Ranking Distributions of an Ordinal Attribute

Nicolas Gravel (), Brice Magdalou and Patrick Moyes ()

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Abstract: This paper establishes foundational equivalences between alternative criteria for comparing distributions of an ordinally measurable attribute. A first criterion is associated with the possibility of going from distribution to the other by a finite sequence of two elementary operations: increments of the attribute and Hammond transfers. The later transfers are like the famous Pigou-Dalton ones, but without the requirement - that would be senseless in an ordinal setting - that the "amount" transferred from the "rich" to the "poor" is fixed. A second criterion is a new easy-to-use statistical criterion associated to a specifically weighted recursion on the cumulative density of the distribution function. A third criterion is that resulting from the comparison of numerical values assigned to distributions by a large class of additively separable social evaluation functions. Dual versions of these criteria are also considered and alternative equivalence results are established. Illustrations of the criteria are also provided.

Keywords: ordinal; qualitative; health; inequality; Hammond transfers; increments; dominance (search for similar items in EconPapers)
Date: 2015-12
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01082996v2
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Citations: View citations in EconPapers (9)

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Related works:
Working Paper: Ranking Distributions of an Ordinal Attribute (2014)
Working Paper: Ranking distributions of an ordinal attribute (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:halshs-01082996

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