On Measuring Influence in Non-Binary Voting Games

• Main Authors: CHUA, Vincent, Ueng, C. H.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2004
• Subjects: Penrose measure; Banzhaf index; ternary games; multicandidate weighted voting games; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/826; https://ink.library.smu.edu.sg/context/soe_research/article/1825/viewcontent/Measuring.pdf
• Institution: Singapore Management University

In this note, we demonstrate using two simple examples that generalization of the Banzhaf measure of voter influence to non-binary voting games that requires as starting position a voter’s membership in a winning coalition is likely to incompletely reflect the influence a voter has on the outcome of a game. Generalization of the Banzhaf measure that takes into consideration all possible pivot moves of a voter including those moves originating from a losing coalition will, on the other hand, result in a measure that is proportional to the Penrose measure only in the ternary case.