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Necessary and sufficient conditions for a resolution of the social choice paradox

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Author Info
Chichilnisky, Graciela
Heal, Geoffrey

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Abstract

We present a restriction on the domain of individual preferences that is both necessary and sufficient for the existence of a social choice rule that is continuous, anonymous, and respects unanimity. The restriction is that the space of preferences be contractible. Contractibility admits a straightforward intuitive explanation, and is a generalisation of conditions such as single peakedness, value restrictedness and limited agreement, which were earlier shown to be sufficient for majority voting to be an acceptable rule. The only restriction on the number of individuals, is that it be finite and at least 2.

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File URL: http://mpra.ub.uni-muenchen.de/8495/
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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8495.

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Date of creation: 25 Nov 1979
Date of revision: 20 Oct 1981
Publication status: Published in Journal of Economic Theory No. 1.31(1983): pp. 68-87
Handle: RePEc:pra:mprapa:8495

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Keywords: social choice; preferences; mathematical modeling;

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Find related papers by JEL classification:
O25 - Economic Development, Technological Change, and Growth - - Development Planning and Policy - - - Industrial Policy
O24 - Economic Development, Technological Change, and Growth - - Development Planning and Policy - - - Trade Policy; Factor Movement; Foreign Exchange Policy
O22 - Economic Development, Technological Change, and Growth - - Development Planning and Policy - - - Project Analysis

References listed on IDEAS
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  1. Chichilnisky, Graciela, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, MIT Press, vol. 97(2), pages 337-52, May. [Downloadable!] (restricted)
  2. Brown, Donald J, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, MIT Press, vol. 89(3), pages 456-69, August. [Downloadable!] (restricted)
  3. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May. [Downloadable!] (restricted)
  4. Coughlin, Peter & Lin, Kuan-Pin, 1981. "Continuity properties of majority rule with intermediate preferences," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 289-296, May. [Downloadable!] (restricted)
  5. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Community preferences and social choice," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 33-61, September. [Downloadable!] (restricted)
  6. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October. [Downloadable!] (restricted)
  7. Chichilnisky, Graciela, 1982. "The topological equivalence of the pareto condition and the existence of a dictator," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 223-233, March. [Downloadable!] (restricted)
  8. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March. [Downloadable!] (restricted)
  9. Chichilnisky, G. & Heal, G.M., 1995. "Social Choice with Infinite Populations: Construction of a Rule and Impossibility Results," Papers 95-19, Columbia - Graduate School of Business.
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  10. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July. [Downloadable!] (restricted)
  11. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August. [Downloadable!] (restricted)
  12. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany. [Downloadable!]
  13. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Chichilnisky, Graciela, 1994. "A robust theory of resource allocation," MPRA Paper 8599, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  2. Chichilnisky, Graciela, 1993. "Topoloy and economics: the contributions of S. Smale," MPRA Paper 8485, University Library of Munich, Germany. [Downloadable!]
  3. Oleksandra Hubal & Michael Zarichnyi, 2005. "Whitney topology and spaces of preference relations," Economics Bulletin, Economics Bulletin, vol. 3(4), pages 1-7. [Downloadable!]
  4. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany. [Downloadable!]
  5. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer, vol. 13(1), pages 11-16, January. [Downloadable!] (restricted)
  6. Alex Coram, 2008. "Social choice and information: a note on the calculus of mappings from utility spaces," Working Papers 2008-04, University of Massachusetts Amherst, Department of Economics. [Downloadable!]
  7. Luc Lauwers, 2002. "A note on Chichilnisky's social choice paradox," Theory and Decision, Springer, vol. 52(3), pages 261-266, May. [Downloadable!] (restricted)
  8. Chichilnisky, Graciela, 1990. "Social choice and the closed convergence topology," MPRA Paper 8353, University Library of Munich, Germany. [Downloadable!]
  9. Luc Lauwers, 2009. "The topological approach to the aggregation of preferences," Social Choice and Welfare, Springer, vol. 33(3), pages 449-476, September. [Downloadable!] (restricted)
  10. Alex Coram, 2006. "Social choice with a continuous ordering function," Working Papers 2006-09, University of Massachusetts Amherst, Department of Economics. [Downloadable!]
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