Inequality measurement with an ordinal and continuous variable

Mesure des Inégalités avec une Variable Ordinale et Continue

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

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Abstract: What would be the analogue of the Lorenz quasi-ordering when the variable of interest is continuous and of a purely ordinal nature? We argue that it is possible to derive such a criterion by substituting for the Pigou-Dalton transfer used in the standard inequality literature what we refer to as a Hammond progressive transfer. According to this criterion, one distribution of utilities is considered to be less unequal than another if it is judged better by both the lexicographic extensions of the maximin and the minimax, henceforth referred to as the leximin and the antileximax, respectively. If one imposes in addition that an increase in someone's utility makes the society better off, then one is left with the leximin, while the requirement that society welfare increases as the result of a decrease of one person's utility gives the antileximax criterion. Incidentally, the paper provides an alternative and simple characterisation of the leximin principle widely used in the social choice and welfare literature.

Keywords: Leximin; Antileximax; Ordinal inequality; Hammond equity principle; Inégalité ordinale; Equité au sens de Hammond (search for similar items in EconPapers)
Date: 2019
Note: View the original document on HAL open archive server: https://hal.science/hal-01945306v1
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Citations: View citations in EconPapers (5)

Published in Social Choice and Welfare, 2019, 52 (3), pp.453-475. ⟨10.1007/s00355-018-1159-8⟩

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Related works:
Journal Article: Inequality measurement with an ordinal and continuous variable (2019)
Working Paper: Inequality Measurement with an Ordinal and Continuous Variable (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01945306

DOI: 10.1007/s00355-018-1159-8

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