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The conditional Shapley–Shubik measure for ternary voting games

Jane Friedman and Cameron Parker

Games and Economic Behavior, 2018, vol. 108, issue C, 379-390

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.

Keywords: Cooperative games; Ternary voting games; Ordinal equivalence; Shapley–Shubik index; Postulates of power measures (search for similar items in EconPapers)
JEL-codes: C71 D72 (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:379-390