Ranking Distributions of an Ordinal Attribute

This paper establishes an equivalence between three incomplete rankings of distributions of an ordinally measurable attribute. The first ranking 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 distributions by a large class of additively separable social evaluation functions. Illustrations of the criteria are also provided.