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A Unifying Impossibility Theorem for Compact Metricsocial Alternatives Space

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Abstract

In Man and Takayama (2013) (henceforth MT) we show that many classical impossibility theorems follow from three simple and intuitive axioms on the social choice correspondence when the set of social alternatives is finite. This note extends the main theorem (Theorem 1) in MT to the case where the set of social alternatives is a compact metric space. We also qualify how versions of Arrow's Impossibility Theorem and the Muller-Satterthwaite Theorem (Muller and Satterthwaite, 1977) can be obtained as corollaries of the extended main theorem. A generalized statement of the Muller-Satterthwaite Theorem for social choice correspondences with weak preferences on a compact metric social alternatives domain under a modified definition of Monotonicity is given. To the best of our knowledge, this is the first paper to document this version of the Muller-Satterthwaite Theorem. This note is mainly technical. Readers interested in the motivations and discussions of our axioms and main theorem should consult MT.

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  • Priscilla Man & Shino Takayama, 2013. "A Unifying Impossibility Theorem for Compact Metricsocial Alternatives Space," Discussion Papers Series 477, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uq2004:477
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    File URL: https://economics.uq.edu.au/files/45773/477.pdf
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    1. Mehta, Ghanshyam, 1977. "Topological Ordered Spaces and Utility Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 779-782, October.
    2. Priscilla Man & Shino Takayama, 2013. "A unifying impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 249-271, October.
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    Cited by:

    1. Paul Frijters & Benno Torgler & Brendan Markey-Towler, 2016. "On the Problem of Constructing Rational Preferences," The Economic Record, The Economic Society of Australia, vol. 92, pages 68-82, June.
    2. Priscilla Man & Shino Takayama, 2013. "A unifying impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 249-271, October.

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    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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