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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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  • 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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    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. Laruelle,Annick & Valenciano,Federico, 2008. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521873871.
    4. 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, June.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 335-351.
    10. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    11. 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.
    12. Vermeule, Adrian, 2007. "Absolute Majority Rules," British Journal of Political Science, Cambridge University Press, vol. 37(4), pages 643-658, October.
    13. 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. Courtin, Sébastien & Laruelle, Annick, 2020. "Multi-dimensional rules," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 1-7.
    2. 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.
    3. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.
    4. Luís Aguiar-Conraria & Pedro C. Magalhães & Christoph A. Vanberg, 2020. "What are the best quorum rules? A laboratory investigation," Public Choice, Springer, vol. 185(1), pages 215-231, October.
    5. Courtin, Sébastien, 2022. "Evaluation of decision power in multi-dimensional rules," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 27-36.
    6. Friedman, Jane & Parker, Cameron, 2018. "The conditional Shapley–Shubik measure for ternary voting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 379-390.
    7. 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.
    8. Yoichi Hizen, 2021. "A Referendum Experiment with Participation Quorums," Kyklos, Wiley Blackwell, vol. 74(1), pages 19-47, February.
    9. 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.
    10. Michela Chessa & Vito Fragnelli, 2022. "The Italian referendum: what can we get from game theory?," Annals of Operations Research, Springer, vol. 318(2), pages 849-869, November.
    11. 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.
    12. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley-Shubik power index for dichotomous multi-type games," Post-Print halshs-01545769, HAL.
    13. 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.
    14. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2020. "Weighted committee games," European Journal of Operational Research, Elsevier, vol. 282(3), pages 972-979.
    15. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2017. "Dichotomous multi-type games with a coalition structure," Post-Print halshs-01545772, HAL.
    16. Sanjay Bhattacherjee & Palash Sarkar, 2021. "Weighted voting procedure having a unique blocker," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 279-295, March.
    17. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(C).
    18. Rodríguez Alcantud, José Carlos & Laruelle, Annick, 2016. "To disqualify or not to qualify: This is the other question," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    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. Sébastien Courtin & Zephirin Nganmeni & Bertrand Tchantcho, 2015. "Dichotomous multi-type games: Shapley-Shubik and Banzhaf-Coleman power indices," THEMA Working Papers 2015-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    21. 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.

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    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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