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On social welfare functionals: Representation theorems and equivalence classes


  • Levin, Vladimir L.


We substantially weaken the traditional unrestricted domain assumption and give axiomatic characterizations of social welfare functionals representable by utility functions of the form , where is a utility profile specifying a concrete welfare situation, and W is a real-valued function belonging to a particular class. Also we consider general equivalence relations on the utility space and obtain representation theorems on utility equivalence classes.

Suggested Citation

  • Levin, Vladimir L., 2010. "On social welfare functionals: Representation theorems and equivalence classes," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 299-305, May.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:299-305

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    References listed on IDEAS

    1. Kevin W. S. Roberts, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 421-439.
    2. Georges Bordes & Peter J. Hammond & Michel Le Breton, 2005. "Social Welfare Functionals on Restricted Domains and in Economic Environments," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(1), pages 1-25, February.
    3. Kevin W. S. Roberts, 1980. "Social Choice Theory: The Single-profile and Multi-profile Approaches," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 441-450.
    4. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, March.
    5. Levin, V. L., 1991. "Some applications of set-valued mappings in mathematical economics," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 69-87.
    6. Neuefeind, Wilhelm & Trockel, Walter, 1995. "Continuous Linear Representability of Binary Relations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 351-356, July.
    7. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," Review of Economic Studies, Oxford University Press, vol. 44(2), pages 199-209.
    8. Levin, Vladimir L., 2009. "New axiomatic characterizations of utilitarianism," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 15-24, July.
    9. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    10. Eric Maskin, 1978. "A Theorem on Utilitarianism," Review of Economic Studies, Oxford University Press, vol. 45(1), pages 93-96.
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