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Hammond’s Equity Principle and the Measurement of Ordinal Inequalities

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What would be the analogue of the Lorenz quasi-ordering when the variable of interest is 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. Incidently, the paper provides an alternative and simple characterisation of the leximin principle widely used in the social choice and welfare literature.

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  • Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2017. "Hammond’s Equity Principle and the Measurement of Ordinal Inequalities," AMSE Working Papers 1703, Aix-Marseille School of Economics, Marseille, France.
  • Handle: RePEc:aim:wpaimx:1703
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    1. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    2. Patrick Moyes, 2013. "Rearrangements and sequential rank order dominance," Post-Print hal-01135291, HAL.
    3. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2014. "Ranking Distributions of an Ordinal Attribute," AMSE Working Papers 1450, Aix-Marseille School of Economics, Marseille, France.
    4. Kevin W. S. Roberts, 1980. "Possibility Theorems with Interpersonally Comparable Welfare Levels," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 409-420.
    5. Tungodden, Bertil, 2000. "Egalitarianism: Is Leximin the Only Option?," Economics and Philosophy, Cambridge University Press, vol. 16(02), pages 229-245, October.
    6. Gevers, Louis, 1979. "On Interpersonal Comparability and Social Welfare Orderings," Econometrica, Econometric Society, vol. 47(1), pages 75-89, January.
    7. Brice Magdalou & Patrick Moyes, 2009. "Deprivation, welfare and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 253-273, February.
    8. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    9. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
    10. Patrick MOYES, 2013. "Rearrangements and Sequential Rank Order Dominance," Cahiers du GREThA 2013-10, Groupe de Recherche en Economie Théorique et Appliquée.
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    12. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
    13. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    14. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-1135, September.
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    More about this item

    Keywords

    ordinal inequality; Hammond equity axiom; leximin; antileximax;

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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