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Quaternary dichotomous voting rules

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  • Annick Laruelle

    ()

  • Federico Valenciano

    ()

Abstract

In this paper we provide a general model of "quaternary" dichotomous voting rules (QVRs), namely, voting rules for making collective dichotomous decisions (to accept or reject a proposal), based on vote profiles in which four options are available to each voter: voting ("yes", "no" or "abstaining") or staying home and not turning out. The model covers most of actual real-world dichotomus rules, where quorums are often required, and some of the extensions considered in the literature. In particular, we address and solve the question of the representability of QVRs by means of weighted rules and extend the notion of "dimension" of a rule.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:38:y:2012:i:3:p:431-454
    DOI: 10.1007/s00355-011-0538-1
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    File URL: http://hdl.handle.net/10.1007/s00355-011-0538-1
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    References listed on IDEAS

    as
    1. François Maniquet & Massimo Morelli, 2015. "Approval quorums dominate participation quorums," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 1-27, June.
    2. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    3. Paulo P. Côrte-Real & Paulo T. Pereira, 2004. "The voter who wasn’t there: Referenda, representation and abstention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 349-369, April.
    4. Keith L. Dougherty & Julian Edward, 2010. "The Properties of Simple Vs. Absolute Majority Rule: Cases Where Absences and Abstentions Are Important," Journal of Theoretical Politics, , vol. 22(1), pages 85-122, January.
    5. Helios Herrera & Andrea Mattozzi, 2010. "Quorum and Turnout in Referenda," Journal of the European Economic Association, MIT Press, vol. 8(4), pages 838-871, June.
    6. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    7. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 335-351.
    8. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 399-431, December.
    9. Vermeule, Adrian, 2007. "Absolute Majority Rules," British Journal of Political Science, Cambridge University Press, vol. 37(04), pages 643-658, October.
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    Cited by:

    1. Yoichi Hizen, 2015. "A referendum experiment with participation quorums," Working Papers SDES-2015-6, Kochi University of Technology, School of Economics and Management, revised Jan 2015.
    2. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley–Shubik power index for dichotomous multi-type games," Theory and Decision, Springer, vol. 81(3), pages 413-426, September.
    3. Luís Francisco Aguiar-Conraria & Pedro C. Magalhães & Christoph A. Vanberg, 2013. "Experimental evidence that quorum rules discourage turnout and promote election boycotts," NIPE Working Papers 14/2013, NIPE - Universidade do Minho.
    4. Guemmegne, Juliette T. & Pongou, Roland, 2014. "A policy-based rationalization of collective rules: Dimensionality, specialized houses, and decentralized authority," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 182-193.
    5. 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.
    6. Courtin, Sébastien & Nganmeni, Zéphirin & Tchantcho, Bertrand, 2017. "Dichotomous multi-type games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 9-17.
    7. Rodríguez Alcantud, José Carlos & Laruelle, Annick, 2016. "To disqualify or not to qualify: This is the other question," IKERLANAK Ikerlanak;2016-102, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    8. Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Majorities with a quorum," IKERLANAK 2010-42, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    9. Luís Aguiar-Conraria & Pedro C. Magalhães & Christoph A. Vanberg, 2016. "Experimental evidence that quorum rules discourage turnout and promote election boycotts," Experimental Economics, Springer;Economic Science Association, vol. 19(4), pages 886-909, December.
    10. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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