# Valence influence in electoral competition with rank objectives

- 30 Downloads

## Abstract

In this paper we examine the effects of valence in a continuous spatial voting model with two incumbent candidates and a potential entrant. All candidates are rank-motivated. We first consider the case where the low valence incumbent (LVC) and the entrant have zero valence, whereas the valence of the high valence incumbent (HVC) is positive. We show that a sufficiently large valence of HVC guarantees a unique equilibrium, where the two incumbents prevent the entry of the third candidate. We also show that an increase in valence allows HVC to adopt a more centrist policy position, while LVC selects a more extreme position. We also examine the existence of equilibrium for the cases where the LVC has higher or lower valence than the entrant.

## Keywords

Valence Candidates Electoral game Rank objectives Electoral equilibrium Distribution of ideal points## Mathematics Subject Classification

C72 D72## Notes

## References

- Anagol S, Fujiwara T (2014) The runner-up effect. No. w20261. National Bureau of Economic ResearchGoogle Scholar
- Aragones E, Palfrey T (2002) Mixed equilibrium in a Downsian model with a favored candidate. J Econ Theory 103:131–161CrossRefGoogle Scholar
- Aragones E, Palfrey T (2005) Electoral competition between two candidates of different quality: the effects of candidate ideology and private information. Soc Choice Strat Decis. Stud Choice Welf 93–112. https://doi.org/10.1007/3-540-27295-X_4
- Aragones E, Palfrey T (2004) The effect of candidate quality on electoral equilibrium: an experimental study. Am Polit Sci Rev 98(1):77–90CrossRefGoogle Scholar
- Aragones E, Xefteris D (2012) Candidate quality in a Downsian model with a continuous policy space. Games Econ Behav 75(2):464–480. https://doi.org/10.1016/j.geb.2011.12.008 CrossRefGoogle Scholar
- Ashworth S, Mesquita EBD (2009) Elections with Platform and Valence Competition. Games Econ Behav 67(1):191–216CrossRefGoogle Scholar
- Banks JS, Duggan J (2005) Probabilistic voting in the spatial model of elections: the theory of office-motivated candidates. Social choice and strategic decisions. Springer, Berlin, pp 15–56CrossRefGoogle Scholar
- Berger MM, Munger MC, Potthoff RF (2000) The Downsian Model Predicts Divergence. J Theor Polit 12(2):228–240CrossRefGoogle Scholar
- Bierbrauer FJ, Boyer PC (2013) Political competition and Mirrleesian income taxation: a first pass. J Public Econ 103:1–14CrossRefGoogle Scholar
- Buisseret P (2017) Electoral competition with entry under non-majoritarian run-off rules. Games Econ Behav 104:494–506CrossRefGoogle Scholar
- Callander S, Wilson CH (2007) Turnout, polarization, and Duverger’s law. J Polit 69(4):1047–1056CrossRefGoogle Scholar
- Cohen RN (1987) Symmetric 2-equilibria of unimodal voter distribution curves. Harvard University, HarvardGoogle Scholar
- Greenberg J, Shepsle KA (1987) The effects of electoral rewards in multiparty competition with entry. Am Polit Sci Rev 81:525–537CrossRefGoogle Scholar
- Groseclose T (2001) A model of candidate location when one candidate has a valence advantage. Am J Polit Sci 45:862–886CrossRefGoogle Scholar
- Haimanko O, Le Breton M, Weber S (2005) Transfers in a Polarized Country: bridging the gap between efficiency and stability. J Public Econ 89(7):1277–1303CrossRefGoogle Scholar
- Herrera H, Levine DK, Martinelli C (2008) Policy platforms, campaign spending and voter participation. J Public Econ 92(3–4):501–513CrossRefGoogle Scholar
- Hummel P (2010) On the nature of equilibria in a Downsian model with candidate valence. Game Econ Behav 70(2):425–445CrossRefGoogle Scholar
- Krasa S, Polborn MK (2010) Competition between specialized candidates. Am Polit Sci Rev 104(4):745–765CrossRefGoogle Scholar
- Krasa S, Polborn MK (2012) Political competition between differentiated candidates. Games Econ Behav 76(1):249–271CrossRefGoogle Scholar
- Mueller D (2003) Public choice III, 3rd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Palfrey T (1984) Spatial equilibrium with entry. Rev Econ Stud 51:139–156CrossRefGoogle Scholar
- Poutvaara P, Takalo T (2007) Candidate quality. Int Tax Public Financ 14(1):7–27CrossRefGoogle Scholar
- Rubinchik A, Weber S. (2007) Existence and uniqueness of an equilibrium in a model of spatial electoral competition with entry. In: Kusuoka S, Yamazaki A (eds) Advances in mathematical economics. Advances in mathematical economics, vol. 10. Springer, Tokyo, pp 101–119Google Scholar
- Schofield N, Zakharov A (2010) A stochastic model of the Russian Duma election. Public Choice 142:177. https://doi.org/10.1007/s11127-009-9483-2 CrossRefGoogle Scholar
- Serra G (2010) Polarization of what? A model of elections with endogenous valence. J Polit 72(2):426–437CrossRefGoogle Scholar
- Shepsle KA, Cohen RN (1990) Multiparty competition, entry, and entry deterrence in spatial models of elections. In: Enelow JM, Hinich MJ (eds) Advances in the spatial theory of voting. Cambridge University Press, CambridgeGoogle Scholar
- Stokes D (1963) Spatial models of candidate competition. Am Polit Sci Rev 57:368–377CrossRefGoogle Scholar
- Stromberg D (2008) How the electoral college influences campaign and policy: the probability of being Florida. Am Econ Rev 98(3):769–807CrossRefGoogle Scholar
- Tsakas N, Xefteris D (2018) Electoral competition with third party entry in the lab. J Econ Behav Org 148:121–134CrossRefGoogle Scholar
- Weber S (1990) On the existence of a fixed-number equilibrium in a multiparty electoral system. Math Soc Sci 20:115–130CrossRefGoogle Scholar
- Weber S (1992) On hierarchical spatial competition. Rev Econ Stud 59:407–425CrossRefGoogle Scholar
- Weber S (1997) Entry deterrence in electoral spatial competition. Soc Choice Welf 15(1):31–56CrossRefGoogle Scholar
- Whiteley P, Stewart MC, Sanders D, Clarke HD (2005) The issue Agenda and voting in 2005. Parliament Stud 58(4):802–817Google Scholar
- Xefteris D (2014) Mixed equilibriums in a three-candidate spatial model with candidate valence. Public Choice 158:101–120CrossRefGoogle Scholar
- Xefteris D (2018) Candidate valence in a spatial model with entry. Public Choice 176(3–4):341–359CrossRefGoogle Scholar
- Zakharov A (2009) A model of candidate location with endogenous valence. Public Choice 138(3–4):347–366. https://doi.org/10.1007/s11127-008-9362-2 CrossRefGoogle Scholar