IDEAS home Printed from https://ideas.repec.org/a/spr/reecde/v26y2022i1d10.1007_s10058-021-00258-3.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10058-021-00258-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10058-021-00258-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Roberts, Fred S., 1991. "Characterizations of the plurality function," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 101-127, April.
    3. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2015. "Distance rationalization of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 345-377, September.
    4. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    5. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    6. 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.
    7. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Sanver, M. Remzi, 2008. "Nash implementability of the plurality rule over restricted domains," Economics Letters, Elsevier, vol. 99(2), pages 298-300, May.
    3. 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.
    4. 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).
    5. 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.
    6. Bock, Hans-Hermann & Day, William H. E. & McMorris, F. R., 1998. "Consensus rules for committee elections," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 219-232, May.
    7. Aleskerov, Fuad & Karabekyan, Daniel & Sanver, M. Remzi & Yakuba, Vyacheslav, 2012. "On the manipulability of voting rules: The case of 4 and 5 alternatives," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 67-73.
    8. Hiroki Saitoh, 2022. "Characterization of tie-breaking plurality rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(1), pages 139-173, July.
    9. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    10. Yuliya A. Veselova, 2020. "Does Incomplete Information Reduce Manipulability?," Group Decision and Negotiation, Springer, vol. 29(3), pages 523-548, June.
    11. Michael Müller, 2024. "Belief-independence and (robust) strategy-proofness," Theory and Decision, Springer, vol. 96(3), pages 443-461, May.
    12. 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.
    13. 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.
    14. Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    15. Bednay, Dezső & Moskalenko, Anna & Tasnádi, Attila, 2019. "Dictatorship versus manipulability," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 72-76.
    16. 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.
    17. James Green-Armytage, 2014. "Strategic voting and nomination," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 111-138, January.
    18. Dominique Lepelley & Boniface Mbih, 1997. "Strategic Manipulation in Committees Using the Plurality Rule: Alternative Concepts and Frequency Calculations," Group Decision and Negotiation, Springer, vol. 6(2), pages 119-138, March.
    19. Ivanov, A., 2022. "On the algorithms of exact estimations of manipulability of social choice rules for the case of 3 alternatives," Journal of the New Economic Association, New Economic Association, vol. 57(5), pages 14-23.
    20. Palash Dey & Y. Narahari, 2015. "Asymptotic Collusion-proofness of Voting Rules: The Case of Large Number of Candidates," Studies in Microeconomics, , vol. 3(2), pages 120-139, December.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:reecde:v:26:y:2022:i:1:d:10.1007_s10058-021-00258-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.