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Stable Coalition Structures and Power Indices for Majority Voting

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  • Takaaki Abe

    (School of Political Science and Economics, Waseda University)

Abstract

An (n,k)-game is a voting game in which each player has exactly one vote, and decisions are made by at least k affirmative votes of the n players. A power index is a measure of the a priori power of the n voters. The purpose of this paper is to show what axioms of power indices generate stable coalition structures for each (n,k)-game. Using the stability notion of the core, we show that a coalition structure containing a minimal winning coalition is stable for a wide range of general power indices satisfying a set of axioms, such as the Shapley-Shubik, Banzhaf, normalized Banzhaf, and Deegan-Packel power indices. Moreover, we also show that a coalition structure that represents a two-party system can be stable if the two large parties are close enough in size. Some unstable coalition structures are also analyzed.

Suggested Citation

  • Takaaki Abe, 2020. "Stable Coalition Structures and Power Indices for Majority Voting," Working Papers 2015, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:2015
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    References listed on IDEAS

    as
    1. Takaaki Abe & Yukihiko Funaki, 2017. "The non-emptiness of the core of a partition function form game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 715-736, August.
    2. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    3. Bloch, Francis & van den Nouweland, Anne, 2014. "Expectation formation rules and the core of partition function games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 339-353.
    4. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    5. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 157-171.
    6. Xue, Licun, 1997. "Nonemptiness of the Largest Consistent Set," Journal of Economic Theory, Elsevier, vol. 73(2), pages 453-459, April.
    7. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 567-582.
    8. Takaaki Abe, 2018. "Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness," Theory and Decision, Springer, vol. 85(3), pages 353-374, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    coalition structure; core; majority voting; power index;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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