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The Owen and Shapley spatial power indices: A comparison and a generalization

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  • Martin, Mathieu
  • Nganmeni, Zephirin
  • Tchantcho, Bertrand

Abstract

Spatial games take into account the position of any voter in the space. In this class of games, two main indices of political power were defined. The first by Owen (1971) and the second, by Shapley (1977), later on extended in a two-dimensional space by Owen and Shapley (1989). We propose a generalization of Owen index. We show that the method proposed by this later in which players ordering is based on the distance between bliss and political issues points, yields the Shapley index if issues can be any point in the space.

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  • Martin, Mathieu & Nganmeni, Zephirin & Tchantcho, Bertrand, 2017. "The Owen and Shapley spatial power indices: A comparison and a generalization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 10-19.
    • Handle: RePEc:eee:matsoc:v:89:y:2017:i:c:p:10-19
    DOI: 10.1016/j.mathsocsci.2017.05.003
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    Cited by:

    1. Philip D. Grech, 2021. "Power in the Council of the EU: organizing theory, a new index, and Brexit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 223-258, February.
    2. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.
    3. Albizuri, M.J. & Goikoetxea, A., 2022. "Probabilistic Owen-Shapley spatial power indices," Games and Economic Behavior, Elsevier, vol. 136(C), pages 524-541.
    4. Arnold Cédrick SOH VOUTSA, 2020. "Deegan-Packel & Johnston spatial power indices and characterizations," THEMA Working Papers 2020-16, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Sascha Kurz, 2018. "Importance In Systems With Interval Decisions," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(06n07), pages 1-23, September.
    6. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.

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