MoshÊ Machover (Department of Philosophy, King's College London, Strand, London WC2R 2LS, UK Recieved December 1995 Revised May 1996) Dan S. Felsenthal (Department of Political Science, University of Haifa, Mount Carmel, Haifa 31905, Israel)
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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.
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