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Seperable Voting Rules and the Strong Referandum Paradox


  • Hayrullah Dindar

    () (Department of Economics,Istanbul Bilgi University)

  • Gilbert Laffond

    () (Laboratoire d'Econometrie, LIRSA)

  • Jean Laine

    () (Murat Sertel Center for Advanced Economic Studies,Istanbul Bilgi University)


This paper provides a model of indirect elections where voters having weak orders as preferences over finitely many alternatives are distributed across a given set of districts. In each district preferences are aggregated into a district preference, and a voting rule selects one or several alternatives from the profile of district preferences. The referendum paradox holds at some profile and some distribution of voters across districts if the outcome of indirect elections does not coincide with the one of direct elections. We prove that whenever an indirect election procedure is separable, it is exposed to the referendum paradox if and only if it is exposed to a stronger version of the referendum paradox, where direct and indirect elections give different outcomes for any distribution of the voters across districts. We prove that many indirect elections based on a tournament solution are separable, whereas some based on a scoring rule are not. Finally, we show that all indirect elections based on a scoring rule are exposed to the strong referendum paradox

Suggested Citation

  • Hayrullah Dindar & Gilbert Laffond & Jean Laine, 2013. "Seperable Voting Rules and the Strong Referandum Paradox," Working Papers 201302, Murat Sertel Center for Advanced Economic Studies, Istanbul Bilgi University.
  • Handle: RePEc:msc:wpaper:201302

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    References listed on IDEAS

    1. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 855-867, October.
    2. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    3. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, March.
    4. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, March.
    5. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    6. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
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    More about this item


    Voting Paradox; Referandum Paradox; Representive Democracy; Gerrymandering;

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior


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