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Size and distribution trade-offs for the leximin ordering

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  • Bart Capéau

Abstract

A relative invariant and an absolute invariant inequality ordering satisfying extreme bottom-sensitivity, are proposed. It is shown that the leximin social welfare ordering can be expressed in terms of a ranking of distributions on the sole basis of their size, measured by the mean, and the degree of inequality, measured according to these inequality concepts. Leximin thus exhibits extreme bottom-sensitivity. This property does not withstand that leximin prefers a larger size of the cake at the cost of higher inequality in a number of cases. These trade-offs between size and equality are characterised in terms of degrees of dominance of the lower parts of the ordinary and absolute Lorenz curves that are accepted by leximin for a given increase in the mean. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Bart Capéau, 2013. "Size and distribution trade-offs for the leximin ordering," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(2), pages 237-248, June.
    • Handle: RePEc:kap:jecinq:v:11:y:2013:i:2:p:237-248
    DOI: 10.1007/s10888-012-9219-2
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    1. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 401-414.
    2. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    3. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    4. Gevers, Louis, 1979. "On Interpersonal Comparability and Social Welfare Orderings," Econometrica, Econometric Society, vol. 47(1), pages 75-89, January.
    5. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    6. Ebert, Udo, 1987. "Size and distribution of incomes as determinants of social welfare," Journal of Economic Theory, Elsevier, vol. 41(1), pages 23-33, February.
    7. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    8. Kristof Bosmans, 2007. "Comparing degrees of inequality aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 405-428, October.
    9. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    10. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    11. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    12. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    13. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 199-209.
    14. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-136, February.
    15. Hammond, Peter J., 1975. "A note on extreme inequality aversion," Journal of Economic Theory, Elsevier, vol. 11(3), pages 465-467, December.
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    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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