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Unimodality and equivalence of simple and coalitional strategy-proofness in convex idempotent interval spaces

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  • Stefano vannucci

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    Abstract

    It is shown that simple and coalitional strategy-proofness of a voting rule as defi?ned on the full unimodal domain of a convex idempotent interval space (X; I) are equivalent properties if (X; I) satis?es interval anti-exchange, a basic property also shared by a large class of convex geometries including -but not reducing to- trees and linear geometries. Therefore, strategy-proof location problems in a vast class of networks fall under the scope of that statement. It is also established that a much weaker minimal anti-exchange property is necessary to ensure equivalence of simple and coalitional strategy-proofness in that setting. An immediate corollary to that result is that such ?unimodal?equivalence fails to hold both in certan median interval spaces including those induced by bounded median semilattices that are not chains, and in certain non-median interval spaces including those induced by Hamming graphs and partial cubes.

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    Paper provided by Department of Economics, University of Siena in its series Department of Economics University of Siena with number 668.

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    Date of creation: Dec 2012
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    Handle: RePEc:usi:wpaper:668

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    1. Le Breton, Michel & Zaporozhets, Vera, 2006. "On the Equivalence of Coalitional and Individual Strategy-Proofness Properties," IDEI Working Papers 408, Institut d'Économie Industrielle (IDEI), Toulouse.
    2. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    3. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    4. Danilov, Vladimir I., 1994. "The structure of non-manipulable social choice rules on a tree," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 123-131, April.
    5. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    6. Ernesto Savaglio & Stefano Vannucci, 2012. "Strategy-proofness and unimodality in bounded distributive lattices," Department of Economics University of Siena 642, Department of Economics, University of Siena.
    7. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
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    Cited by:
    1. Ernesto Savaglio & Stefano Vannucci, 2014. "Strategy-proofness and single-peackedness in bounded distributive lattices," Papers 1406.5120, arXiv.org.

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