Relative multi-dimensional poverty measurement and Deaton’s distance function

In multi-dimensional poverty measurement, Deaton, A. (The Rev. Econ. Stud. 46(3), 391–405, 1979) proposed assessing an individual’s contribution to poverty as the fraction of the poverty line bundle to which the individual is indifferent. In this paper, we provide an axiomatic characterization of the set of measures that are concave transformations of Deaton’s measure. This result is derived from two key axioms. The first is a transfer principle, which states that a progressive transfer between two poor individuals with homothetic preferences reduces poverty. The second axiom requires that an individual’s contribution to poverty remains unchanged when their preferences over the poverty line bundle change, provided their preferences toward their own consumption remain the same.