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Ternary Voting Games


  • 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)


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.

Suggested Citation

  • MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 335-351.
  • Handle: RePEc:spr:jogath:v:26:y:1997:i:3:p:335-351

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