Ranking distributions of an ordinal variable

We establish an equivalence between three criteria for comparing dis- tributions of an ordinal variable 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/or 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 class of additively separable social evaluation functions. The third criterion is a new statis- tical test based on a weighted recursion of the cumulative distribution. We also identify an exact test for the possibility of going from one dis- tribution to another by a finite sequence of Hammond transfers only. An illustration of the usefulness of our approach for evaluating distributions of self-reported happiness level is also provided