Ranking Distributions of an Ordinal Attribute

Nicolas Gravel (1) , Brice Magdalou (2) , Patrick Moyes (3)

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille
2 LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée
3 GREThA - Groupe de Recherche en Economie Théorique et Appliquée

This paper establishes an equivalence between three incomplete rank-ings of distributions of an ordinally measurable attribute. The first rank-ing is that associated with the possibility of going from distribution to the other by a finite sequence of two elementary operations: increments of the attribute and the so-called Hammond transfer. The later transfer is like the Pigou-Dalton transfer, but without the requirement -that would be senseless in an ordinal setting -that the "amount" transferred from the "rich" to the "poor" is fixed. The second ranking is an easy-to-use statistical criterion associated to a specifically weighted recursion on the cumulative density of the distribution function. The third ranking is that resulting from the comparison of numerical values assigned to distribu-tions by a large class of additively separable social evaluation functions. Illustrations of the criteria are also provided.

Mots clés: ordinal; qualitative; health; inequality; Hammond transfers; increments; dominance

Domaines: Economies et finances

Nicolas Gravel, Brice Magdalou, Patrick Moyes. Ranking Distributions of an Ordinal Attribute. 2014. ⟨halshs-01082996v1⟩