Multiparty spatial competition with probabilistic voting

I develop a general model of multiparty competition in which parties model voters' choices by means of probabilistic choice rules. The model is specified in terms of an issue salience coefficient which varies with the importance voters attach to issues, as opposed to unmeasured nonissue motivations. I show that when the policy salience coefficient is sufficiently low, then both vote-maximizing and rank-maximizing parties have a dominant strategy: to adopt the "most popular platform,'' which maximizes voter utilities over the entire electorate. This most popular platform therefore represents a convergent equilibrium when all parties are vote- or rank-maximizing. Numerical estimates suggest that this equilibrium result holds for degrees of issue voting which exceed the parameters behavioral researchers have estimated for various historical elections.