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Generic impossibility of Arrow’s impossibility theorem

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  • Noguchi, Mitsunori
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    Abstract

    Our major objective is to show that if there are infinitely many alternatives and society can be decomposed into the sum of two non-negligible coalitions, the set of all Arrovian collective choice rules that satisfy the ultrafilter property (its set of decisive coalitions form an ultrafilter), is nowhere dense in the set of all Arrovian collective choice rules. This result entails that (1) almost all Arrovian collective choice rules are non-dictatorial and (2) in any neighborhood of a dictatorial Arrovian collective choice rule, a nondictatorial Arrovian collective choice rule can be found, i.e., the property of admitting a dictator is not a locally stable property for Arrovian collective choice rules in the sense that the property does not withstand a small perturbation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 4-5 ()
    Pages: 391-400

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:391-400

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Arrow’s impossibility theorem; Social welfare function; Collective choice rule; Filter; Ultrafilter;

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    1. Bossert, Walter & Suzumura, Kotaro, 2009. "Consistency, Choice and Rationality," PIE/CIS Discussion Paper 428, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    2. Campbell, Donald E., 1990. "Intergenerational social choice without the Pareto principle," Journal of Economic Theory, Elsevier, vol. 50(2), pages 414-423, April.
    3. Campbell, Donald E & Kelly, Jerry S, 1996. "Arrovian Social Choice Correspondences," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 803-23, November.
    4. James Redekop, 1996. "Arrow theorems in mixed goods, stochastic, and dynamic economic environments," Social Choice and Welfare, Springer, vol. 13(1), pages 95-112, January.
    5. Blair, Douglas H. & Bordes, Georges & Kelly, Jerry S. & Suzumura, Kotaro, 1976. "Impossibility theorems without collective rationality," Journal of Economic Theory, Elsevier, vol. 13(3), pages 361-379, December.
    6. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer, vol. 26(1), pages 211-215, 07.
    7. Redekop, James, 1991. "Social welfare functions on restricted economic domains," Journal of Economic Theory, Elsevier, vol. 53(2), pages 396-427, April.
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