On the Influence of Extreme Parties in Electoral Competition with Policy-Motivated Candidates

We study and compare equilibrium platforms in models of one-dimensional electoral competition with two and four policy-motivated parties. We first analyse the plurality game, where the party that gets the most votes is elected and implements its proposed platform. Restrictions on the set of credible announcements are needed to get existence of equilibria. Comparing equilibria with two and four parties, we obtain that moderate parties react to the introduction of extreme parties by proposing the same or more extreme equilibrium platforms. We then study the proportional system, where the policy implemented is a weighted sum of the proposals, with the voting shares as weights. Here, the existence of extreme parties leads moderate ones to choose more centrist platforms.