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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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  • Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
  • Handle: RePEc:eee:jetheo:v:31:y:1983:i:1:p:68-87
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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. repec:ebl:ecbull:v:3:y:2005:i:4:p:1-7 is not listed on IDEAS
    4. 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.
    5. Chichilnisky, Graciela, 1990. "Social choice and the closed convergence topology," MPRA Paper 8353, University Library of Munich, Germany.
    6. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    7. 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.
    8. David Canning, 2007. "Valuing Lives Equally and Welfare Economics," PGDA Working Papers 2707, Program on the Global Demography of Aging.
    9. Graciela Chichilnisky, 1985. "Von Neumann-Morgenstern Utilities and Cardinal Preferences," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 633-641, November.
    10. David Canning, 2013. "Axiomatic Foundations For Cost‐Effectiveness Analysis," Health Economics, John Wiley & Sons, Ltd., vol. 22(12), pages 1405-1416, December.
    11. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    12. 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.
    13. 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.
    14. Luc Lauwers, 2002. "A note on Chichilnisky's social choice paradox," Theory and Decision, Springer, vol. 52(3), pages 261-266, May.
    15. Andrea Attar & Thomas Mariotti & François Salanié, 2019. "On a class of smooth preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 37-57, May.
    16. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    17. Alex Coram, 2006. "Social choice with a continuous ordering function," UMASS Amherst Economics Working Papers 2006-09, University of Massachusetts Amherst, Department of Economics.
    18. Crespo, Juan A. & Sanchez-Gabites, J.J, 2016. "Solving the Social Choice problem under equality constraints," MPRA Paper 72757, University Library of Munich, Germany.
    19. Weinberger, Shmuel, 2004. "On the topological social choice model," Journal of Economic Theory, Elsevier, vol. 115(2), pages 377-384, April.
    20. A. Georges L. Romme, 2004. "Unanimity Rule and Organizational Decision Making: A Simulation Model," Organization Science, INFORMS, vol. 15(6), pages 704-718, December.
    21. Greenfield, Mark & Zhang, Jun, 2018. "Null preference and the resolution of the topological social choice paradox," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 47-51.
    22. 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.
    23. 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.
    24. Chichilnisky, Graciela, 1993. "Topoloy and economics: the contributions of S. Smale," MPRA Paper 8485, University Library of Munich, Germany.

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    • 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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