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Social Choice with Analytic Preferences

  • Michel Le Breton


    (Universite de la Mediterranee)

  • John A. Weymark


    (Department of Economics, Vanderbilt University)

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.

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Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0023.

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Date of creation: Jun 2000
Date of revision: Mar 2001
Handle: RePEc:van:wpaper:0023
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  1. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
  2. 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.
  3. EHLERS, Lars & STORCKEN, Ton, 2002. "Arrow's Theorem in Spatial Environments," Cahiers de recherche 2002-03, Universite de Montreal, Departement de sciences economiques.
  4. 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 537-58, September.
  5. Campbell, Donald E., 1993. "Euclidean individual preference and continuous social preference," European Journal of Political Economy, Elsevier, vol. 9(4), pages 541-550, November.
  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. Kannai, Yakar, 1974. "Approximation of convex preferences," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 101-106, August.
  8. Kim Border, 1984. "An impossibility theorem for spatial models," Public Choice, Springer, vol. 43(3), pages 293-305, January.
  9. Redekop, James, 1993. "The questionnaire topology on some spaces of economic preferences," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 479-494.
  10. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-32, July.
  11. Wagneur, Edouard, 1979. "Saturation Locale et Concepts Primitifs de la Theorie du Consommateur," Econometrica, Econometric Society, vol. 47(6), pages 1549-53, November.
  12. Charles K. Rowley (ed.), 1993. "Social Choice Theory," Books, Edward Elgar Publishing, volume 0, number 586, 10.
  13. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
  14. 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.
  15. Donaldson, David & Weymark, John A., 1988. "Social choice in economic environments," Journal of Economic Theory, Elsevier, vol. 46(2), pages 291-308, December.
  16. LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
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