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Ternary Voting Games

Author

Listed:
  • 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)

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.

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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    Citations

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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
    2. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    3. Fabien Lange & Michel Grabisch, 2011. "New axiomatizations of the Shapley interaction index for bi-capacities," Post-Print hal-00625355, HAL.
    4. Roland Pongou & Bertrand Tchantcho & Lawrence Diffo Lambo, 2011. "Political influence in multi-choice institutions: cyclicity, anonymity, and transitivity," Theory and Decision, Springer, vol. 70(2), pages 157-178, February.
    5. Sanne Zwart, 2007. "Fixing the Quorum: Representation versus Abstention," Economics Working Papers ECO2007/07, European University Institute.
    6. Bertrand Tchantcho & Lawrence Diffo Lambo & Roland Pongou & Joël Moulen, 2010. "On the equilibrium of voting games with abstention and several levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 379-396, March.
    7. Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
    8. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," Post-Print halshs-00260863, HAL.
    9. Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 485-506, December.
    10. László Á. Kóczy & Miklós Pintér, 2011. "The men who weren't even there: Legislative voting with absentees," Working Paper Series 1104, Óbuda University, Keleti Faculty of Business and Management.
    11. LINDNER, Ines, 2005. "Voting games with abstention : A probabilistic characterization of power and a special case of Penrose’s Limit Theorem," LIDAM Discussion Papers CORE 2005078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. 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.
    13. Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Post-Print halshs-00142479, HAL.
    14. Fabien Lange & Michel Grabisch, 2006. "Interaction transform for bi-set functions over a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00186891, HAL.
    15. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "A model of influence with a continuum of actions," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 576-587.
    16. Sanne Zwart, 2010. "Ensuring a representative referendum outcome: the daunting task of setting the quorum right," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 643-677, April.
    17. Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Quaternary dichotomous voting rules," IKERLANAK 2010-41, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    18. René Brink & Frank Steffen, 2012. "Axiomatizations of a positional power score and measure for hierarchies," Public Choice, Springer, vol. 151(3), pages 757-787, June.
    19. Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Majorities with a quorum," IKERLANAK 2010-42, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    20. Perry, Jonathan & Powers, Robert C., 2010. "Anonymity, monotonicity, and quota pair systems," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 57-60, July.
    21. 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.
    22. Alaitz Artabe & Annick Laruelle & Federico Valenciano, 2012. "Preferences, actions and voting rules," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 15-28, March.
      • Artabe Echevarria, Alaitz & Laruelle, Annick & Valenciano Llovera, Federico, 2011. "Preferences, actions and voting rules," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    23. Annick Laruelle & Federico Valenciano, 2012. "Quaternary dichotomous voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 431-454, March.
    24. 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.

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