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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.

Suggested Citation

  • Chichilnisky, Graciela & Heal, Geoffrey, 1979. "Necessary and sufficient conditions for a resolution of the social choice paradox," MPRA Paper 8495, University Library of Munich, Germany, revised 20 Oct 1981.
  • Handle: RePEc:pra:mprapa:8495
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    References listed on IDEAS

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    1. 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.
    2. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, Oxford University Press, vol. 97(2), pages 337-352.
    3. 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.
    4. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 89(3), pages 456-469.
    5. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Community preferences and social choice," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 33-61, September.
    6. 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.
    7. 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.
    8. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
    9. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    10. Graciela Chichilnisky & Geoffrey Heal, 1997. "Social choice with infinite populations: construction of a rule and impossibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 303-318.
    11. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    12. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    13. 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.
    14. Maurice Salles, 2005. "Social Choice," Post-Print halshs-00337075, HAL.
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    Citations

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    Cited by:

    1. 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.
    2. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
    3. Graciela Chichilnisky, 1985. "Von Neumann-Morgenstern Utilities and Cardinal Preferences," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 633-641, November.
    4. repec:ebl:ecbull:v:3:y:2005:i:4:p:1-7 is not listed on IDEAS
    5. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 11-16, January.
    6. Chichilnisky, Graciela, 1990. "Social choice and the closed convergence topology," MPRA Paper 8353, University Library of Munich, Germany.
    7. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    8. Alex Coram, 2006. "Social choice with a continuous ordering function," UMASS Amherst Economics Working Papers 2006-09, University of Massachusetts Amherst, Department of Economics.
    9. Luc Lauwers, 2009. "The topological approach to the aggregation of preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 449-476, September.
    10. David Canning, 2007. "Valuing Lives Equally and Welfare Economics," PGDA Working Papers 2707, Program on the Global Demography of Aging.
    11. Crespo, Juan A. & Sanchez-Gabites, J.J, 2016. "Solving the Social Choice problem under equality constraints," MPRA Paper 72757, University Library of Munich, Germany.
    12. David Canning, 2013. "Axiomatic Foundations For Cost‐Effectiveness Analysis," Health Economics, John Wiley & Sons, Ltd., vol. 22(12), pages 1405-1416, December.
    13. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    14. Weinberger, Shmuel, 2004. "On the topological social choice model," Journal of Economic Theory, Elsevier, vol. 115(2), pages 377-384, April.
    15. Graciela Chichilnisky, 1996. "A robust theory of resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 1-10, January.
    16. 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.
    17. Chichilnisky, Graciela, 1996. "Limited arbitrage is necessary and sufficient for the non-emptiness of the core," Economics Letters, Elsevier, vol. 52(2), pages 177-180, August.
    18. Alex Coram, 2008. "Social choice and information: a note on the calculus of mappings from utility spaces," UMASS Amherst Economics Working Papers 2008-04, University of Massachusetts Amherst, Department of Economics.
    19. Chichilnisky, Graciela, 1993. "Topoloy and economics: the contributions of S. Smale," MPRA Paper 8485, University Library of Munich, Germany.
    20. Luc Lauwers, 2002. "A note on Chichilnisky's social choice paradox," Theory and Decision, Springer, vol. 52(3), pages 261-266, May.

    More about this item

    Keywords

    social choice; preferences; mathematical modeling;

    JEL classification:

    • O25 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Industrial Policy
    • O24 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Trade Policy; Factor Movement; Foreign Exchange Policy
    • O22 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Project Analysis

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