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On the manipulability of a class of social choice functions: plurality kth rules

Author

Listed:
  • Dezső Bednay

    (Corvinus University of Budapest)

  • Attila Tasnádi

    (Corvinus University of Budapest)

  • Sonal Yadav

    (Umea University)

Abstract

In this paper we introduce the plurality kth social choice function selecting an alternative, which is ranked kth in the social ranking following the number of top positions of alternatives in the individual ranking of voters. As special case the plurality 1st is the same as the well-known plurality rule. Concerning individual manipulability, we show that the larger k the more preference profiles are individually manipulable. We also provide maximal non-manipulable domains for the plurality kth rules. These results imply analogous statements on the single non-transferable vote rule. We propose a decomposition of social choice functions based on plurality kth rules, which we apply for determining non-manipulable subdomains for arbitrary social choice functions. We further show that with the exception of the plurality rule all other plurality kth rules are group manipulable, i.e. coordinated misrepresentation of individual rankings are beneficial for each group member, with an appropriately selected tie-breaking rule on the set of all profiles.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:reecde:v:26:y:2022:i:1:d:10.1007_s10058-021-00258-3
    DOI: 10.1007/s10058-021-00258-3
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    References listed on IDEAS

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    More about this item

    Keywords

    Voting rules; Dictatorship; Manipulability;
    All these keywords.

    JEL classification:

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

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