Classical inequality indices, welfare functions, and the dual decomposition

We consider the classical inequality measures due to Gini, Bonferroni, and De Vergottini and we present a brief review of the three inequality indices and the associated welfare functions, in the correspondence scheme introduced by Blackorby and Donaldson, and Weymark. The three classical inequality indices incorporate different value judgments in the measurement of inequality, leading to different behavior under income transfers between individuals in the population. The welfare functions associated with the Gini, Bonferroni, and (normalized) De Vergottini indices are Schur-concave OWA functions, with larger weights for lower incomes. We examine the dual decomposition and the orness degree of the three welfare functions in the standard framework of aggregation functions on the [0; 1]n domain, and show that it offers interesting insight on the distinct and complementary nature of the classical inequality indices.