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Non-manipulable domains for the Borda count

Author

Listed:
  • Martin Barbie
  • Clemens Puppe
  • Attila Tasnádi

Abstract

We characterize the preference domains on which the Borda count satisfies Arrow’s “independence of irrelevant alternatives” condition. Under a weak richness condition, these domains are obtained by fixing one preference ordering and including all its cyclic permutations (“Condorcet cycles”). We then ask on which domains the Borda count is non-manipulable. It turns out that it is non-manipulable on a broader class of domains when combined with appropriately chosen tie-breaking rules. On the other hand, we also prove that the rich domains on which the Borda count is non-manipulable for all possible tie-breaking rules are again the cyclic permutation domains. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Martin Barbie & Clemens Puppe & Attila Tasnádi, 2006. "Non-manipulable domains for the Borda count," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 411-430, January.
    • Handle: RePEc:spr:joecth:v:27:y:2006:i:2:p:411-430
    DOI: 10.1007/s00199-004-0603-4
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    Cited by:

    1. Kentaro Hatsumi & Dolors Berga & Shigehiro Serizawa, 2014. "A maximal domain for strategy-proof and no-vetoer rules in the multi-object choice model," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 153-168, February.
    2. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    3. Krzysztof Kontek & Honorata Sosnowska, 2020. "Specific Tastes or Cliques of Jurors? How to Reduce the Level of Manipulation in Group Decisions?," Group Decision and Negotiation, Springer, vol. 29(6), pages 1057-1084, December.
    4. Ollár, Mariann, 2010. "Monotonicity and robustness of majority rule," Economics Letters, Elsevier, vol. 107(2), pages 288-290, May.
    5. Bandhu, Sarvesh & Mondal, Bishwajyoti & Pramanik, Anup, 2022. "Strategy-proofness of the unanimity with status-quo rule over restricted domains," Economics Letters, Elsevier, vol. 210(C).
    6. Dany R. DOMBOU T., 2017. "How Borda voting rule can respect Arrow IIA and avoid cloning manipulation," Journal of Economics Bibliography, KSP Journals, vol. 4(3), pages 234-243, September.
    7. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 151-162, June.
    8. Michael Müller, 2024. "Belief-independence and (robust) strategy-proofness," Theory and Decision, Springer, vol. 96(3), pages 443-461, May.
    9. Pongou, Roland & Tchantcho, Bertrand, 2021. "Round-robin political tournaments: Abstention, truthful equilibria, and effective power," Games and Economic Behavior, Elsevier, vol. 130(C), pages 331-351.
    10. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 461-471, June.
    11. Sanver, M. Remzi, 2008. "Nash implementability of the plurality rule over restricted domains," Economics Letters, Elsevier, vol. 99(2), pages 298-300, May.
    12. Clemens Puppe & Attila Tasnádi, 2008. "Nash implementable domains for the Borda count," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 367-392, October.
    13. Christian Basteck, 2022. "Characterising scoring rules by their solution in iteratively undominated strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 161-208, July.
    14. Csóka, Péter & Kondor, Gábor, 2019. "Delegációk igazságos kiválasztása társadalmi választások elméletével [Choosing a fair delegation by social choice theory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 771-787.
    15. Dezső Bednay & Attila Tasnádi & Sonal Yadav, 2022. "On the manipulability of a class of social choice functions: plurality kth rules," Review of Economic Design, Springer;Society for Economic Design, vol. 26(1), pages 127-148, March.

    More about this item

    Keywords

    Voting; Borda count; Strategy-proofness; Restricted domains.;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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