An Inequality Measure for Stochastic Allocations

Few papers in the literature on inequality measurement deal with uncertainty. None, that we know of, provide explicit guidance on how to account for the possibility that a cohort’s rank may not be fixed (e.g., socioeconomic mobility). We present a set of axioms implying such a class of inequality measures under uncertainty that is a one-parameter extension of the Generalized Gini-mean. In particular, our measure can simultaneously accommodate a preference for “shared destiny”, a preference for probabilistic mixtures over unfair allocations, and a preference for fairness “for sure” over fairness in expectation.

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