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Three ways to compute accurately the probability of the referendum paradox

Author

Listed:
  • Dominique Lepelley

    (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

  • Vincent Merlin

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Louis Rouet

    (ISTO - Institut des Sciences de la Terre d'Orléans - INSU - CNRS - Institut national des sciences de l'Univers - UO - Université d'Orléans - UT - Université de Tours - CNRS - Centre National de la Recherche Scientifique)

Abstract

In a recent paper published in MSS, Wilson and Pritchard (2007) exhibit some results suggesting that the limiting probability of the referendum paradox given in Feix et al. (2004) could be wrong. After having explained the origin of this disagreement, we propose in this note some further analytical (and complementary) methods to compute the probability of this paradox.

Suggested Citation

  • Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2011. "Three ways to compute accurately the probability of the referendum paradox," Post-Print halshs-00602133, HAL.
    • Handle: RePEc:hal:journl:halshs-00602133
    DOI: 10.1016/j.mathsocsci.2011.04.006
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    References listed on IDEAS

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    1. 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, December.
    2. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    3. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2004. "The probability of conflicts in a U.S. presidential type election," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 227-257, January.
    4. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    5. Marc R. Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2009. "On the Probability to Act in the European Union," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 197-211, Springer.
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    Cited by:

    1. Laurent, Thibault & Le Breton, Michel & Lepelley, Dominique & de Mouzon, Olivier, 2017. "Exploring the Effects on the Electoral College of National and Regional Popular Vote Interstate Compact: An Electoral Engineering Perspective," TSE Working Papers 17-861, Toulouse School of Economics (TSE), revised May 2018.
    2. Olivier Mouzon & Thibault Laurent & Michel Le Breton & Dominique Lepelley, 2020. "The theoretical Shapley–Shubik probability of an election inversion in a toy symmetric version of the US presidential electoral system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 363-395, March.
    3. Herrade Igersheim & François Durand & Aaron Hamlin & Jean-François Laslier, 2018. "Comparing Voting Methods : 2016 US Presidential Election," Working Papers halshs-01972097, HAL.
    4. Herrade Igersheim & François Durand & Aaron Hamlin & Jean-François Laslier, 2018. "Comparing Voting Methods : 2016 US Presidential Election," PSE Working Papers halshs-01972097, HAL.
    5. Marina Bannikova & Artyom Jelnov & Pavel Jelnov, 2021. "The Number of Parties and Decision-Making in Legislatures," Games, MDPI, vol. 12(4), pages 1-10, October.
    6. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    7. Dominique Lepelley & Vincent R Merlin & Jean-louis Rouet & Laurent Vidu, 2014. "Referendum paradox in a federal union with unequal populations: the three state case," Economics Bulletin, AccessEcon, vol. 34(4), pages 2201-2207.
    8. Maaser, Nicola & Napel, Stefan, 2012. "A note on the direct democracy deficit in two-tier voting," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 174-180.
    9. Serguei Kaniovski & Alexander Zaigraev, 2018. "The probability of majority inversion in a two-stage voting system with three states," Theory and Decision, Springer, vol. 84(4), pages 525-546, June.

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