Abstract
Previous models of elections have emphasized the convergence of parties to the center of the electorate in order to maximize votes received. More recent models of elections demonstrate that this need not be the case if asymmetry of party valences is assumed and a stochastic model of voting within elections is also assumed. This model seems able to reconcile the widely accepted median voter theorem and the instability theorems that apply when considering multidimensional policy spaces. However, these models have relied on there being a singular party bundle offered to all voters in the electorate. In this paper, we seek to extend these ideas to more complex electorates, particularly those where there are regional parties which run for office in a fraction of the electorate. We derive a convergence coefficient and out forth necessary and sufficient conditions for a generalized vector of party positions to be a local Nash equilibrium; when the necessary condition fails, parties have incentive to move away from these positions. For practical applications, we pair this finding with a microeconometric method for estimating parameters from an electorate with multiple regions which does not rely on independence of irrelevant alternatives but allows estimation of parameters at both aggregate and regional levels. We demonstrate the effectiveness of this model by analyzing the 2004 Canadian election.
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- 1.
This can be conceptualized as an average assessment of the parties quality to govern among all members of the electorate, regardless of sociodemographic identity.
- 2.
To match up with the empirical applications later in the paper, the utility individual i gains from having party j in office is compared to a base party, j=1. As is normal, we assume this party has a utility of zero and the other utilities are compared to this party. Thus, the utility gained by i by voting for j can also be seen as \(u_{ij}^{\ast }(x_{i},z_{j})=\lambda_{j}-\beta (\sum_{m=1}^{w}((x_{jm}-x_{im})^{2}-(x_{1}m-x_{im})^{2}))+ \alpha_{ij}\) where the summation is of the Euclidian distances for each dimension of the policy space. This places our model in line with the latent utility models that are commonly used in microeconometric theory and bridges the gap between our theoretical model and the corresponding empirical model.
- 3.
In this paper, we assume that this term is common among all members of a specific sociodemographic group. However, we can set up these terms to represent individuals with individual level random effects.
- 4.
It is interesting to note that the convergence coefficient need not be positive, as is the case with c BQ (z ∗). This simple indicates a particularly strong desire to stay in the given position. A negative convergence coefficient indicates a quickly changing local maximum, meaning that a small departure from this position would result in a large decrease in vote share.
References
Adams J (2001) Party competition and responsible party government. University of Michigan Press, Ann Arbor
Adams J, Merrill S III (1999) Modeling party strategies and policy representation in multiparty elections: why are strategies so extreme? Am J Polit Sci 43:765–781
Benoit K, Laver M (2006) Party policy in modern democracies. Routledge, London
Blais A, Fournier P, Gidengil E, Nevitte N, Everitt J (2006) Election 2006: how big were the changes… really? Working paper, Universite de Montreal
Caplin A, Nalebuff B (1991) Aggregation and social choice: a mean voter theorem. Econometrica 59:1–23
Dow JK, Endersby J (2004) Multinomial logit and multinomial probit: a comparison of choice models for voting research. Elect Stud 23:107–122
Downs A (1957) An economic theory of democracy. Harper and Row, New York
Gelman A, Park D, Shor B, Bafumi J, Cortina J (2008) Red state, blue state, rich state, poor state: why Americans vote the way they do. Princeton University Press, Princeton
Hotelling H (1929) Stability in competition. Econ J 39:41–57
Kramer G (1978) Existence of electoral equilibrium. In: Ordeshook P (ed) Game theory and political science. New York University Press, New York, pp 375–389
Merrill S, Grofman B (1999) A united theory of voting. Cambridge University Press, Cambridge
Patty JW (2005) Local equilibrium equivalence in probabilistic voting models. Games Econ Behav 51:523–536
Patty JW (2007) Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters. Soc Choice Welf 29:149–173
Penn E (2003) A model of far-sighted voting. Unpublished paper, Harvard University
Poole K, Rosenthal H (1984) US presidential elections 1968–1980. Am J Polit Sci 28:283–312
Quinn K, Martin A, Whitford A (1999) Voter choice in multiparty democracies. Am J Polit Sci 43:1231–1247
Riker WH, Ordeshook PC (1973) An introduction to positive political theory. Prentice-Hall, Englewood Cliffs
Schofield N (2007) The mean voter theorem: necessary and sufficient conditions for convergent equilibrium. Rev Econ Stud 74:965–980
Schofield N, Martin A, Quinn K, Whitford A (1998) Multiparty electoral competition in the Netherlands and Germany: a model based on multinomial probit. Public Choice 97:257–293
Train K (2003) Discrete choice methods for simulation. Cambridge University Press, Cambridge
Yamamoto T (2011) A multinomial response model for varying choice sets, with application to partially contested multiparty elections. Working paper
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Appendix
Appendix
This appendix gives the algorithm for the Gibbs sampling.
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McAlister, K., Jeon, J.S., Schofield, N. (2013). Modeling Elections with Varying Party Bundles: Applications to the 2004 Canadian Election. In: Schofield, N., Caballero, G., Kselman, D. (eds) Advances in Political Economy. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35239-3_14
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