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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. 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.
    4. 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.
    5. 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.
    6. Laszlo A. Koczy & Miklos Pinter, 2011. "The men who weren't even there: Legislative voting with absentees," CERS-IE WORKING PAPERS 1129, Institute of Economics, Centre for Economic and Regional Studies.
    7. 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.
    8. 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.
    9. 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.
    10. Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00142479, HAL.
      • Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Post-Print halshs-00142479, HAL.
      • Agnieszka Rusinowska & Michel Grabisch, 2007. "Influence Indices," Working Papers 0705, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    11. 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.
    12. 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.
    13. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," Post-Print halshs-00260863, HAL.
    14. 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.
    15. 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).
    16. 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.
    17. Fabien Lange & Michel Grabisch, 2011. "New axiomatizations of the Shapley interaction index for bi-capacities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00625355, HAL.
    18. 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.
    19. Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Quaternary dichotomous voting rules," IKERLANAK 2010-41, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    20. 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.
    21. Sanne Zwart, 2007. "Fixing the Quorum: Representation versus Abstention," Economics Working Papers ECO2007/07, European University Institute.
    22. 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.
    23. Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Majorities with a quorum," IKERLANAK 2010-42, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    24. Perry, Jonathan & Powers, Robert C., 2010. "Anonymity, monotonicity, and quota pair systems," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 57-60, July.

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