The Lorenz relation as intersection ordering of a class of inequality measures

The “intersection approach” provides a formal solution to the problem of finding a suitable basis for interdistributional comparisons, or, in other words, to the problem of “defining” the measurement of inequality/concentration. The question of comparability between distributions (e.g. income distributions) from the point of view of degree of inequality lies at the core of our advocacy of dominance orderings. The Lorenz ordering (LO) is the intersection of the class of all relative inequality measures satisfying Pigou-Dalton condition. It is a partial order strictly related to other well known preorderings, namely stochastic orderings and majorization. In this paper, we provide a brief survey of functionals consistent with the LO as a basis for unambiguous statistical measure of inequality.