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An axiomatization of the mixed utilitarian–maximin social welfare orderings

Author

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  • Walter Bossert

    (University of Montreal)

  • Kohei Kamaga

    (Sophia University)

Abstract

We axiomatize the class of mixed utilitarian–maximin social welfare orderings. These orderings are convex combinations of utilitarianism and the maximin rule. Our first step is to show that the conjunction of the weak Suppes–Sen principle, the Pigou–Dalton transfer principle, continuity and the composite transfer principle is equivalent to the existence of a continuous and monotone ordering of pairs of average and minimum utilities that can be used to rank utility vectors. Using this observation, the main result of the paper establishes that the utilitarian–maximin social welfare orderings are characterized by adding the axiom of cardinal full comparability. In addition, we examine the consequences of replacing cardinal full comparability with ratio-scale full comparability and translation-scale full comparability, respectively. We also discuss the classes of normative inequality measures corresponding to our social welfare orderings.

Suggested Citation

  • Walter Bossert & Kohei Kamaga, 2020. "An axiomatization of the mixed utilitarian–maximin social welfare orderings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 451-473, March.
    • Handle: RePEc:spr:joecth:v:69:y:2020:i:2:d:10.1007_s00199-018-1168-y
    DOI: 10.1007/s00199-018-1168-y
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    1. Figuières, Charles & Long, Ngo Van & Tidball, Mabel, 2017. "The MBR intertemporal choice criterion and Rawls’ just savings principle," Mathematical Social Sciences, Elsevier, vol. 85(C), pages 11-22.
    2. Kevin W. S. Roberts, 1980. "Interpersonal Comparability and Social Choice Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 421-439.
    3. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587.
    4. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    5. Tol, Richard S.J., 2013. "Climate policy with Bentham–Rawls preferences," Economics Letters, Elsevier, vol. 118(3), pages 424-428.
    6. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    7. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    8. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-1135, September.
    9. Cowell, F A, 1985. "'A Fair Suck of the Sauce Bottle' or What Do You Mean by Inequality?," The Economic Record, The Economic Society of Australia, vol. 61(173), pages 567-579, June.
    10. Blackorby, Charles & Donaldson, David & Weymark, John A, 1984. "Social Choice with Interpersonal Utility Comparisons: A Diagrammatic Introduction," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 327-356, June.
    11. Alvarez-Cuadrado, Francisco & Van Long, Ngo, 2009. "A mixed Bentham-Rawls criterion for intergenerational equity: Theory and implications," Journal of Environmental Economics and Management, Elsevier, vol. 58(2), pages 154-168, September.
    12. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    13. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    14. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    15. Deschamps, Robert & Gevers, Louis, 1978. "Leximin and utilitarian rules: A joint characterization," Journal of Economic Theory, Elsevier, vol. 17(2), pages 143-163, April.
    16. Kaname Miyagishima & Kristof Bosmans & Erwin Ooghe, 2014. "A characterization of maximin: corrigendum," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 219-220, October.
    17. Kamaga, Kohei, 2018. "When do utilitarianism and egalitarianism agree on evaluation? An intersection approach," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 41-48.
    18. 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.
    19. Kristof Bosmans & Erwin Ooghe, 2013. "A characterization of maximin," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 151-156, November.
    20. Kui Ou-Yang, 2018. "Generalized rawlsianism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 265-279, February.
    21. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    22. Ngo Long, 2007. "Toward a Theory of a Just Savings Principle," International Economic Association Series, in: John Roemer & Kotaro Suzumura (ed.), Intergenerational Equity and Sustainability, chapter 15, pages 291-319, Palgrave Macmillan.
    23. John Roemer & Kotaro Suzumura (ed.), 2007. "Intergenerational Equity and Sustainability," International Economic Association Series, Palgrave Macmillan, number 978-0-230-23676-9, December.
    24. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    25. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    26. 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.
    27. Kaname Miyagishima, 2010. "A characterization of the maximin social ordering," Economics Bulletin, AccessEcon, vol. 30(2), pages 1278-1282.
    28. Blackorby, Charles & Bossert, Walter & Donaldson, David, 2002. "Utilitarianism and the theory of justice," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 11, pages 543-596, Elsevier.
    29. John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 241-256.
    30. Eric Maskin, 1978. "A Theorem on Utilitarianism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 93-96.
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    More about this item

    Keywords

    Social welfare ordering; Utilitarianism; Maximin principle; Normative inequality index;
    All these keywords.

    JEL classification:

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

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