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.
SMU Economics and Statistics Working Paper Series No. 27-2004
Chua, Vincent and Ueng, C. H..
On Measuring Influence in Non-Binary Voting Games. (2004). SMU Economics and Statistics Working Paper Series No. 27-2004. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/826
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