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Manipulability measures of common social choice functions

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  • David A. Smith

    (1750 Mission Street #43, San Francisco, CA 94103, USA)

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    Abstract

    All social choice functions are manipulable when more than two alternatives are available. I evaluate the manipulability of the Borda count, plurality rule, minimax set, and uncovered set. Four measures of manipulability are defined and computed stochastically for small numbers of agents and alternatives. Social choice rules derived from the minimax and uncovered sets are found to be relatively immune to manipulation whether a sole manipulating agent has complete knowledge or absolutely no knowledge of the preferences of the others. The Borda rule is especially manipulable if the manipulating agent has complete knowledge of the others.

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    Bibliographic Info

    Article provided by Springer in its journal Social Choice and Welfare.

    Volume (Year): 16 (1999)
    Issue (Month): 4 ()
    Pages: 639-661

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    Handle: RePEc:spr:sochwe:v:16:y:1999:i:4:p:639-661

    Note: Received: 5 January 1996/Accepted: 31 July 1998
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    Cited by:
    1. Marc Vorsatz, 2004. "Scoring Rules on Dichotomous Preferences," UFAE and IAE Working Papers 617.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    2. Fuad Aleskerov & Daniel Karabekyan & M. Sanver & Vyacheslav Yakuba, 2011. "An individual manipulability of positional voting rules," SERIEs, Spanish Economic Association, vol. 2(4), pages 431-446, December.
    3. James Schummer, 1999. "Almost-dominant Strategy Implementation," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1278, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Wonki Jo Cho, 2013. "Impossibility Results for Parametrized Notions of Efficiency and Strategyproofness in Exchange Economies," The School of Economics Discussion Paper Series, Economics, The University of Manchester 1314, Economics, The University of Manchester.
    5. Mostapha Diss, 2013. "Strategic manipulability of self-­selective social choice rules," Working Papers halshs-00785366, HAL.
    6. Aki Lehtinen, 2007. "The Borda rule is also intended for dishonest men," Public Choice, Springer, vol. 133(1), pages 73-90, October.
    7. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer, vol. 39(3), pages 461-471, June.
    8. Green-Armytage, James, 2011. "Strategic voting and nomination," MPRA Paper 32200, University Library of Munich, Germany.
    9. Aki Lehtinen, 2007. "The Welfare Consequences of Strategic Voting in Two Commonly Used Parliamentary Agendas," Theory and Decision, Springer, vol. 63(1), pages 1-40, August.
    10. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.
    11. Schummer, James, 2004. "Almost-dominant strategy implementation: exchange economies," Games and Economic Behavior, Elsevier, vol. 48(1), pages 154-170, July.
    12. Mostapha Diss, 2013. "Strategic manipulability of self-selective social choice rules," Working Papers, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure 1302, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
    13. Yager, Ronald R., 2002. "Defending against strategic manipulation in uninorm-based multi-agent decision making," European Journal of Operational Research, Elsevier, Elsevier, vol. 141(1), pages 217-232, August.
    14. Pritchard, Geoffrey & Wilson, Mark C., 2009. "Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 35-57, July.
    15. Donald Campbell & Jerry Kelly, 2009. "Gains from manipulating social choice rules," Economic Theory, Springer, vol. 40(3), pages 349-371, September.

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