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The conditional Shapley–Shubik measure for ternary voting games

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  • Friedman, Jane
  • Parker, Cameron

Abstract

Ternary voting games (TVGs) model situations where a voter has three options, which can be thought of as yes, no, and abstention. This paper presents ϕ˜, an extension of the Shapley–Shubik power measure to ternary voting games. ϕ˜ measures a voter's power as the probability that the voter will be pivotal given that they do not abstain. This contrasts with other extensions of the Shapley–Shubik measure to TVGs, which measure power as the probability that a player's vote is pivotal no matter what that vote is. Desirable properties of power measures in SVGs are extended to TVGs and ϕ˜ is shown to satisfy these properties.

Suggested Citation

  • Friedman, Jane & Parker, Cameron, 2018. "The conditional Shapley–Shubik measure for ternary voting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 379-390.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:379-390
    DOI: 10.1016/j.geb.2018.03.014
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    More about this item

    Keywords

    Cooperative games; Ternary voting games; Ordinal equivalence; Shapley–Shubik index; Postulates of power measures;
    All these keywords.

    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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