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Social choice and the topology of spaces of preferences

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  • Chichilnisky, Graciela

Abstract

Social choice theory is concerned with providing a rationale for social decisions when individuals have diverse opinions. Voting is an obvious way in which societies aggregate individual preferences to obtain social ones. The procedure of voting registers individual comparisons between alternatives, called ordinal preferences, rather than intensities of preferences among these alternatives, called cardinal preferences, and this is one source of so-called paradox of social choice. It is the purpose of this paper to study the paradox of social choice and to show that it arises, in part, because of the topological structure of spaces of ordinal preferences.

Suggested Citation

  • Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:8006
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    File URL: https://mpra.ub.uni-muenchen.de/8006/1/MPRA_paper_8006.pdf
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    Citations

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    Cited by:

    1. Baryshnikov, Yuliy M., 2000. "On isotopic dictators and homological manipulators," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 123-134, February.
    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. Andrea Beltratti & Graciela Chichilnisky & Geoffrey Heal, 1993. "Sustainable Growth and the Green Golden Rule," NBER Working Papers 4430, National Bureau of Economic Research, Inc.
    5. repec:ebl:ecbull:v:3:y:2005:i:4:p:1-7 is not listed on IDEAS
    6. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    7. Tanaka, Yasuhito, 2009. "On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem when individual preferences are weak orders," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 241-249, March.
    8. Chichilnisky, Graciela, 1990. "General equilibrium and social choice with increasing returns," MPRA Paper 8124, University Library of Munich, Germany.
    9. Weinberger, Shmuel, 2004. "On the topological social choice model," Journal of Economic Theory, Elsevier, vol. 115(2), pages 377-384, April.
    10. Chichilnisky, Graciela, 1986. "Topological complexity of manifolds of preferences," MPRA Paper 8119, University Library of Munich, Germany.
    11. 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.
    12. Graciela Chichilnisky, 1990. "On The Mathematical Foundations Of Political Economy," Contributions to Political Economy, Oxford University Press, vol. 9(1), pages 25-41.
    13. Luigi Marengo & Simona Settepanella, 2010. "Social choice among complex objects," LEM Papers Series 2010/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    14. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    15. Maurice Salles, 2014. "‘Social choice and welfare’ at 30: its role in the development of social choice theory and welfare economics," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 1-16, 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 & 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.
    18. Vicki Knoblauch, 2015. "Two preference metrics provide settings for the study of properties of binary relations," Theory and Decision, Springer, vol. 79(4), pages 615-625, December.
    19. Tanaka, Yasuhito, 2007. "A topological approach to Wilson's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 184-191, February.
    20. repec:spr:sochwe:v:48:y:2017:i:4:d:10.1007_s00355-017-1032-1 is not listed on IDEAS
    21. Daniela Bubboloni & Michele Gori, 2014. "Anonymous and neutral majority rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 377-401, August.
    22. repec:spr:series:v:9:y:2018:i:3:d:10.1007_s13209-018-0182-4 is not listed on IDEAS
    23. 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

    preferences; social choice; individual preference; social preference; topological structure; topology; ordinal preferences; cardinal preferences;

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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