Gravel, N., Magdalou, B., & Moyes, P. (2020). Ranking distributions of an ordinal variable. Economic Theory.

Author:Nicolas Gravel, Brice Magdalou, Patrick Moyes
Publisher: Springer
Year : 2020
Pages : 48p.
Series :Economic Theory


We establish an equivalence between three criteria for comparing distributions 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 statistical test based on a weighted recursion of the cumulative distribution. We also identify an exact test for the possibility of going from one distribution 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.

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