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The strong referendum paradox

Author

Listed:
  • Hayrullah Dindar

    (Istanbul Bilgi University)

  • Gilbert Laffond

    (Istanbul Bilgi University, LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM])

  • Jean Lainé

    (LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM])

Abstract

We study 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.
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Suggested Citation

  • Hayrullah Dindar & Gilbert Laffond & Jean Lainé, 2017. "The strong referendum paradox," Post-Print hal-03271187, HAL.
    • Handle: RePEc:hal:journl:hal-03271187
    DOI: 10.1007/s11135-016-0361-y
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    References listed on IDEAS

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    1. G. Laffond & J. Lainé, 2013. "Unanimity and the Anscombe’s paradox," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 590-611, October.
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    4. Sebastian Bervoets & Vincent Merlin, 2012. "Gerrymander-proof representative democracies," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 473-488, August.
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    10. 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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