Inequality, welfare and order statistics

Abstract

In this paper we use the distributions of order statistics to define functions with the appropriate properties and represent social preferences regarding income distributions. Following the approach of Yaari (1987, 1988), this allows constructing a set of social welfare functions from which the corresponding inequality indices are derived. The obtained measures incorporate diverse normative criteria, with different degrees of preference for equality. The generalized Gini coefficients and the family of indices proposed in Aaberge (2000) are obtained as particular cases. This approach shows that each of these families of indices characterizes the income distribution, but for a change of scale.