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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

March 1997 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. Journal of Economic Literature classification: D71. Keywords: social welfare functionals, Arrow's theorem, Wilson's theorem, welfarism, neutrality, restricted domains, economic domains, economic environments.

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 97023.

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Date of creation: Mar 1997
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Handle: RePEc:wop:stanec:97023

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Keywords: social welfare functionals; Arrow's theorem; Wilson's theorem; welfarism; neutrality; restricted domains; economic domains; economic environments;

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References

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  1. Donaldson, David & Weymark, John A., 1988. "Social choice in economic environments," Journal of Economic Theory, Elsevier, vol. 46(2), pages 291-308, December.
  2. Roberts, Kevin, 1983. "Social choice rules and real-valued representations," Journal of Economic Theory, Elsevier, vol. 29(1), pages 72-94, 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. d'Aspremont, Claude & Gevers, Louis, 1977. "Equity and the Informational Basis of Collective Choice," Review of Economic Studies, Wiley Blackwell, vol. 44(2), pages 199-209, June.
  5. 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.
  6. 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.
  7. Weymark, John A., 1998. "Welfarism on economic domains1," Mathematical Social Sciences, Elsevier, vol. 36(3), pages 251-268, December.
  8. 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.
  9. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
  10. 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.
  11. Peter J. Hammond, 1999. "Roberts' Weak Welfarism Theorem: A Minor Correction," Working Papers 99021, Stanford University, Department of Economics.
  12. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-35, September.
  13. Roberts, Kevin W S, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 421-39, January.
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Cited by:
  1. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2002. "In Defense of Welfarism," Cahiers de recherche 2002-02, Universite de Montreal, Departement de sciences economiques.
  2. Michel Le Breton & John A. Weymark, 2002. "Arrovian Social Choice Theory on Economic Domains," Vanderbilt University Department of Economics Working Papers 0206, Vanderbilt University Department of Economics, revised Sep 2003.
  3. Levin, Vladimir L., 2010. "On social welfare functionals: Representation theorems and equivalence classes," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 299-305, May.
  4. Blackorby, Charles & Bossert, Walter & Donaldson, David, 2004. "Multi-Profile Welfarism : A Generalisation," The Warwick Economics Research Paper Series (TWERPS) 710, University of Warwick, Department of Economics.
  5. Marc Fleurbaey & Philippe Mongin, 2004. "The News of the Death of Welfare Economics is Greatly Exaggerated," Working Papers hal-00242931, HAL.
  6. Yukinori Iwata, 2009. "Consequences, opportunities, and Arrovian impossibility theorems with consequentialist domains," Social Choice and Welfare, Springer, vol. 32(3), pages 513-531, March.
  7. Peter J. Hammond, 1999. "Roberts' Weak Welfarism Theorem: A Minor Correction," Working Papers 99021, Stanford University, Department of Economics.
  8. Yukinori Iwata, 2014. "On the informational basis of social choice with the evaluation of opportunity sets," Social Choice and Welfare, Springer, vol. 43(1), pages 153-172, June.

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