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An axiomatization of the mixed utilitarian–maximin social welfare orderings

  • Walter Bossert
  • Kohei Kamaga
Research Article
  • 55 Downloads

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.

Keywords

Social welfare ordering Utilitarianism Maximin principle Normative inequality index 

JEL Classification

D63 

References

  1. Aczél, J.: Lectures on Functional Equations and Their Applications. Academic Press, New York (1966)Google Scholar
  2. Alvarez-Cuadrad, F., Long, N.V.: A mixed Bentham–Rawls criterion for intergenerational equity: theory and implications. J. Environ. Econ. Manag. 58, 154–168 (2009)CrossRefGoogle Scholar
  3. Atkinson, A.B.: On the measurement of inequality. J. Econ. Theory 2, 244–263 (1970)CrossRefGoogle Scholar
  4. Bentham, J.: An Introduction to the Principles of Morals and Legislation. Payne, London (1789)CrossRefGoogle Scholar
  5. Blackorby, C., Bossert, W., Donaldson, D.: Utilitarianism and the theory of justice. In: Arrow, K.J., Sen, A.K., Suzumura, K. (eds.) Handbook of Social Choice and Welfare, vol. I, pp. 543–596. North-Holland, Amsterdam (2002)CrossRefGoogle Scholar
  6. Blackorby, C., Bossert, W., Donaldson, D.: Population Issues in Social Choice Theory, Welfare Economics, and Ethics. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  7. Blackorby, C., Donaldson, D.: A theoretical treatment of indices of absolute inequality. Int. Econ. Rev. 21, 107–136 (1980)CrossRefGoogle Scholar
  8. Blackorby, C., Donaldson, D., Weymark, J.A.: Social choice with interpersonal utility comparisons: a diagrammatic introduction. Int. Econ. Rev. 25, 327–356 (1984)CrossRefGoogle Scholar
  9. Bosmans, K., Ooghe, E.: A characterization of maximin. Econ. Theory Bull. 1, 151–156 (2013)CrossRefGoogle Scholar
  10. Bossert, W., Pfingsten, A.: Intermediate inequality: concepts, indices, and welfare implications. Math. Soc. Sci. 19, 117–134 (1990)CrossRefGoogle Scholar
  11. Bossert, W., Weymark, J.A.: Utility in social choice. In: Barberà, S., Hammond, P.J., Seidl, C. (eds.) Handbook of Utility Theory, vol. 2: Extensions, pp. 1099–1177. Kluwer Academic Publishers, Dordrecht (2004)CrossRefGoogle Scholar
  12. Chakravarty, S.R.: Inequality, Polarization and Poverty. Springer, New York (2010)Google Scholar
  13. Cowell, F.A.: ‘A fair suck of the sauce bottle’ or what do you mean by equality? Econ. Rec. 61, 567–579 (1985)CrossRefGoogle Scholar
  14. Dalton, H.: The measurement of the inequality of incomes. Econ. J. 30, 348–361 (1920)CrossRefGoogle Scholar
  15. d’Aspremont, C., Gevers, L.: Equity and the informational basis of collective choice. Rev. Econ. Stud. 44, 199–209 (1977)CrossRefGoogle Scholar
  16. d’Aspremont, C., Gevers, L.: Social welfare functionals and interpersonal comparability. In: Arrow, K.J., Sen, A.K., Suzumura, K. (eds.) Handbook of Social Choice and Welfare, vol. I, pp. 459–541. North-Holland, Amsterdam (2002)CrossRefGoogle Scholar
  17. Deschamps, R., Gevers, L.: Leximin and utilitarian rules: a joint characterization. J. Econ. Theory 17, 143–163 (1978)CrossRefGoogle Scholar
  18. Figuières, C., Long, N.V., Tidball, M.: The MBR intertemporal choice criterion and Rawls’ just saving principle. Math. Soc. Sci. 85, 11–22 (2017)CrossRefGoogle Scholar
