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An axiomatic approach to the measurement of envy

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  • Bosmans, K.G.M.

    (Microeconomics & Public Economics)

  • Öztürk, Z.E.

    (Microeconomics & Public Economics)

Abstract

We characterize a class of envy measures. There are three key axioms. Decomposability requires that overall envy is the sum of the envy within and between subgroups. The other two axioms deal with the two-individual setting and specify how the envy measure should react to simple changes in the individuals’ commodity bundles. The characterized class measures the envy of one individual to another by the relative utility difference (using the envious’ utility function) between the bundle of the envied and the bundle of the envious. The particular utility representation to be used is fixed by the axioms. The class measures overall envy by the sum of these (transformed) relative utility differences. We discuss our results in the light of previous contributions to envy measurement and multidimensional inequality measurement.

Suggested Citation

  • Bosmans, K.G.M. & Öztürk, Z.E., 2013. "An axiomatic approach to the measurement of envy," Research Memorandum 063, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2013063
    DOI: 10.26481/umagsb.2013063
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    References listed on IDEAS

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    1. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    2. Fujinaka, Yuji & Wakayama, Takuma, 2015. "Maximal manipulation of envy-free solutions in economies with indivisible goods and money," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 165-185.
    3. Arnsperger, Christian, 1994. "Envy-Freeness and Distributive Justice," Journal of Economic Surveys, Wiley Blackwell, vol. 8(2), pages 155-186, June.
    4. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    5. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    6. Fleurbaey, Marc, 2012. "Fairness, Responsibility, and Welfare," OUP Catalogue, Oxford University Press, number 9780199653591.
    7. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2015. "What do normative indices of multidimensional inequality really measure?," Journal of Public Economics, Elsevier, vol. 130(C), pages 94-104.
    8. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    9. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    10. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521887427, January.
    11. Samuelson, Paul A, 1977. "Reaffirming the Existence of "Reasonable" Bergson-Samuelson Social Welfare Functions," Economica, London School of Economics and Political Science, vol. 44(173), pages 81-88, February.
    12. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    13. , & , & ,, 2014. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, vol. 9(3), September.
    14. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    15. Satya R. Chakravarty, 2009. "Inequality, Polarization and Poverty," Economic Studies in Inequality, Social Exclusion, and Well-Being, Springer, number 978-0-387-79253-8, Fall.
    16. repec:zbw:hohpro:325 is not listed on IDEAS
    17. Frank Cowell & Udo Ebert, 2004. "Complaints and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 71-89, August.
    18. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
    19. Fleurbaey, Marc, 2007. "Two criteria for social decisions," Journal of Economic Theory, Elsevier, vol. 134(1), pages 421-447, May.
    20. Serge-Christophe Kolm, 1995. "The Economics Of Social Sentiments: The Case Of Envy," The Japanese Economic Review, Japanese Economic Association, vol. 46(1), pages 63-87, March.
    21. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    22. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
    23. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    24. M. Fleurbaey & F. Maniquet, 2008. "Fair social orderings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(1), pages 25-45, January.
    25. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
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    1. An axiomatic approach to the measurement of envy
      by maximorossi in NEP-LTV blog on 2013-11-18 17:43:39

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    Cited by:

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    3. Mornet, Pauline, 2016. "On the axiomatization of the weakly decomposable inequality indices," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 71-78.
    4. William C. Grant, 2023. "Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors," Games, MDPI, vol. 14(3), pages 1-16, May.

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    More about this item

    JEL classification:

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

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