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Ternary Voting Games

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Author Info
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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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.

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Publisher Info
Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 26 (1997)
Issue (Month): 3 ()
Pages: 335-351
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Handle: RePEc:spr:jogath:v:26:y:1997:i:3:p:335-351

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  1. Pongou, Roland & Tchantcho, Bertrand & Diffo Lambo, Lawrence, 2008. "Political Influence in Multi-Choice Institutions: Cyclicity, Anonymity and Transitivity," MPRA Paper 18240, University Library of Munich, Germany, revised 20 Oct 2009. [Downloadable!]
  2. Agnieszka Rusinowska & Michel Grabisch, 2007. "Influence Indices," Working Papers 0705, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure. [Downloadable!]
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  3. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," Working Papers 0801, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure. [Downloadable!]
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  4. Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer, vol. 25(2), pages 485-506, December. [Downloadable!] (restricted)
  5. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985_v1, HAL. [Downloadable!]
  6. LINDNER, Ines, 2005. "Voting games with abstention : A probabilistic characterization of power and a special case of PenroseÕs Limit Theorem," CORE Discussion Papers 2005078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  7. Ines Lindner, 2008. "A Special Case of Penrose’s Limit Theorem When Abstention is Allowed," Theory and Decision, Springer, vol. 64(4), pages 495-518, June. [Downloadable!] (restricted)
  8. Jesús Mario Bilbao & Julio R. Fernández & Nieves Jiménez & Jorge Jesús López, 2004. "Probabilistic values for bicooperative games," Economic Working Papers at Centro de Estudios Andaluces E2004/54, Centro de Estudios Andaluces. [Downloadable!]
  9. Jesús Mario Bilbao & Julio R. Fernández & Nieves Jiménez & Jorge Jesús López, 2004. "The Shapley value for bicooperative games," Economic Working Papers at Centro de Estudios Andaluces E2004/56, Centro de Estudios Andaluces. [Downloadable!]
  10. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Working Papers 0831, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure. [Downloadable!]
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