Local Nash Equilibrium in Multiparty Politics

We present a model of multi-party, “spatial” competition under proportional rule with both electoral and coalitional risk. Each party consists of a set of delegates with heterogeneous policy preferences. These delegates choose one delegate as leader or agent. This agent announces the policy declaration (or manifesto) to the electorate prior to the election. The choice of the agent by each party elite is assumed to be a local Nash equilibrium to a game form g̃. This game form encapsulates beliefs of the party elite about the nature of both electoral risk and the post-election coalition bargaining game. It is demonstrated, under the assumption that g̃ is smooth, that, for almost all parameter values, a locally isolated, local Nash equilibrium exists. In the final section of the paper some empirical work is reviewed in order to obtain some insights into why parties do not simply converge to an electoral center in order to maximize expected vote shares.