The orness value for rank-dependent welfare functions and rank-dependent poverty measures

We propose two distribution-sensitivity criteria to classify the rank-dependent welfare functions. These criteria compare the reaction of the welfare function to lossy transfers and lossy equalization transfers among individuals. We see that these classifications in terms of their distribution-sensitivity to these transfers can be established focusing only on the weights assigned to each welfare function. We also propose a criterion to sort the rank-dependent welfare functions and the rank-dependent poverty measures in terms of a mathematical value called orness. We provide a classification in terms of the orness value for the welfare functions of the S-Gini family, the Bonferroni index and the De Vergottini index. Another classification is provided for the poverty measures of the Poverty Gap Ratio, the Sen indices, the Thon index and the Thon family of indices, the Kakwani family of indices and the S-Gini family of indices. Finally, we prove that the orness classification for welfare functions and the orness classification for poverty measures can be interpreted as a distribution-sensitive classification since they have a direct link with the classifications proposed above. Moreover, we see that for a subset of welfare functions and another subset of poverty measures, the orness classification and the distribution-sensitivity classification based on lossy transfers and lossy equalization transfers are equivalent.