Axiomatic characterization of the Gini coefficient and Lorenz curve orderings

Abstract

This paper is concerned with distributions of income and the ordering of related Lorenz curves. By introducing appropriate preference relations on the set of Lorenz curves, two alternative axiomatic characterizations of Lorenz curve orderings are proposed. Moreover, the Gini coefficient is recognized to be rationalizable under both axiom sets; as a result, a complete axiomatic characterization of the Gini coefficient is obtained. Furthermore, axiomatic characterizations of the extended Gini family and an alternative "generalized" Gini family of inequality measures are proposed