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Quaternary dichotomous voting rules

Author

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  • Laruelle, Annick
  • Valenciano Llovera, Federico

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.

Suggested Citation

  • Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Quaternary dichotomous voting rules," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    • Handle: RePEc:ehu:ikerla:6412
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    References listed on IDEAS

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    1. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, January.
    2. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, September.
    3. William S. Zwicker, 2009. "Anonymous Voting Rules with Abstention: Weighted Voting," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 239-258, Springer.
    4. 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.
    5. 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.
    6. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    7. 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.
    8. Vermeule, Adrian, 2007. "Absolute Majority Rules," British Journal of Political Science, Cambridge University Press, vol. 37(4), pages 643-658, October.
    9. 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.
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    Cited by:

    1. 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.
    2. repec:ehu:ikerla:6259 is not listed on IDEAS
    3. Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Majorities with a quorum," IKERLANAK 2010-42, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

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