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The power of the largest player

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  • Kurz, Sascha

Abstract

Decisions in a shareholder meeting or a legislative committee are often modeled as a weighted game. Influence of a member is then measured by a power index. A large variety of different indices has been introduced in the literature. This paper analyzes how power indices differ with respect to the largest possible power of a non-dictatorial player. It turns out that the considered set of power indices can be partitioned into two classes. This may serve as another indication which index to use in a given application.

Suggested Citation

  • Kurz, Sascha, 2018. "The power of the largest player," Economics Letters, Elsevier, vol. 168(C), pages 123-126.
    • Handle: RePEc:eee:ecolet:v:168:y:2018:i:c:p:123-126
    DOI: 10.1016/j.econlet.2018.04.034
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    References listed on IDEAS

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    1. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    2. De, Anindya & Diakonikolas, Ilias & Servedio, Rocco A., 2017. "The Inverse Shapley value problem," Games and Economic Behavior, Elsevier, vol. 105(C), pages 122-147.
    3. Sascha Kurz & Nicola Maaser & Stefan Napel, 2017. "On the Democratic Weights of Nations," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1599-1634.
    4. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    5. Sascha Kurz, 2016. "The inverse problem for power distributions in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 65-88, June.
    6. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Noga Alon & Paul Edelman, 2010. "The inverse Banzhaf problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 371-377, March.
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    More about this item

    Keywords

    Power measurement; Weighted games;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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