysed as a cooperative game. In (Heilmann and Wintein 2017) however, we show that there are fair division problems that cannot be properly analysed using the claims approach whereas they are naturally represented as cooperative games. Hence, the games approach to fairness has a scope that is strictly broader than that of the claims approach, which may be a reason to favour the former over the latter.…”

“…But Saul may wonder whether there are there further reasons for, or against, trading in the claims for the games approach to fairness. The best advice we can give Saul at this point is to read (Heilmann and Wintein 2017), where the trade-off between the claims and games approach is discussed in detail. Here, we can only mention two important considerations that we think Saul should be aware of.…”

“…Indeed, her choice to adopt a particular approach may be dependent on the nature of the fair division problem at hand. See Heilmann and Wintein (2017) for more details.…”