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Symmetry vs. complexity in proving the Muller-Satterthwaite theorem

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  • Uuganbaatar Ninjbat

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    (Department of Economics, Stockholm School of Economics)

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    Abstract

    In this short note, we first provide two rather straightforward proofs for the Muller - Satterthwaite theorem in the baseline cases of 2 person 3 alternatives, and 2 person n ≥ 3 alternatives. We also show that it suffices to prove the result in the special case of 3 alternatives (with arbitrary N individuals) as it then can easily be extended to the general case. We then prove the result in the decisive case of 3 alternatives (with arbitrary N individuals) by induction on N.

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    File URL: http://www.accessecon.com/Pubs/EB/2012/Volume32/EB-12-V32-I2-P137.pdf
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    Bibliographic Info

    Article provided by AccessEcon in its journal Economics Bulletin.

    Volume (Year): 32 (2012)
    Issue (Month): 2 ()
    Pages: 1434-1441

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    Handle: RePEc:ebl:ecbull:eb-11-00813

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    Related research

    Keywords: the Muller-Satterthwaite Theorem; Monotone social choice functions;

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    1. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    2. Bettina Klaus & Olivier Bochet, 2010. "The Relation between Monotonicity and Strategy-Proofness," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 10.01, Université de Lausanne, Faculté des HEC, DEEP.
    3. Miller, Michael K., 2009. "Social choice theory without Pareto: The pivotal voter approach," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 251-255, September.
    4. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
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