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We propose a model of endogenous party platforms with stochastic membership. The parties' proposals depend on their membership, while the membership depends both on the proposals of the parties and on the unobserved idiosyncratic preferences of citizens over parties. An equilibrium of the model obtains when the members of each party prefer the proposal of the party to which they belong to, rather than the proposal of the other party. We prove the existence of such an equilibrium and study its qualitative properties. For the cases in which parties use either the average or the median to aggregate the preferences of their members, we show that if the unobserved idiosyncratic characteristics of the parties are similar, then parties make different proposals in the stable equilibria. Conversely, we argue that if parties differ substantially in their unobserved idiosyncratic characteristics, then the unique equilibrium is convergent.
Political parties Stochastic membership Divergent equilibria Political competition Spatial model Candidates