Pair-Based Decomposable Inequality Measures

Abstract

Four axioms are introduced in order to characterize the family of pair-based decomposable inequality measures, which is embraced in the class of weakly decomposable inequality measures. Three axioms, namely, normalization by pairs, aggregation by pairs, and decomposition by pairs enable the pair-based family of inequality measures to be deduced and to be decomposed into within- and between-group components. The weights of population shares that bring out those within- and between-group estimators have the particularity to be unique and to sum to unity. By invoking the fourth axiom of symmetry by pairs, it is proved that pair-based inequality measures and their two decomposed components are U-statistics, so that, statistical information may be inferred.