Abstract
This article deals with inequality measures on income distributions. These measures are assumed to fulfil common axioms like the Principle of Progressive Transfers, Normalization, and Symmetry. Strict Monotonicity will be defined and is included in the basic set of axioms. If the measures are especially based on bilateral comparisons and if two additional conditions are fulfilled the bilateral inequality measure must be proportional to the absolute distance of the two incomes involved. It is remarkable that all these conditions do not give an answer whether an inequality measure for two incomes should be a quasi-convex or a quasi-concave function. This question is controversely discussed in economic research. Our surprising answer, however, is given by use of RAO's statistic concept defining the diversity of a population.
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