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Referendum paradox in a federal union with unequal populations: the three state case

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 - UMR7327 - BRGM - Bureau de Recherches Géologiques et Minières - OSUC - Observatoire des Sciences de l'Univers en région Centre - INSU - CNRS - Institut national des sciences de l'Univers - Observatoire de Paris - PSL - Université Paris Sciences et Lettres - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique - INSU - CNRS - Institut national des sciences de l'Univers - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Laurent Vidu

    (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)

Abstract

In a federal union, a referendum paradox occurs each time a decision taken by representatives elected in separate jurisdictions (districts, states, regions) conflicts with the decision that would have been adopted if the voters had directly given their opinion via a referendum (Nurmi 1999). Assuming that the population is split into three jurisdictions of respective size n1, n2 and n3, we derive exact formulas for the probability of the referendum paradox under the Impartial Culture model. Then we use these results to show that, in our model, allocating seats to the juridictions proportionally to the square root of their size is an apportionment rule that fails to minimize the probability of the referendum paradox in some federations.

Suggested Citation

  • Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet & Laurent Vidu, 2014. "Referendum paradox in a federal union with unequal populations: the three state case," Post-Print halshs-01102577, HAL.
    • Handle: RePEc:hal:journl:halshs-01102577
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    References listed on IDEAS

    as
    1. Rahhal Lahrach & Vincent Merlin, 2012. "Which voting rule minimizes the probability of the referendum paradox? Lessons from French data," Post-Print halshs-00658580, HAL.
    2. Fabrice Barthélémy & Dominique Lepelley & Mathieu Martin, 2013. "On the likelihood of dummy players in weighted majority games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 263-279, July.
    3. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    4. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    5. Lepelley, Dominique & Merlin, Vincent & Rouet, Jean-Louis, 2011. "Three ways to compute accurately the probability of the referendum paradox," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 28-33, July.
    6. Rahhal Lahrach & Vincent Merlin, 2012. "Which Voting Rule Minimizes the Probability of the Referendum Paradox? Lessons from French Data," Studies in Choice and Welfare, in: Dan S. Felsenthal & Moshé Machover (ed.), Electoral Systems, chapter 0, pages 129-150, Springer.
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    Cited by:

    1. Michael Geruso & Dean Spears & Ishaana Talesara, 2022. "Inversions in US Presidential Elections: 1836–2016," American Economic Journal: Applied Economics, American Economic Association, vol. 14(1), pages 327-357, January.
    2. 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.
    3. 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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    More about this item

    Keywords

    federalism; indirect voting; apportionment; paradoxes; probability;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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