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Social Choice and Welfare

, Volume 43, Issue 2, pp 429–446 | Cite as

Policy convergence in a two-candidate probabilistic voting model

  • Alexei V. ZakharovEmail author
  • Constantine S. Sorokin
Original Paper

Abstract

We propose a generalization of the probabilistic voting model in two-candidate elections. We allow the candidates have general von Neumann–Morgenstern utility functions defined over the voting outcomes. We show that the candidates will choose identical policy positions only if the electoral competition game is constant-sum, such as when both candidates are probability-of-win maximizers or vote share maximizers, or for a small set of functions that for each voter define the probability of voting for each candidate, given candidate policy positions. At the same time, a pure-strategy local Nash equilibrium (in which the candidates do not necessarily choose identical positions) exists for a large set of such functions. Hence, if the candidate payoffs are unrestricted, the “mean voter theorem” for probabilistic voting models is shown to hold only for a small set of probability of vote functions.

Keywords

Nash Equilibrium Policy Position Vote Function Policy Platform Fair Lottery 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

Constantine Sorokin acknowledges the support of the HSE International Laboratory of Decision Choice and Analysis. Alexei Zakharov acknowledges the support of NES Center for the Study of Diversity and Social Interactions.

References

  1. Alesina A (1988) Credibility and policy convergence in a two-party system with rational voters. Am Econ Rev 78(4):796–805Google Scholar
  2. Anderson R, Zam W (2001) Genericity with infinitely many parameters. Adv Theor Econ 1(1):1–65CrossRefGoogle Scholar
  3. Ashworth S, Bueno de Mesquita E (2009) Elections with platform and valence competition. Games Econ Behav 67(1):191–216CrossRefGoogle Scholar
  4. Banks J, Duggan J (2005) Probabilistic voting in the spatial model of elections: the theory of office-motivated candidates. In: Austen-Smith D, Duggan J (eds) Social choice and strategic decisions. Springer, New YorkGoogle Scholar
  5. Besley T, Coate S (1997) An economic model of representative democracy. Quart J Econ 112(1):85–114CrossRefGoogle Scholar
  6. Calvert RL (1985) Robustness of the multidimensional voting model: candidate motivations. Uncertain Convergence Am J Polit Sci 29(1):69–95CrossRefGoogle Scholar
  7. Duggan J (2000) Equilibrium equivalence under expected plurality and probability of winning maximization. mimeo, University of Rochester, New YorkGoogle Scholar
  8. Duggan J, Fey M (2005) Electoral competition with policy-motivated candidates. Games Econ Behav 51(2):490–522CrossRefGoogle Scholar
  9. Gallagher M (1992) Comparing proportional representation electoral systems: quotas, thresholds, paradoxes and majorities. Br J Polit Sci 22:469–496CrossRefGoogle Scholar
  10. Groseclose T (2001) A model of candidate location when one candidate has a valence advantage. Am J Polit Sci 45(5):862–886CrossRefGoogle Scholar
  11. Grossman G, Helpman E (2001) Special interest politics. MIT Press, CambridgeGoogle Scholar
  12. Hinich M (1977) Equilibrium in spatial voting: the median voter result is an artifact. J Econ Theory 16:208–219CrossRefGoogle Scholar
  13. Hinich M, Ledyard J, Ordeshook P (1972) Nonvoting and the existence of equilibrium under majority rule. J Econ Theory 4:144–153CrossRefGoogle Scholar
  14. Hojman D (2004) So, do you really want to be a senator? The political economy of candidate motivation and electoral defeat in Chile. University of Liverpool research paper no 0403Google Scholar
  15. Laver M, Shepsle K (1996) Making and breaking governments: cabinets and legislatures in parliamentary democracies. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  16. Ledyard J (1984) The pure theory of large two-candidate elections. Public Choice 44:7–41CrossRefGoogle Scholar
  17. Lijphart A (1990) The political consequences of electoral laws. Am Polit Sci Rev 84:481–496CrossRefGoogle Scholar
  18. Lin T-M, Enelow J, Dorussen H (1999) Equilibrium in multicandidate probabilistic spatial voting. Public Choice 98:59–82CrossRefGoogle Scholar
  19. McKelvey R, Patty JW (2006) A theory of voting in large elections. Games Econ Behav 57(1):155–180CrossRefGoogle Scholar
  20. Osborne MJ, Slivinski A (1996) A model of political competition with citizen-candidates. Q J Econ 111(1):65–96Google Scholar
  21. Patty JW (2005) Local equilibrium equivalence in probabilistic voting models. Games Econ Behav 51(1):523–536Google Scholar
  22. Patty JW (2007) Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters. Soc Choice Welf 29(1):149–173CrossRefGoogle Scholar
  23. Patty JW, Snyder JM, Ting MM (2008) Two’s a company, three’s an equilibrium: strategic voting and multicandidate elections. Mimeo, Harvard University, New YorkGoogle Scholar
  24. Quinn KM, Martin AD, Whitford AB (1999) Voter choice in multi-party democracies: a test of competing theories and models. 43(4):1231–1247Google Scholar
  25. Schofield N (2007) The mean voter theorem: necessary and sufficient conditions for convergent equilibrium. Rev Econ Stud 74:965–980CrossRefGoogle Scholar
  26. Schofield N, Sened I (2006) Multiparty democracy: elections and legislative politics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  27. Schofield N, Zakharov A (2010) A stochastic model of the 2007 Russian Duma election. Public Choice 142(1–2):177–194Google Scholar
  28. Simpser A (2013) Why governments and parties manipulate elections: theory, practice, and implications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  29. Snyder J, Ting M, Ansolabehere S (2005) Legislative bargaining under weighted voting. Am Econ Rev 95(4):981–1004CrossRefGoogle Scholar
  30. Zakharov AV (2009) Candidate location and endogenous valence. Public Choice 138(3–4):347–366CrossRefGoogle Scholar
  31. Zakharov AV (2012) Probabilistic voting equilibria under nonlinear candidate payoffs. J Theor Polit 24(2):235–247CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Higher School of EconomicsMoscowRussia
  2. 2.Higher School of Economics International Laboratory of Decision Choice and AnalysisMoscowRussia

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