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Strategy-proofness and unimodality in bounded distributive lattices

  • Ernesto Savaglio

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  • Stefano Vannucci

    ()

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    It is shown that a social choice rule f : X N ? X as defined on a bounded distributive lattice (X, ) is strategy-proof on the set of all profiles of unimodal total preorders on X if and only if it can be represented as an iterated median of projections and constants. The equivalence of individual and coalitional strategy-proofness that is known to hold in more specialized unimodal domains fails in such a more general setting.

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    File URL: http://www.econ-pol.unisi.it/quaderni/642.pdf
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    Paper provided by Department of Economics, University of Siena in its series Department of Economics University of Siena with number 642.

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    Date of creation: Jun 2012
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    Handle: RePEc:usi:wpaper:642
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    1. Barbera, S. & Masso, J. & Neme, A., 1992. "Voting Under Constraints," UFAE and IAE Working Papers 200.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    2. 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.
    3. Heal, G.M. & Chichilnisky, G., 1995. "The Geometry of Implementation: A Necessary and Sufficient Condition for Straightforward Games," Papers 95-22, Columbia - Graduate School of Business.
    4. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    5. Monjardet, B., 1990. "Arrowian characterizations of latticial federation consensus functions," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 51-71, August.
    6. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    7. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Individual versus group strategy-proofness: when do they coincide?," UFAE and IAE Working Papers 761.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    8. Michel Breton & Vera Zaporozhets, 2009. "On the equivalence of coalitional and individual strategy-proofness properties," Social Choice and Welfare, Springer, vol. 33(2), pages 287-309, August.
    9. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    10. 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.
    11. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    12. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 153-70, January.
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