Summary
We unify and extend much of the literature on probabilistic voting in two-candidate elections. We give existence results for mixed and pure strategy equilibria of the electoral game. We prove general results on optimality of pure strategy equilibria vis-a-vis a weighted utilitarian social welfare function, and we derive the well-known “mean voter” result as a special case. We establish broad conditions under which pure strategy equilibria exhibit “policy coincidence,” in the sense that candidates pick identical platforms. We establish the robustness of equilibria with respect to variations in demographic and informational parameters. We show that mixed and pure strategy equilibria of the game must be close to being in the majority rule core when the core is close to non-empty and voters are close to deterministic. This controverts the notion that the median (in a one-dimensional model) is a mere “artifact.” Using an equivalence between a class of models including the binary Luce model and a class including additive utility shock models, we then derive a general result on optimality vis-a-vis the Nash social welfare function.
The second author gratefully acknowledges support from the National Science Foundation, grant number SES-0213738.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aliprantis, C. and K. Border (1994) Infinite Dimensional Analysis: A Hitchhiker’s Guide New York: Springer-Verlag.
Aliprantis, C. and O. Burkinshaw (1990) Principles of Real Analysis New York: Academic Press.
Ball, R. (1999) Discontinuity and non-existence of equilibrium in the probabilistic spatial voting model. Social Choice and Welfare, 16: 533–556.
Banks, J. S. and J. Duggan (2004) Existence of Nash equilibria on convex sets. Mimeo. University of Rochester.
Banks, J. S. and J. Duggan (2002) A multi-dimensional model of repeated elections. Mimeo. University of Rochester.
Banks, J. S., J. Duggan, and M. Le Breton (2004) Social choice and electoral competition in the general spatial model. Journal of Economic Theory, forthcoming.
Besley, T. and S. Coate (1997) An economic model of representative democracy. Quarterly Journal of Economics, 112: 85–114.
Black, D. (1958) The Theory of Committees and Elections Cambridge: Cambridge University Press.
Calvert, R. (1985) Robustness of the multidimensional voting model: candidate motivations, uncertainty, and convergence. American Journal of Political Science, 29: 69–95.
Coughlin, P. (1992) Probabilistic Voting Theory Cambridge: Cambridge University Press.
Coughlin, P. and S. Nitzan (1981) Electoral outcomes with probabilistic voting and Nash social welfare maxima. Journal of Public Economics, 15: 113–121.
Downs, A. (1957) An Economic Theory of Democracy New York: Harper and Row.
Duggan, J. (2000) Equilibrium equivalence under expected plurality and probability of winning maximization. Mimeo. University of Rochester.
Glicksberg, I. (1952) A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium. Proceedings of the American Mathematical Society, 3: 170–174.
Hinich, M. (1977) Equilibrium in spatial voting: the median voter result is an artifact. Journal of Economic Theory, 16: 208–219.
Hinich, M. (1978) The mean versus the median in spatial voting games. In P. Ordeshook (ed) Game Theory and Political Science New York: NYU Press.
Hinich, M., J. Ledyard, and P. Ordeshook (1972) Nonvoting and the existence of equilibrium under majority rule. Journal of Economic Theory, 4: 144–153.
Hinich, M., J. Ledyard, and P. Ordeshook (1973) A theory of electoral equilibrium: a spatial analysis based on the theory of games. Journal of Politics, 35: 154–193.
Hotelling, H. (1929) Stability in competition. Economic Journal, 39: 41–57.
Kramer, G. (1978) Robustness of the median voter result. Journal of Economic Theory, 19: 565–567.
Laussel, D. and M. Le Breton (2002) Unidimensional Downsian politics: median, utilitarian or what else? Economics Letters, 76: 351–356.
Ledyard, J. (1984) The pure theory of large two-candidate elections. Public Choice, 44: 7–41.
Lindbeck, A. and J. Weibull (1987) Balanced-budget redistribution as the outcome of political competition. Public Choice, 52: 273–297.
Lindbeck, A. and J. Weibull (1993) A model of political equilibrium in a representative democracy. Journal of Public Economics, 51: 195–209.
Luenberger, D. (1969) Optimization by Vector Space Methods New York: Wiley.
McKelvey, R. and J. Patty (2003) A theory of voting in large elections. Mimeo. Carnegie Mellon University.
Osborne, M. and A. Slivinski (1996) A model of political competition with citizen-Candidates. Quarterly Journal of Economics, 111: 65–96.
Patty, J. (2002) Equivalence of objectives in two candidate elections. Public Choice, 112: 151–166.
Patty, J. (2003) Local equilibrium equivalence in probabilistic voting models. Mimeo. Carnegie Mellon University.
Plott, C. (1967) A notion of equilibrium and its possibility under majority rule. American Economic Review, 57: 787–806.
Rosen, J. (1965) Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33: 520–534.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Banks, J.S., 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. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27295-X_2
Download citation
DOI: https://doi.org/10.1007/3-540-27295-X_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22053-4
Online ISBN: 978-3-540-27295-3
eBook Packages: Business and EconomicsEconomics and Finance (R0)