IDEAS home Printed from https://ideas.repec.org/p/ucy/cypeua/09-2015.html
   My bibliography  Save this paper

Stability in electoral competition: A case for multiple votes

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://papers.econ.ucy.ac.cy/RePEc/papers/09-15.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Osborne Martin J., 1993. "Candidate Positioning and Entry in a Political Competition," Games and Economic Behavior, Elsevier, vol. 5(1), pages 133-151, January.
    2. Haan, Marco & Volkerink, Bjorn, 2001. "A runoff system restores the principle of minimum differentiation," European Journal of Political Economy, Elsevier, vol. 17(1), pages 157-162, March.
    3. Brusco, Sandro & Dziubiński, Marcin & Roy, Jaideep, 2012. "The Hotelling–Downs model with runoff voting," Games and Economic Behavior, Elsevier, vol. 74(2), pages 447-469.
    4. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    5. Ben D. MacArthur & Richard O. C. Oreffo, 2005. "Bridging the gap," Nature, Nature, vol. 433(7021), pages 19-19, January.
    6. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2005. "Transfers in a polarized country: bridging the gap between efficiency and stability," Journal of Public Economics, Elsevier, vol. 89(7), pages 1277-1303, July.
    7. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-1037, July.
    8. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.
    9. Dellis, Arnaud & Oak, Mandar P., 2006. "Approval voting with endogenous candidates," Games and Economic Behavior, Elsevier, vol. 54(1), pages 47-76, January.
    10. repec:ulb:ulbeco:2013/162238 is not listed on IDEAS
    11. Thomas R. Palfrey, 1984. "Spatial Equilibrium with Entry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(1), pages 139-156.
    12. Myerson, Roger B., 1999. "Theoretical comparisons of electoral systems," European Economic Review, Elsevier, vol. 43(4-6), pages 671-697, April.
    13. Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
    14. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    15. 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.
    16. 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.
    17. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    18. Dodge Cahan & Arkadii Slinko, 2017. "Nonconvergent Electoral Equilibria under Scoring Rules: Beyond Plurality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(2), pages 445-460, April.
    19. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    20. Matsushima, Noriaki, 2007. "Uncertainty of voters' preferences and differentiation in a runoff system," European Journal of Political Economy, Elsevier, vol. 23(4), pages 1185-1189, December.
    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. 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. 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.
    3. Arnaud Dellis, 2022. "Does Party Polarization Affect the Electoral Prospects of a New Centrist Candidate?," Games, MDPI, vol. 13(4), pages 1-20, July.
    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. Bol, Damien & Matakos, Konstantinos & Troumpounis, Orestis & Xefteris, Dimitrios, 2019. "Electoral rules, strategic entry and polarization," Journal of Public Economics, Elsevier, vol. 178(C).
    6. 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.
    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. 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.
    10. Tarbush, Bassel, 2018. "Hotelling competition and the gamma distribution," Games and Economic Behavior, Elsevier, vol. 111(C), pages 222-240.

    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. 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.
    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. 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.
    4. Arnaud Dellis & Alexandre Gauthier-Belzile & Mandar Oak, 2017. "Policy Polarization and Strategic Candidacy in Elections under the Alternative-Vote Rule," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 173(4), pages 565-590, December.
    5. Damien Bol & Arnaud Dellis & Mandar oak, 2015. "Endogenous Candidacy in Electoral Competition: A Survey," School of Economics and Public Policy Working Papers 2015-19, University of Adelaide, School of Economics and Public Policy.
    6. 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.
    7. Arnaud Dellis, 2022. "Does Party Polarization Affect the Electoral Prospects of a New Centrist Candidate?," Games, MDPI, vol. 13(4), pages 1-20, July.
    8. Arnaud Dellis & Sean D’Evelyn & Katerina Sherstyuk, 2011. "Multiple votes, ballot truncation and the two-party system: an experiment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(2), pages 171-200, July.
    9. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    10. 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.
    11. Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
    12. Brusco, Sandro & Dziubiński, Marcin & Roy, Jaideep, 2012. "The Hotelling–Downs model with runoff voting," Games and Economic Behavior, Elsevier, vol. 74(2), pages 447-469.
    13. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 329-352, February.
    14. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
    15. Richard Chisik & Robert Lemke, 2006. "When winning is the only thing: pure strategy Nash equilibria in a three-candidate spatial voting model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 209-215, January.
    16. Alexander Shapoval & Shlomo Weber & Alexei Zakharov, 2019. "Valence influence in electoral competition with rank objectives," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 713-753, September.
    17. Krasa, Stefan & Polborn, Mattias, 2010. "The binary policy model," Journal of Economic Theory, Elsevier, vol. 145(2), pages 661-688, March.
    18. 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.
    19. Granić, Đura-Georg, 2017. "The problem of the divided majority: Preference aggregation under uncertainty," Journal of Economic Behavior & Organization, Elsevier, vol. 133(C), pages 21-38.
    20. Buisseret, Peter, 2017. "Electoral competition with entry under non-majoritarian run-off rules," Games and Economic Behavior, Elsevier, vol. 104(C), pages 494-506.

    More about this item

    Keywords

    Hotelling-Downs model; equilibrium; multiple votes;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ucy:cypeua:09-2015. 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: the person in charge (email available below). General contact details of provider: https://www.ucy.ac.cy/econ/?lang=en .

    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.