Measurement of Income Inequality : The η;−invariance and its Associated Lorenz Dominance

In a recent paper, Yoshida (Social Choice and Welfare 24 : 557−574 ; 2005) has proposed a new concept of intermediate inequality which is referred to as the η−inequality equivalence. The aim of this paper is to characterize the class of inequality measures possessing this property in terms of the associated Lorenz dominance. For each η ∈ [0,1], we place a class М(η) of inequality measures satisfying the η−inequality　equivalence. Then we show that a necessary and sufficient condition for two income distributions to be ranked unambiguously according to the class М(η) is that the associated η−Lorenz curves do not intersect.