Why Measuring Inequality by the Variance Makes Sense from a Theoretical Point of View

Abstract

The variance, which has many advantages as a measure of inequality, is a quadratic form in incomes. In this paper we develop a characterization of the variance by showing that among all quadratic forms in incomes, it is the only one that satisfies absolute inequality invariance, symmetry, the principle of transfers and the principle of population. A numerical illustration of several inequality indices, including the variance, is also presented in the paper.