Decomposition properties of dual choice functionals

Abstract

The Gini coefficient is a well-known measure of inequality, and it satisfies a non-overlapping additive decomposition property (Ebert 1988b). The Gini coefficient is related to the dual theory of choice, as developed by Yaari (1987, 1988). We determine which other dual choice functionals satisfy a non-overlapping additive decomposition property that is weaker than the additive one suggested in Ebert (1988b). It turns out that the only functionals that do are those that arise from the Lebesgue measure, the measure associated with the Gini coefficient, and degenerate delta functions.