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Stability in electoral competition: A case for multiple votes

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  • Dimitrios Xefteris

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 if (k=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

  • Dimitrios Xefteris, 2015. "Stability in electoral competition: A case for multiple votes," University of Cyprus Working Papers in Economics 09-2015, University of Cyprus Department of Economics.
    • Handle: RePEc:ucy:cypeua:09-2015
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    References listed on IDEAS

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    16. Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
    17. 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.
    18. Dellis, Arnaud, 2009. "Would letting people vote for multiple candidates yield policy moderation?," Journal of Economic Theory, Elsevier, vol. 144(2), pages 772-801, March.
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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. Ružica Savčić & Dimitrios Xefteris, 2021. "Apostolic voting," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(3), pages 1400-1417, November.
    3. 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.
    4. Damien Bol & Arnaud Dellis & Mandar Oak, 2016. "Comparison of Voting Procedures Using Models of Electoral Competition with Endogenous Candidacy," Studies in Political Economy, in: Maria Gallego & Norman Schofield (ed.), The Political Economy of Social Choices, pages 21-54, Springer.
    5. Arnaud Dellis, 2022. "Does Party Polarization Affect the Electoral Prospects of a New Centrist Candidate?," Games, MDPI, vol. 13(4), pages 1-20, July.
    6. 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.
    7. 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.
    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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