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

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  • Chichilnisky, Graciela
  • Heal, Geoffrey

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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Bibliographic 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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References

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  1. 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.
  2. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, Elsevier, vol. 5(2), pages 267-277, October.
  3. Brown, Donald J, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 89(3), pages 456-69, August.
  4. DEBREU, Gérard, . "Smooth preferences," CORE Discussion Papers RP -132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, Elsevier, vol. 2(1), pages 103-106, March.
  6. Coughlin, Peter & Lin, Kuan-Pin, 1981. "Continuity properties of majority rule with intermediate preferences," Mathematical Social Sciences, Elsevier, Elsevier, vol. 1(3), pages 289-296, May.
  7. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Community preferences and social choice," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 33-61, September.
  8. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  9. 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.
  10. Chichilnisky, Graciela, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 97(2), pages 337-52, May.
  11. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, Elsevier, vol. 8(1), pages 26-38, May.
  12. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
  13. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, Elsevier, vol. 1(2), pages 178-202, August.
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Citations

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Cited by:
  1. Luc Lauwers, 2002. "A note on Chichilnisky's social choice paradox," Theory and Decision, Springer, Springer, vol. 52(3), pages 261-266, May.
  2. David Canning, 2013. "Axiomatic Foundations For Cost‐Effectiveness Analysis," Health Economics, John Wiley & Sons, Ltd., vol. 22(12), pages 1405-1416, December.
  3. Chichilnisky, Graciela, 1994. "A robust theory of resource allocation," MPRA Paper 8599, University Library of Munich, Germany.
  4. Kronewetter, Jason & Saari, Donald G., 2008. "From decision problems to dethroned dictators," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 745-761, July.
  5. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, Elsevier, vol. 40(1), pages 1-39, July.
  6. Chichilnisky, Graciela, 1993. "Topoloy and economics: the contributions of S. Smale," MPRA Paper 8485, University Library of Munich, Germany.
  7. Alex Coram, 2008. "Social choice and information: a note on the calculus of mappings from utility spaces," UMASS Amherst Economics Working Papers, University of Massachusetts Amherst, Department of Economics 2008-04, .
  8. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
  9. repec:ebl:ecbull:v:3:y:2005:i:4:p:1-7 is not listed on IDEAS
  10. Alex Coram, 2006. "Social choice with a continuous ordering function," UMASS Amherst Economics Working Papers, University of Massachusetts Amherst, Department of Economics 2006-09, .
  11. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer, Springer, vol. 13(1), pages 11-16, January.
  12. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
  13. Chichilnisky, Graciela, 1985. "Von Neuman- Morgenstern utilities and cardinal preferences," MPRA Paper 8090, University Library of Munich, Germany.
  14. David Canning, 2007. "Valuing Lives Equally and Welfare Economics," PGDA Working Papers, Program on the Global Demography of Aging 2707, Program on the Global Demography of Aging.
  15. Ju, Biung-Ghi, 2004. "Continuous selections from the Pareto correspondence and non-manipulability in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 573-592, August.
  16. Luc Lauwers, 2009. "The topological approach to the aggregation of preferences," Social Choice and Welfare, Springer, Springer, vol. 33(3), pages 449-476, September.
  17. Chichilnisky, Graciela, 1990. "Social choice and the closed convergence topology," MPRA Paper 8353, University Library of Munich, Germany.

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