The conditional Shapley-Shubik measure for ternary voting games

• 成果类型: Article
• 署名作者: Friedman, Jane; Parker, Cameron
• 署名单位: University of San Diego
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2018.03.014
• 发表日期: 2018
• 页码: 379-390
• 关键词: Cooperative games; Ternary voting games; Ordinal equivalence; Shapley-Shubik index; Postulates of power measures

摘要

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 (phi) over tilde, an extension of the Shapley-Shubik power measure to ternary voting games. (phi) over tilde 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 (phi) over tilde is shown to satisfy these properties. (C) 2018 Elsevier Inc. All rights reserved.