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Strategy-proofness and unimodality in bounded distributive lattices

  • Ernesto Savaglio

    ()

  • 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 Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    2. G. Chichilnisky & G. M. Heal, 1997. "The geometry of implementation: a necessary and sufficient condition for straightforward games (*)," Social Choice and Welfare, Springer, vol. 14(2), pages 259-294.
    3. 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).
    4. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    5. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
    6. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Monjardet, B., 1990. "Arrowian characterizations of latticial federation consensus functions," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 51-71, August.
    12. James Schummer & Rakesh V. Vohra, 1999. "Strategy-proof Location on a Network," Discussion Papers 1253, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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