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Topological aggregation of preferences: the case of a continuum of agents

Author

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  • E. IndurÂin

    (Departmento de MatemÂtica e InformÂtica, Universidad Pßblica de Navarra, Campus ArrosadÎa s.n., E-31006 Pamplona, Spain)

  • J. C. Candeal

    (Departamento de AnÂlisis EconÕmico, Universidad de Zaragoza, Doctor Cerrada 1 y 3, E-50005 Zaragoza, Spain)

  • G. Chichilnisky

    (Department of Economics, Columbia University, 405 Law Memorial Library, New York, NY 10027, USA)

Abstract

This paper studies the topological approach to social choice theory initiated by G. Chichilnisky (1980), extending it to the case of a continuum of agents. The social choice rules are continuous anonymous maps defined on preference spaces which respect unanimity. We establish that a social choice rule exists for a continuum of agents if and only if the space of preferences is contractible. We provide also a topological characterization of such rules as generalized means or mathematical expectations of individual preferences.

Suggested Citation

  • E. IndurÂin & J. C. Candeal & G. Chichilnisky, 1997. "Topological aggregation of preferences: the case of a continuum of agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 333-343.
  • Handle: RePEc:spr:sochwe:v:14:y:1997:i:2:p:333-343 Note: Received: 30 November 1994/Accepted: 22 April 1996
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    References listed on IDEAS

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    1. Dan S. Felsenthal & MoshÚ Machover, 2004. "Qualified Majority Voting Explained," Homo Oeconomicus, Institute of SocioEconomics, vol. 21, pages 573-576.
    2. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    3. Algaba, E. & Bilbao, J. M. & Fernandez Garcia, J. R. & Lopez, J. J., 2003. "Computing power indices in weighted multiple majority games," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 63-80, August.
    4. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    5. Chang, Pao-Li & Chua, Vincent C.H. & Machover, Moshe, 2006. "L S Penrose's limit theorem: Tests by simulation," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 90-106, January.
    6. Thomas Stratmann & Martin Baur, 2002. "Plurality Rule, Proportional Representation, and the German Bundestag: How Incentives to Pork-Barrel Differ Across Electoral Systems," CESifo Working Paper Series 650, CESifo Group Munich.
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    Cited by:

    1. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    2. Remy Oddou, 2017. "Welfarism and segregation in endogenous jurisdiction formation models," EconomiX Working Papers 2017-43, University of Paris Nanterre, EconomiX.

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