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Homotopy properties of Pareto aggregation rules

Author

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  • Gleb Koshevoy

    (Russian Academy of Sciences, Central Economics and Mathematics Institute Krasikova 32, Moscow 117418, Russia)

Abstract

We establish that the Pareto property is inconsistent with non-dictatorship for social choice rules defined on two-dimensional choice spaces. In addition, we consider applications of this result in higher dimensions. We also establish the existence of Pareto rules with infinite populations, and show that in this case there is a strong manipulator.

Suggested Citation

  • Gleb Koshevoy, 1997. "Homotopy properties of Pareto aggregation rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 295-302.
  • Handle: RePEc:spr:sochwe:v:14:y:1997:i:2:p:295-302
    Note: Received: 30 December 1994/Accepted: 22 April 1996
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    Cited by:

    1. Yasuhito Tanaka, 2005. "On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem (forthcoming in ``Applied Mathematics and Computation''(Elsevier))," Public Economics 0506012, University Library of Munich, Germany, revised 17 Jun 2005.
    2. Kari Saukkonen, 2007. "Continuity of social choice functions with restricted coalition algebras," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 637-647, June.
    3. 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.
    4. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    5. Yasuhito Tanaka, 2005. "A topological approach to the Arrow impossibility theorem when individual preferences are weak orders (forcoming in ``Applied Mathematics and Compuation''(Elsevier))," Public Economics 0506013, University Library of Munich, Germany, revised 17 Jun 2005.
    6. Yasuhito Tanaka, 2005. "A topological proof of Eliaz's unified theorem of social choice theory (forthcoming in "Applied Mathematics and Computation")," Public Economics 0510021, University Library of Munich, Germany, revised 26 Oct 2005.
    7. Baryshnikov, Yuliy M., 2000. "On isotopic dictators and homological manipulators," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 123-134, February.
    8. Tanaka, Yasuhito, 2007. "A topological approach to Wilson's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 184-191, February.

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