Valence competition in the spatial stochastic model

The mean voter theorem of the stochastic spatial electoral model provides no explanation as to why multi-party systems under proportional representation display such diversity. Here, we extend the spatial model to include valence. Valence may be either a stochastic variable describing the variation in popularity for each candidate in the electorate or, alternatively, it will be generated by activist coalitions responding to the willingness of the candidate to pursue the interests of the coalition. In a general model of multiple candidates (or political agents), the first- and second-order conditions for pure strategy Nash equilibria are developed. It is shown that rational candidates will balance the gradient of electoral pull against the gradients generated by contending activist coalitions. The resulting Nash equilibria will almost never be at the mean of the voter distribution.