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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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    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. Michel Le Breton & Dominique Lepelley & Antonin Macé & Vincent Merlin, 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.
    6. Abidi Perier, Zineb & Merlin, Vincent, 2025. "Testing Penrose Limit Theorem: A case study of French local data," Mathematical Social Sciences, Elsevier, vol. 137(C).
    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. 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.
    10. 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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