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The roll call interpretation of the Shapley value

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  • Kurz, Sascha
  • Napel, Stefan

Abstract

The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter’s Shapley value can be interpreted as the probability of being pivotal, i.e., to bring about the required majority or to make this impossible for others. We characterize the joint probability distributions over cooperation patterns that permit this roll call interpretation: individual votes may be interdependent but must be exchangeable.

Suggested Citation

  • Kurz, Sascha & Napel, Stefan, 2018. "The roll call interpretation of the Shapley value," Economics Letters, Elsevier, vol. 173(C), pages 108-112.
    • Handle: RePEc:eee:ecolet:v:173:y:2018:i:c:p:108-112
    DOI: 10.1016/j.econlet.2018.09.025
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    References listed on IDEAS

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    1. Giulia Bernardi & Josep Freixas, 2018. "The Shapley value analyzed under the Felsenthal and Machover bargaining model," Public Choice, Springer, vol. 176(3), pages 557-565, September.
    2. Felsenthal, Dan S & Machover, Moshe, 1996. "Alternative Forms of the Shapley Value and the Shapley-Shubik Index," Public Choice, Springer, vol. 87(3-4), pages 315-318, June.
    3. Xingwei Hu, 2006. "An Asymmetric Shapley–Shubik Power Index," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 229-240, August.
    4. 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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    Cited by:

    1. Sascha Kurz & Issofa Moyouwou & Hilaire Touyem, 2021. "Axiomatizations for the Shapley–Shubik power index for games with several levels of approval in the input and output," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 569-594, April.
    2. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.

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    More about this item

    Keywords

    Shapley value; Shapley–Shubik index; Roll call model; Voting power;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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