On the axiomatization of the weakly decomposable inequality indices

In this paper, we focus on a decomposition property recently introduced in the inequality literature and known as the weak decomposition. Such a property provides interesting analyses by allowing one to separate the within-group contribution to total inequality from the between-group contribution. A limitation of the current method of decomposition is that, depending on the structure-absolute, relative, compromise-of the inequality index, specific weights have to be used. To avoid such a problem, we propose a unique decomposition property where the weighting functions depend on the size of the population and the mean income. This allows us to characterize a large family of weakly decomposable inequality indices without any recourse to implicit invariance value judgments.