James E. Foster and Artyom A. Shneyerov,A General Class of Additively Decomposable Inequality Measures,Economic Theory, Vol. 14, No. 1 (Jul., 1999), pp. 89-111
Summary. This paper presents and characterizes a two-parameter class of in equality measures that contains the generalized entropy measures, the variance of logarithms, the path independent measures of Foster and Shneyerov (1999) and several new classes of measures. The key axiom is a generalized form of additive decomposability which defines the within-group and between-group in equality terms using a generalized mean in place of the arithmetic mean. Our characterization result is proved without invoking any regularity assumption (such as continuity) on the functional form of the inequality measure; instead, it relies on a minimal form of the transfer principle - or consistency with the Lorenz criterion - over two-person distributions.