A note on measures of distance between income distributions (Q1095021)

A well-established tradition in the measurement of inequality is to define a social evaluation function W on the set of income distributions, and compute the inequality within a distribution by comparing its equally distributed equivalent income with its mean income. The purpose of this note is to show that a class of statistical distance functions proposed recently to measure the inequality of incomes between populations by \textit{U. Ebert} [J. Econ. Theory 32, 266-274 (1984; Zbl 0532.90026)], fails to capture differences in welfares of different populations (this distance is not coherent with any W), and to axiomatically characterize a more satisfactory distance measure.