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The prediction value

Author

Listed:
  • Maurice Koster

    (University of Amsterdam)

  • Sascha Kurz

    (University of Bayreuth)

  • Ines Lindner

    (VU University)

  • Stefan Napel

    (University of Bayreuth
    Public Choice Research Centre)

Abstract

We introduce the prediction value (PV) of player i as the difference between the conditional expectations of v(S) when i cooperates or not in a probabilistic TU game. The latter combines a standard TU game and a probability distribution over the set of coalitions. The PV reflects the importance of information about a given player’s behavior for predicting, e.g., committee decisions that are subject to opinion interdependencies. The PV is characterized by anonymity, linearity, a consistency requirement and two normalization conditions. Every multinomial probabilistic value, hence every binomial semivalue, coincides with the PV for a particular family of probability distributions. So the PV can be regarded as a power index in specific cases. Conversely, some semivalues—including the Banzhaf but not the Shapley value—can be interpreted in terms of informational importance.

Suggested Citation

  • Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.
    • Handle: RePEc:spr:sochwe:v:48:y:2017:i:2:d:10.1007_s00355-016-1012-x
    DOI: 10.1007/s00355-016-1012-x
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    Cited by:

    1. Grimmett, Geoffrey R., 2019. "On influence and compromise in two-tier voting systems," Mathematical Social Sciences, Elsevier, vol. 100(C), pages 35-45.
    2. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.

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    More about this item

    Keywords

    Influence; Voting games; Cooperative games; Banzhaf value; Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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