Multidimensional inequality and inframodular order

International audience; Motivated by the pertinence of Pigou–Dalton (PD) transfers for inequality measurement when only one attribute is involved, we show that inframodular functions are consistent with multidimensional PD transfers and that weakly inframodular functions fit more accurately with the traditional notion of PD transfers. We emphasize, for inequality rankings of allocations of multiple attributes in a population, the similarities of the inframodular order, defined using inframodular functions, with the concave order in the unidimensional framework.