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A note on monotonic power indices, smaller coalitions, and new members

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  • Dominik Karos

    (University of Oxford)

Abstract

Brams’ paradox of new members and Shenoy’s paradox of smaller coalitions are, in a sense, equivalent. They are both implied by the monotonicity of a power index: while the first is exhibited on every simple game that is not strong, the latter can be observed on every simple game in which players are not almost symmetric. For the Shapley–Shubik index, this symmetry condition is not only necessary but also sufficient to avoid the paradox of smaller coalitions.

Suggested Citation

  • Dominik Karos, 2016. "A note on monotonic power indices, smaller coalitions, and new members," Theory and Decision, Springer, vol. 81(1), pages 89-100, June.
    • Handle: RePEc:kap:theord:v:81:y:2016:i:1:d:10.1007_s11238-015-9530-z
    DOI: 10.1007/s11238-015-9530-z
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    References listed on IDEAS

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    1. Dinko Dimitrov & Claus-Jochen Haake, 2008. "A note on the paradox of smaller coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 571-579, May.
    2. Karos, Dominik, 2014. "Coalition formation in general apex games under monotonic power indices," Games and Economic Behavior, Elsevier, vol. 87(C), pages 239-252.
    3. Dominik Karos, 2013. "Bargaining and Power," Working Papers 2013.63, Fondazione Eni Enrico Mattei.
    4. Sagonti, Emanuela, 1991. "On the Strong Monotonicity of Power Indices," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(1), pages 13-22.
    5. Karos, Dominik, 2013. "Bargaining and Power," Climate Change and Sustainable Development 156490, Fondazione Eni Enrico Mattei (FEEM).
    6. 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.
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