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International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 562813, 30 pages
Research Article

Application of a Theorem in Stochastic Models of Elections

1Center in Political Economy, Washington University, 1 Brookings Drive, Saint Louis, MO 63130, USA
2State University, Higher School of Economics, 117218 Novocheremushkinskaya St. 34-1, Apt. 68 Moscow, Russia

Received 2 July 2009; Revised 2 December 2009; Accepted 11 February 2010

Academic Editor: Martin Bohner

Copyright © 2010 Norman Schofield et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Previous empirical research has developed stochastic electoral models for Israel, Turkey, and other polities. The work suggests that convergence to an electoral center (often predicted by electoral models) is a nongeneric phenomenon. In an attempt to explain nonconvergence, a formal model based on intrinsic valence is presented. This theory showed that there are necessary and sufficient conditions for convergence. The necessary condition is that a convergence coefficient c is bounded above by the dimension w of the policy space, while a sufficient condition is that the coefficient is bounded above by 1. This coefficient is defined in terms of the difference in exogenous valences, the “spatial coefficient”, and the electoral variance. The theoretical model is then applied to empirical analyses of elections in the United States and Britain. These empirical models include sociodemographic valence and electoral perceptions of character trait. It is shown that the model implies convergence to positions close to the electoral origin. To explain party divergence, the model is then extended to incorporate activist valences. This extension gives a first-order balance condition that allows the party to calculate the optimal marginal condition to maximize vote share. We argue that the equilibrium positions of presidential candidates in US elections and by party leaders in British elections are principally due to the influence of activists, rather than the centripetal effect of the electorate.