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Fairness and Aggregation

Published online by Cambridge University Press:  08 June 2015

A. C. PASEAU  and
BEN SAUNDERS
A. C. PASEAU
Affiliation:
Wadham College, Oxford, [email protected]
BEN SAUNDERS
Affiliation:
University of Southampton, [email protected]
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Abstract

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 (proportionality and shortfall minimization) 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.

Type
Research Article
Information
Utilitas , Volume 27 , Issue 4 , December 2015 , pp. 460 - 469
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Copyright
Copyright © Cambridge University Press 2015 

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References

1 E.g. Geoffrey Cupit, ‘Fairness, by Nicholas Rescher [book review]’, Mind 113 (2002), pp. 387–90, at 389.

2 E.g. Brams, Steven J. and Taylor, Alan D., Fair Division: From Cake-cutting to Dispute Resolution (Cambridge, 1996).CrossRefGoogle Scholar

3 A seminal paper on the bankruptcy (or conflicting claim) problem is Aumann, R. and Maschler, M., ‘Game Theoretic Analysis of a Bankruptcy Problem from the Talmud’, Journal of Economic Theory 36 (1985), pp. 195–213.CrossRefGoogle Scholar For a survey of the ensuing literature, see Thomson, W., ‘Axiomatic and Game-theoretic Analysis of Bankruptcy and Taxation Problems: A Survey’, Mathematical Social Sciences 45 (2003), pp. 249–97.CrossRefGoogle Scholar

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8 Broome, ‘Fairness’, p. 93.

9 Shortfall minimization is discussed in Nicholas Rescher, Fairness (New Brunswick, NJ, 2002), pp. 52–3, and endorsed by Cupit, ‘Fairness [review]’.

10 Broome, ‘Fairness’, p. 95.

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13 The authors share authorship and credit equally for this work. A predecessor of this article was presented at the Universities of Stirling (September 2012), St Andrews (September 2012) and Oxford (January 2013). The authors thank these audiences, along with John Broome, Hugo Dixon, Hugh Lazenby, Patrick Tomlin and two anonymous referees for the journal for their comments.