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

  • Chichilnisky, Graciela
  • Heal, Geoffrey

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/8495/1/MPRA_paper_8495.pdf
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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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Web page: http://mpra.ub.uni-muenchen.de

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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.
  2. 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.
  3. KIRMAN, Alan P. & SONDERMANN, Dieter, . "Arrow's theorem, many agents, and indivisible dictators," CORE Discussion Papers RP -118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  5. 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.
  6. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
  7. 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.
  8. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
  9. 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.
  10. Brown, Donald J, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, MIT Press, vol. 89(3), pages 456-69, August.
  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.
  12. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
  13. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Community preferences and social choice," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 33-61, September.
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