The “probability of a fit choice”

This paper attempts to model elections by incorporating voter judgments about candidate and leader competence. The proposed model can be linked to Madison’s understanding of the nature of the choice of Chief Magistrate (Madison, James Madison: writings. The Library of America, New York, 1999 [1787]) and Condorcet’s work on the so-called “Jury Theorem” (Condorcet 1994 [1785]). Electoral models use the notion of a Nash Equilibrium. This notion generally depends on a fixed point argument. For deterministic electoral models, there will typically be no equilibrium. Instead we introduce the idea of a preference field, $$H,$$ for the society. A condition called half-openess of $$H$$ is sufficient to guarantee existence of a local direction gradient, $$d,$$ Even when $$d$$ is not well-defined we can use the idea of the heart for the society. This is an attractor of the set of social moves that can occur. As an application, a stochastic model of elections is considered, and applied to the 2008 presidential election in the United States. In such a stochastic model the electoral origin will satisfy the first order condition for a local Nash equilibrium. We then show how to compute the Hessian of each candidate’s vote share function, and obtain necessary and sufficient conditions for convergence to the electoral origin, suggesting that there will be a social direction gradient. The origin maximizes aggregrate voter utility and can be interpreted as a fit choice for the polity. Copyright Springer-Verlag Berlin Heidelberg 2013