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Social Choice with Analytic Preferences

Author

Listed:
  • Michel Le Breton

    () (Universite de la Mediterranee)

  • John A. Weymark

    () (Department of Economics, Vanderbilt University)

Abstract

Arrow's axioms for social welfare functions are shown to be inconsistent when the set of alternatives is the nonnegative orthant in a multidimensional Euclidean space and preferences are assumed to be either the set of analytic classical economic preferences or the set of Euclidean spatial preferences. When either of these preference domains is combined with an agenda domain consisting of compact sets with nonempty interiors, strengthened versions of the Arrovian social choice correspondence axioms are shown to be consistent. To help establish the economic possibility theorem, an ordinal version of the Analytic Continuation Principle is developed.

Suggested Citation

  • Michel Le Breton & John A. Weymark, 2000. "Social Choice with Analytic Preferences," Vanderbilt University Department of Economics Working Papers 0023, Vanderbilt University Department of Economics, revised Mar 2001.
  • Handle: RePEc:van:wpaper:0023
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    References listed on IDEAS

    as
    1. Redekop, James, 1993. "The questionnaire topology on some spaces of economic preferences," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 479-494.
    2. LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
    3. Kim Border, 1984. "An impossibility theorem for spatial models," Public Choice, Springer, vol. 43(3), pages 293-305, January.
    4. Wagneur, Edouard, 1979. "Saturation Locale et Concepts Primitifs de la Theorie du Consommateur," Econometrica, Econometric Society, vol. 47(6), pages 1549-1553, November.
    5. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-832, July.
    6. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    7. Campbell, Donald E., 1993. "Euclidean individual preference and continuous social preference," European Journal of Political Economy, Elsevier, vol. 9(4), pages 541-550, November.
    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. Ehlers,Lars & Storcken,Ton, 2001. "Arrow's Theorem in Spatial Environments," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Donaldson, David & Weymark, John A., 1988. "Social choice in economic environments," Journal of Economic Theory, Elsevier, vol. 46(2), pages 291-308, December.
    11. Sen, Amartya K, 1979. "Personal Utilities and Public Judgements: Or What's Wrong with Welfare Economics?," Economic Journal, Royal Economic Society, vol. 89(355), pages 537-558, September.
    12. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    13. Bailey, Martin J, 1979. "The Possibility of Rational Social Choice in an Economy," Journal of Political Economy, University of Chicago Press, vol. 87(1), pages 37-56, February.
    14. Charles K. Rowley (ed.), 1993. "Social Choice Theory," Books, Edward Elgar Publishing, volume 0, number 586.
    15. Ehud Kalai & Eitan Muller & Mark Satterthwaite, 1979. "Social welfare functions when preferences are convex, strictly monotonic, and continuous," Public Choice, Springer, vol. 34(1), pages 87-97, March.
    16. Kannai, Yakar, 1974. "Approximation of convex preferences," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 101-106, August.
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    Cited by:

    1. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 01-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. 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.
    3. Ehlers, Lars & Storcken, Ton, 2009. "Oligarchies in spatial environments," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 250-256, March.
    4. Ehlers,Lars & Storcken,Ton, 2001. "Arrow's Theorem in Spatial Environments," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. repec:spr:etbull:v:1:y:2013:i:1:d:10.1007_s40505-013-0004-6 is not listed on IDEAS

    More about this item

    Keywords

    Axiomatic social choice; Arrow's theorem; spatial preferences; analytic continuation principle;

    JEL classification:

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

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