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Social Welfare Functionals on Restricted Domains and in Economic Environments

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  • GEORGES BORDES
  • PETER J. HAMMOND
  • MICHEL LE BRETON

Abstract

Arrow's “impossibility” and similar classical theorems are usually proved for an unrestricted domain of preference profiles. Recent work extends Arrow's theorem to various restricted but “saturating” domains of privately oriented, continuous, (strictly) convex, and (strictly) monotone “economic preferences” for private and/or public goods. For strongly saturating domains of more general utility profiles, this paper provides similar extensions of Wilson's theorem and of the strong and weak “welfarism” results due to d'Aspremont and Gevers and to Roberts. Hence, for social welfare functionals with or without interpersonal comparisons of utility, most previous classification results in social choice theory apply equally to strongly saturating economic domains.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jpbect:v:7:y:2005:i:1:p:1-25
    DOI: 10.1111/j.1467-9779.2005.00191.x
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    References listed on IDEAS

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    1. 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.
    2. Kalai, Ehud & Ritz, Zvi, 1980. "Characterization of the private alternatives domains admitting arrow social welfare functions," Journal of Economic Theory, Elsevier, vol. 22(1), pages 23-36, February.
    3. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    4. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-1135, September.
    5. 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.
    6. Border, Kim C., 1983. "Social welfare functions for economic environments with and without the pareto principle," Journal of Economic Theory, Elsevier, vol. 29(2), pages 205-216, April.
    7. Donaldson, David & Weymark, John A., 1988. "Social choice in economic environments," Journal of Economic Theory, Elsevier, vol. 46(2), pages 291-308, December.
    8. Peter J. Hammond, 2023. "Roberts’ weak welfarism theorem: a minor correction," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 121-134, January.
    9. Weymark, John A., 1998. "Welfarism on economic domains1," Mathematical Social Sciences, Elsevier, vol. 36(3), pages 251-268, December.
    10. Ritz, Zvi, 1985. "Restricted domains, arrow social welfare functions and noncorruptible and nonmanipulable social choice correspondences: The case of private and public alternatives," Journal of Economic Theory, Elsevier, vol. 35(1), pages 1-18, February.
    11. Ritz, Zvi, 1983. "Restricted domains, arrow-social welfare functions and noncorruptible and non-manipulable social choice correspondences: The case of private alternatives," Mathematical Social Sciences, Elsevier, vol. 4(2), pages 155-179, April.
    12. Bordes, Georges & Breton, Michel Le, 1989. "Arrovian theorems with private alternatives domains and selfish individuals," Journal of Economic Theory, Elsevier, vol. 47(2), pages 257-281, April.
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    Cited by:

    1. Charles Blackorby & Walter Bossert & David Donaldson, 2005. "Multi-profile welfarism: A generalization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(2), pages 253-267, April.
    2. Marc Fleurbaey & Philippe Mongin, 2005. "The news of the death of welfare economics is greatly exaggerated," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 381-418, December.
    3. Yukinori Iwata, 2014. "On the informational basis of social choice with the evaluation of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 153-172, June.
    4. Peter J. Hammond, 2023. "Roberts’ weak welfarism theorem: a minor correction," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 121-134, January.
    5. Le Breton, Michel & Weymark, John A., 2002. "Arrovian Social Choice Theory on Economic Domains," IDEI Working Papers 143, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2003.
    6. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2002. "In Defense of Welfarism," Cahiers de recherche 2002-02, Universite de Montreal, Departement de sciences economiques.
    7. Yukinori Iwata, 2009. "Consequences, opportunities, and Arrovian impossibility theorems with consequentialist domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 513-531, March.
    8. Levin, Vladimir L., 2010. "On social welfare functionals: Representation theorems and equivalence classes," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 299-305, May.

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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