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Power in plurality games

Author

Listed:
  • René Van den Brink

    (Department of Economics and Tinbergen Institute - VU University)

  • Dinko Dimitrov

    (Saarland University)

  • Agnieszka Rusinowska

    (Centre d'Economie de la Sorbonne, CNRS - Université Paris 1 Panthéon-Sorbonne, Paris School of Economics)

Abstract

Simple games in partition function form are used to model voting situations where a coalition being winning or losing might depend on the way players outside that coalition organize themselves. Such a game is called a plurality voting game if in every partition there is at least one winning coalition. In the present paper, we introduce a power index for this class of voting games and provide an axiomatic characterization. This power index is based on equal weight for every partition, equal weight for every winning coalition in a partition, and equal weight for each player in a winning coalition. Since some of the axioms we develop are conditioned on the power impact of losing coalitions becoming winning in a partition, our characterization heavily depends on a new result showing the existence of such elementary transitions between plurality voting games in terms of single embedded winning coalitions. The axioms restrict then the impact of such elementary transitions on the power of different types of players

Suggested Citation

  • René Van den Brink & Dinko Dimitrov & Agnieszka Rusinowska, 2024. "Power in plurality games," Documents de travail du Centre d'Economie de la Sorbonne 24014, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:24014
    as

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    File URL: http://mse.univ-paris1.fr/pub/mse/CES2024/24014.pdf
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    References listed on IDEAS

    as
    1. Grabisch, Michel & Funaki, Yukihiko, 2012. "A coalition formation value for games in partition function form," European Journal of Operational Research, Elsevier, vol. 221(1), pages 175-185.
    2. René Brink & Dinko Dimitrov & Agnieszka Rusinowska, 2021. "Winning coalitions in plurality voting democracies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 509-530, April.
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    6. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 175-186.
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    8. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
    9. J. M. Alonso-Meijide & M. Álvarez-Mozos & M. G. Fiestras-Janeiro, 2017. "Power Indices and Minimal Winning Coalitions for Simple Games in Partition Function Form," Group Decision and Negotiation, Springer, vol. 26(6), pages 1231-1245, November.
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    More about this item

    Keywords

    axiomatization; power index; plurality game; winning coalition;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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