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Power Indices and Minimal Winning Coalitions for Simple Games in Partition Function Form

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  • J. M. Alonso-Meijide

    (Universidade de Santiago de Compostela)

  • M. Álvarez-Mozos

    (Universitat de Barcelona)

  • M. G. Fiestras-Janeiro

    (Universidade de Vigo)

Abstract

We propose a generalization of simple games to partition function form games based on a monotonicity property that we define in this context. This property allows us to properly speak about minimal winning embedded coalitions. We propose and characterize two power indices based on such coalitions. Finally, the new indices are used to study the distribution of power in the Parliament of Andalusia that emerged after the elections of March 22, 2015.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:26:y:2017:i:6:d:10.1007_s10726-017-9542-x
    DOI: 10.1007/s10726-017-9542-x
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    References listed on IDEAS

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    Cited by:

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    2. G. Arévalo-Iglesias & M. Álvarez-Mozos, 2020. "Power distribution in the Basque Parliament using games with externalities," Theory and Decision, Springer, vol. 89(2), pages 157-178, September.
    3. Saavedra–Nieves, Alejandro & Casas–Méndez, Balbina, 2023. "On the centrality analysis of covert networks using games with externalities," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1365-1378.
    4. Josep Freixas & Montserrat Pons, 2021. "An Appropriate Way to Extend the Banzhaf Index for Multiple Levels of Approval," Group Decision and Negotiation, Springer, vol. 30(2), pages 447-462, April.

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