Orness values for rank-dependent welfare functions and poverty measures

The rank-dependent welfare functions and the rank-dependent poverty measures are weighted sums of the income and the gap of an individual, respectively, where the weights only depend on the position of each individual. In this work we show that an OWA operator is underlying in the definition of every rankdependent welfare function and every rank-dependent poverty measure. For each OWA operator assigned to the welfare functions and poverty measures we compute the corresponding orness value. Then, we establish a classification for the two classes of measures in terms of their orness value. Welfare functions and poverty measures account for the distribution-sensitivity. That is, if a transfer of income takes place from an individual, poor in poverty, to another individual with less income, then, the magnitude of the increase on welfare or the decrease on poverty should be higher for lower incomes involved. Therefore, welfare functions and poverty measures can be classified in terms of their magnitude of change for different transfers. We prove that the orness classification of the welfare functions and the poverty measures can be interpreted as a classification in terms of their distribution-sensitivity. Specifically, in this work, we prove that for a subset of these two classes, the measures for which the weights are linear, the orness classification and the distribution-sensitivity classification for some defined transfers are equivalent.