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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 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
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  1. Helios Herrera & Andrea Mattozzi, 2010. "Quorum and Turnout in Referenda," Journal of the European Economic Association, European Economic Association, vol. 8(4), pages 838-871, 06.
  2. Paulo P. Côrte-Real & Paulo T. Pereira, 2004. "The voter who wasn’t there: Referenda, representation and abstention," Social Choice and Welfare, Springer, vol. 22(2), pages 349-369, 04.
  3. 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.
  4. Taylor Alan & Zwicker William, 1993. "Weighted Voting, Multicameral Representation, and Power," Games and Economic Behavior, Elsevier, vol. 5(1), pages 170-181, January.
  5. 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).
  6. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer, vol. 21(3), pages 399-431, December.
  7. repec:cup:cbooks:9780521873871 is not listed on IDEAS
  8. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
  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, , vol. 22(1), pages 85-122, January.
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