Published online by Cambridge University Press: 08 June 2015
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.
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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.