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Stability in electoral competition: A case for multiple votes

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  • Xefteris, Dimitrios

Abstract

It is well known that the Hotelling–Downs model generically fails to admit an equilibrium when voting takes place under the plurality rule (Osborne, 1993). This paper studies the Hotelling–Downs model considering that each voter is allowed to vote for up to k candidates and demonstrates that an equilibrium exists for a non-degenerate class of distributions of voters' ideal policies – which includes all log-concave distributions – if and only ifk≥2. That is, the plurality rule (k=1) is shown to be the unique k-vote rule which generically precludes stability in electoral competition. Regarding the features of k-vote rules' equilibria, first, we show that there is no convergent equilibrium and, then, we fully characterize all divergent equilibria. We study comprehensively the simplest kind of divergent equilibria (two-location ones) and we argue that, apart from existing for quite a general class of distributions when k≥2, they have further attractive properties – among others, they are robust to free-entry and to candidates' being uncertain about voters' preferences.

Suggested Citation

  • Xefteris, Dimitrios, 2016. "Stability in electoral competition: A case for multiple votes," Journal of Economic Theory, Elsevier, vol. 161(C), pages 76-102.
  • Handle: RePEc:eee:jetheo:v:161:y:2016:i:c:p:76-102
    DOI: 10.1016/j.jet.2015.11.003
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    References listed on IDEAS

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    2. Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
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    Citations

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    Cited by:

    1. Tsakas, Nikolas & Xefteris, Dimitrios, 2018. "Electoral competition with third party entry in the lab," Journal of Economic Behavior & Organization, Elsevier, vol. 148(C), pages 121-134.
    2. David Ronayne, 2018. "Extreme idealism and equilibrium in the Hotelling–Downs model of political competition," Public Choice, Springer, vol. 176(3), pages 389-403, September.
    3. Damien Bol & Arnaud Dellis & Mandar Oak, 2016. "Comparison of Voting Procedures using Models of Electoral Competition with Endogenous Candidacy," School of Economics Working Papers 2016-02, University of Adelaide, School of Economics.
    4. Cahan, Dodge & McCabe-Dansted, John & Slinko, Arkadii, 2018. "Asymmetric equilibria in spatial competition under weakly concave scoring rules," Economics Letters, Elsevier, vol. 167(C), pages 71-74.
    5. Dodge Cahan & Arkadii Slinko, 2018. "Electoral competition under best-worst voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 259-279, August.
    6. Arnaud Dellis & Mandar Oak, 2016. "Multiple votes, multiple candidacies and polarization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 1-38, January.
    7. Ruzica Savcic & Dimitrios Xefteris, 2020. "Apostolic Voting," University of Cyprus Working Papers in Economics 08-2020, University of Cyprus Department of Economics.
    8. Arnaud Dellis & Mandar Oak, 2016. "Multiple votes, multiple candidacies and polarization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 1-38, January.
    9. Tarbush, Bassel, 2018. "Hotelling competition and the gamma distribution," Games and Economic Behavior, Elsevier, vol. 111(C), pages 222-240.
    10. Bol, Damien & Matakos, Konstantinos & Troumpounis, Orestis & Xefteris, Dimitrios, 2019. "Electoral rules, strategic entry and polarization," Journal of Public Economics, Elsevier, vol. 178(C).

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    More about this item

    Keywords

    Hotelling–Downs model; Equilibrium; Multiple votes;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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