Transfer principles and a classification of concentration measures

Abstract

In this article we show that the notion of concentration (or inequality) can best be studied by applying a number of transfer principles. We prove this by showing that transfer principles imply other natural concentration requirements such as the principle of nominal increase. We moreover exhibit a relation between Dalton's transfer principle and the Lorenz dominance order. We distinguish between simple and stronger transfer principles, leading to a classification of concentration measures. Finally, it is shown that the coefficient of variation and some measures derived from it are the "ultimate best" ones.