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An axiomatic characterization of the Owen–Shapley spatial power index


  • Hans Peters

    () (Maastricht University)

  • José M. Zarzuelo

    () (The University of the Basque Country)


Abstract We present an axiomatic characterization of the Owen–Shapley spatial power index for the case where issues are elements of two-dimensional space. This characterization employs a version of the transfer condition, which enables us to unravel a spatial game into spatial games connected to unanimity games. The other axioms include two conditions concerned particularly with the spatial positions of the players, besides spatial versions of anonymity and dummy. The last condition says that dummy players can be left out in a specific way without changing the power of the other players. We show that this condition can be weakened to requiring dummies to have zero power if we add a condition of positional continuity. We also show that the axioms in our characterization(s) are logically independent.

Suggested Citation

  • Hans Peters & José M. Zarzuelo, 2017. "An axiomatic characterization of the Owen–Shapley spatial power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 525-545, May.
  • Handle: RePEc:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0544-8
    DOI: 10.1007/s00182-016-0544-8

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    References listed on IDEAS

    1. Francesco Passarelli & Jason Barr, 2007. "Preferences, the Agenda Setter, and the Distribution of Power in the EU," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 41-60, January.
    2. 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.
    3. Einy, Ezra & Haimanko, Ori, 2011. "Characterization of the Shapley–Shubik power index without the efficiency axiom," Games and Economic Behavior, Elsevier, vol. 73(2), pages 615-621.
    4. Ezra Einy, 1987. "Semivalues of Simple Games," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 185-192, May.
    5. Matthew Braham & Manfred J. Holler, 2005. "The Impossibility of a Preference-Based Power Index," Journal of Theoretical Politics, , vol. 17(1), pages 137-157, January.
    6. Stefan Napel & Mika Widgrén, 2005. "The Possibility of a Preference-Based Power Index," Journal of Theoretical Politics, , vol. 17(3), pages 377-387, July.
    7. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
    8. Shenoy, Prakash P., 1982. "The Banzhaf power index for political games," Mathematical Social Sciences, Elsevier, vol. 2(3), pages 299-315, April.
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    More about this item


    Simple game; Constellation; Spatial game; Owen–Shapley spatial power index;

    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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