  19. Hammond, P.J.: Why ethical measures of inequality need interpersonal comparisons. Theory Decis. 7, 263–274 (1976)CrossRefGoogle Scholar
  20. Hammond, P.J.: Equity in two person situations: some consequences. Econometrica 47, 1127–1135 (1979)CrossRefGoogle Scholar
  21. Kamaga, K.: When do utilitarianism and egalitarianism agree on evaluation? An intersection approach. Math. Soc. Sci. 94, 41–48 (2018)CrossRefGoogle Scholar
  22. Kolm, S.-C.: The optimal production of social justice. In: Margolis, J., Guitton, H. (eds.) Public Economics, pp. 145–200. Macmillan, London (1969)CrossRefGoogle Scholar
  23. Kolm, S.-C.: Unequal inequalities. I. J. Econ. Theory 12, 416–442 (1976)CrossRefGoogle Scholar
  24. Long, N.V.: Toward a theory of a just savings principle. In: Roemer, J.E., Suzumura, K. (eds.) Intergenerational Equity and Sustainability, pp. 291–319. Palgrave, London (2007)CrossRefGoogle Scholar
  25. Long, N.V., Martinet, V.: Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives. Soc. Choice Welfare 50, 35–64 (2018)CrossRefGoogle Scholar
  26. Maskin, E.: A theorem on utilitarianism. Rev. Econ. Stud. 45, 93–96 (1978)CrossRefGoogle Scholar
  27. Mehran, F.: Linear measures of income inequality. Econometrica 44, 805–809 (1976)CrossRefGoogle Scholar
  28. Miyagishima, K.: A characterization of the maximin social ordering. Econ. Bull. 30, 1278–1282 (2010)Google Scholar
  29. Miyagishima, K., Bosmans, K., Ooghe, E.: A characterization of maximin: corrigendum. Econ. Theory Bull. 2, 219–220 (2014)CrossRefGoogle Scholar
  30. Ou-Yang, K.: Generalized Rawlsianism. Soc. Choice Welfare 50, 265–279 (2018)CrossRefGoogle Scholar
  31. Pigou, A.C.: Wealth and Welfare. Macmillan, London (1912)Google Scholar
  32. Rawls, J.: A Theory of Justice. Harvard University Press, Cambridge (1971)Google Scholar
  33. Roberts, K.W.S.: Interpersonal comparability and social choice theory. Rev. Econ. Stud. 47, 421–439 (1980)CrossRefGoogle Scholar
  34. Sen, A.K.: Collective Choice and Social Welfare. Holden-Day, Amsterdam (1970)Google Scholar
  35. Sen, A.K.: On Economic Inequality. Clarendon, Oxford (1973)CrossRefGoogle Scholar
  36. Shorrocks, A.F., Foster, J.E.: Transfer sensitive inequality measures. Rev. Econ. Stud. 54, 485–497 (1987)CrossRefGoogle Scholar
  37. Strasnick, S.: Social choice and the derivation of Rawls’s difference principle. J. Philos. 73, 85–99 (1976)CrossRefGoogle Scholar
  38. Suppes, P.: Some formal models of grading principles. Synthese 6, 284–306 (1966)CrossRefGoogle Scholar
  39. Tol, R.S.J.: Climate policy with Bentham–Rawls preferences. Econ. Lett. 118, 424–428 (2013)CrossRefGoogle Scholar
  40. Tsui, K.-Y., Weymark, J.A.: Social welfare orderings for ratio-scale measurable utilities. Econ. Theory 10, 241–256 (1997).  https://doi.org/10.1007/s001990050156 CrossRefGoogle Scholar
  41. Weymark, J.A.: Generalized Gini inequality indices. Math. Soc. Sci. 1, 409–430 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Economics and CIREQUniversity of MontrealMontrealCanada
  2. 2.Faculty of EconomicsSophia UniversityTokyoJapan

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