IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-14-00642.html
   My bibliography  Save this article

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

Author

Listed:
  • Dominique Lepelley

    (CEMOI, Université de la Réunion)

  • Vincent R Merlin

    (CREM, CNRS, Université de Caen)

  • Jean-louis Rouet

    (ISTO UMR 7327 - CNRS/ISTU - BRGM - Université d''Orléans)

  • Laurent Vidu

    (CREM, Université de Caen)

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 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.
    • Handle: RePEc:ebl:ecbull:eb-14-00642
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2014/Volume34/EB-14-V34-I4-P201.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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.
    5. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Herrade Igersheim & François Durand & Aaron Hamlin & Jean-François Laslier, 2018. "Comparing Voting Methods : 2016 US Presidential Election," Working Papers halshs-01972097, HAL.
    4. Zineb Abidi & Matthieu Leprince & Vincent Merlin, 2020. "Power Inequality in Inter-communal Structures: The Simulated Impact of a Reform in the Case of the Municipalities in Western France," Post-Print halshs-02996998, HAL.
    5. Herrade Igersheim & François Durand & Aaron Hamlin & Jean-François Laslier, 2018. "Comparing Voting Methods : 2016 US Presidential Election," PSE Working Papers halshs-01972097, HAL.
    6. Serguei Kaniovski, 2008. "The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 281-300, August.
    7. 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.
    8. Fabrice Barthelemy & Mathieu Martin, 2011. "A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the US Presidential Elections," Annals of Economics and Statistics, GENES, issue 101-102, pages 87-106.
    9. Laruelle, Annick & Valenciano, Federico, 2002. "Inequality among EU citizens in the EU's Council decision procedure," European Journal of Political Economy, Elsevier, vol. 18(3), pages 475-498, September.
    10. Madeleine Hosli & Rebecca Moody & Bryan O’Donovan & Serguei Kaniovski & Anna Little, 2011. "Squaring the circle? Collective and distributive effects of United Nations Security Council reform," The Review of International Organizations, Springer, vol. 6(2), pages 163-187, July.
    11. Mika Widgren, 2003. "Power in the Design of Constitutional Rules," European Economy Group Working Papers 23, European Economy Group.
    12. Diana Cheng & Peter Coughlin, 2017. "Using equations from power indices to analyze figure skating teams," Public Choice, Springer, vol. 170(3), pages 231-251, March.
    13. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.
    14. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    15. Dennis Leech, 2002. "An Empirical Comparison of the Performance of Classical Power Indices," Political Studies, Political Studies Association, vol. 50(1), pages 1-22, March.
    16. Stefan Napel & Mika Widgrén, 2005. "The Possibility of a Preference-Based Power Index," Journal of Theoretical Politics, , vol. 17(3), pages 377-387, July.
    17. Mika WidgrÚn & Stefan Napel, 2002. "The Power of a Spatially Inferior Player," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 327-343.
    18. Fabrice Barthélémy & Mathieu Martin, 2021. "Dummy Players and the Quota in Weighted Voting Games: Some Further Results," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 299-315, Springer.
    19. René Brink & Frank Steffen, 2012. "Axiomatizations of a positional power score and measure for hierarchies," Public Choice, Springer, vol. 151(3), pages 757-787, June.
    20. Ibrahima Dia & Eric Kamwa, 2020. "The Voting Power in the Inter-communal Council of Martinique and Guadeloupe [Le Pouvoir de Vote dans les Etablissements Publics de Coopération Intercommunale de la Martinique et de la Guadeloupe]," Post-Print hal-01631190, HAL.

    More about this item

    Keywords

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

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ebl:ecbull:eb-14-00642. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: John P. Conley (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.