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Quaternary dichotomous voting rules

  • Annick Laruelle

    ()

  • Federico Valenciano

    ()

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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File URL: http://hdl.handle.net/10.1007/s00355-011-0538-1
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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 38 (2012)
Issue (Month): 3 (March)
Pages: 431-454

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Handle: RePEc:spr:sochwe:v:38:y:2012:i:3:p:431-454
DOI: 10.1007/s00355-011-0538-1
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Order Information: Web: http://www.springer.com/economics/economic+theory/journal/355

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  1. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 335-351.
  2. Vermeule, Adrian, 2007. "Absolute Majority Rules," British Journal of Political Science, Cambridge University Press, vol. 37(04), pages 643-658, October.
  3. Laruelle,Annick & Valenciano,Federico, 2008. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521873871, Junio.
  4. MANIQUET, François & MORELLI, Massimo & ,, 2013. "Approval quorums dominate participation quorums," CORE Discussion Papers 2013054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Paulo P. Corte-Real & Paulo Trigo Pereira, 2002. "The voter who wasn't there: Referenda, Representation and Abstention," Working Papers Department of Economics 2002/04, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
  6. Taylor Alan & Zwicker William, 1993. "Weighted Voting, Multicameral Representation, and Power," Games and Economic Behavior, Elsevier, vol. 5(1), pages 170-181, January.
  7. Helios Herrera & Andrea Mattozzi, 2010. "Quorum and Turnout in Referenda," Journal of the European Economic Association, MIT Press, vol. 8(4), pages 838-871, 06.
  8. 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.
  9. 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, SAGE Publishing, vol. 22(1), pages 85-122, January.
  10. 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.
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