Abstract

We establish an equivalence between three criteria for comparing distributions of an ordinally measurable attribute taking finitely many values. The first criterion is the possibility of going from one distribution to the other by a finite sequence of increments and Hammond transfers. The latter transfers are like the Pigou-Dalton ones, but without the requirement that the amount transferred be fixed. The second criterion is the unanimity of all comparisons of the distributions performed by a large class of additively separable social evaluation functions. The third criterion is a new statistical test based on a weighted recursion of the cumulative distribution.