IDEAS home Printed from https://ideas.repec.org/p/ema/worpap/2011-17.html

On the Likelihood of Dummy players in Weighted Majority Games

Author

Listed:
  • Fabrice Barthelemy

    (THEMA, Universite de Cergy-Pontoise)

  • Dominique Lepelley

    (CEMOI,universite de la réunion)

  • Mathieu Martin

    (THEMA, Universite de Cergy-Pontoise)

Abstract

When the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to investigate the conditions that give rise to such a phenomenon and to compute its likelihood. It is shown that the probability of having a dummy player is surprisingly high and some paradoxical results are observed.

Suggested Citation

  • Fabrice Barthelemy & Dominique Lepelley & Mathieu Martin, 2011. "On the Likelihood of Dummy players in Weighted Majority Games," Thema Working Papers 2011-17, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    • Handle: RePEc:ema:worpap:2011-17
    as

    Download full text from publisher

    File URL: https://thema-cergy.eu/repec/pdf/2011-17.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Boratyn, Daria & Kirsch, Werner & Słomczyński, Wojciech & Stolicki, Dariusz & Życzkowski, Karol, 2020. "Average weights and power in weighted voting games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 90-99.
    2. Zineb Abidi & Matthieu Leprince & Vincent Merlin, 2020. "Power Inequality in Inter-communal Structures: The Simulated Impact of a Reform in the Case of the Municipalities in Western France," Post-Print halshs-02996998, HAL.
    3. Fabrice Barthelemy & Dominique Lepelley & Mathieu Martin & Hatem Smaoui, 2021. "Dummy Players and the Quota in Weighted Voting Games," Group Decision and Negotiation, Springer, vol. 30(1), pages 43-61, February.
    4. Dominique Lepelley & Vincent R Merlin & Jean-louis Rouet & Laurent Vidu, 2014. "Referendum paradox in a federal union with unequal populations: the three state case," Economics Bulletin, AccessEcon, vol. 34(4), pages 2201-2207.
    5. Sylvain Béal & Marc Deschamps & Mostapha Diss & Issofa Moyouwou, 2022. "Inconsistent weighting in weighted voting games," Public Choice, Springer, vol. 191(1), pages 75-103, April.
    6. Fabrice Barthélémy & Mathieu Martin, 2021. "Dummy Players and the Quota in Weighted Voting Games: Some Further Results," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 299-315, Springer.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ema:worpap:2011-17. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Lisa Collin (email available below). General contact details of provider: https://edirc.repec.org/data/themafr.html .

    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.