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Spatial Power Indices with a Finite Number of Issues

Author

Listed:
  • M. Josune Albizuri

    (University of the Basque Country)

  • Alex Goikoetxea

    (University of the Basque Country)

  • Jose M. Zarzuelo

    (University of the Basque Country)

Abstract

The Owen-Shapley spatial power index measures the power in a voting situation taking into account the ideological location of the voters. This spatial index assumes that voters face a continuum of issues, and these issues have the same relevance, and therefore are equally likely. In this work, we introduce a family of spatial power indices, where each member of the family is a modified version of the Owen-Shapley spatial power index. Unlike the case of the Owen-Shapley index, in this paper, we consider a more realistic assumption, namely, that voters face a finite number of issues and that these issues may have different relevance. Additionally, we provide an axiomatic characterization of this family using three basic axioms: equal power change property, anonymity, and dummy player property. Furthermore, we prove that these axioms are independent. Finally, an application for the Basque Parliament after the 2020 elections is also provided to study the distribution of power among the parties.

Suggested Citation

  • M. Josune Albizuri & Alex Goikoetxea & Jose M. Zarzuelo, 2025. "Spatial Power Indices with a Finite Number of Issues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(3), pages 373-394, June.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:3:d:10.1007_s00186-025-00895-2
    DOI: 10.1007/s00186-025-00895-2
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    References listed on IDEAS

    as
    1. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    2. 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.
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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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