Ternary Voting Games

Moshé Machover and Dan S. Felsenthal
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Dan S. Felsenthal: Department of Political Science, University of Haifa, Mount Carmel, Haifa 31905, Israel

International Journal of Game Theory, 1997, vol. 26, issue 3, 335-351

Abstract: We define ternary voting games $(TVGs)$, a generalization of simple voting games $(SVGs)$. In a play of an SVG each voter has just two options: voting `yes' or `no'. In a TVG a third option is added: abstention. Every SVG can be regarded as a (somewhat degenerate) TVG; but the converse is false. We define appropriate generalizations of the Shapley-Shubik and Banzhaf indices for TVGs. We define also the responsiveness (or degree of democratic participation) of a TVG and determine, for each n, the most responsive TVGs with n voters. We show that these maximally responsive TVGs are more responsive than the corresponding SVGs.

Date: 1998-05-19
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