Inverse stochastic dominance, inequality measurement and Gini index.

We investigate the relationship between the third degree inverse stochastic dominance criterion introduced in Muliere and Scarsini (1989)[A note on stochastic dominance and inequality measures. Journal of Economic Theory, 49, 314-323] and inequality dominance when Lorenz curves intersect. We propose a new definition of transfer sensitivity aimed at strengthening the Pigou-Dalton Principle of Transfers. Our definition is dual to that suggested by Shorrocks and Foster (1987) [Transfer sensitive inequality measures. Review of Economic Studies, 14 , 485-497]. It involves a regressive transfer and a progressive transfer both from the same donor, leaving the Gini index unchanged. We prove that finite sequences of these transfers and/or progressive transfers characterize the third degree inverse stochastic dominance criterion. This criterion allows us to make unanimous inequality judgements even when Lorenz curves intersect. The Gini coefficient becomes relevant in these cases in order to conclusively rank the distributions.