Distribution-sensitivity of rank-dependent poverty measures

We propose a criterion to rank poverty measures on the basis of distribution-sensitivity. The criterion compares reactions to 'lossy' transfers among the poor. We focus on the class of rank-dependent poverty measures and provide distribution-sensitivity rankings of the poverty gap ratio, the first and second Sen measures, the Thon measure, the Shorrocks measure, and the Thon, Kakwani and S-Gini classes of measures. Moreover, we discuss the relationship between the proposed criterion and two alternative distribution-sensitivity criteria based on the Arrow-Pratt theory of risk aversion. Finally, we provide an empirically tractable necessary and sufficient condition for unanimous poverty rankings by all continuous and replication invariant rank-dependent poverty measures that exhibit a predetermined minimum degree of distribution-sensitivity.