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Stability in electoral competition: A case for multiple votes

Listed author(s):
  • Dimitrios Xefteris

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.

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File URL: http://papers.econ.ucy.ac.cy/RePEc/papers/09-15.pdf
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Paper provided by University of Cyprus Department of Economics in its series University of Cyprus Working Papers in Economics with number 09-2015.

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Length: 30 pages
Date of creation: Nov 2015
Handle: RePEc:ucy:cypeua:09-2015
Contact details of provider: Web page: http://www.ucy.ac.cy/econ/en

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  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. Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
  3. Mark Bagnoli & Ted Bergstrom, 2005. "Log-concave probability and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 445-469, 08.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
  9. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-1037, July.
  10. 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.
  11. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, 01.
  12. Dellis, Arnaud & Oak, Mandar P., 2006. "Approval voting with endogenous candidates," Games and Economic Behavior, Elsevier, vol. 54(1), pages 47-76, January.
  13. repec:ulb:ulbeco:2013/162238 is not listed on IDEAS
  14. Thomas R. Palfrey, 1984. "Spatial Equilibrium with Entry," Review of Economic Studies, Oxford University Press, vol. 51(1), pages 139-156.
  15. Myerson, Roger B., 1999. "Theoretical comparisons of electoral systems," European Economic Review, Elsevier, vol. 43(4-6), pages 671-697, April.
  16. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  17. 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.
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