Strategic Party Formation on a Circle

We study a spatial model of party formation in which the set of agendas is the unit circle. We characterize the sets of pure-strategy Nash equilibria under the plurality and proportional rules. In both rules, multiple configurations of parties are possible in Nash equilibrium. We refine our predictions using a new notion called “defection-proof” Nash equilibrium. Under the plurality rule, only those Nash equilibria in which either two or three parties exist are defection-proof, whereas multiple parties exist in any defectionproof Nash equilibrium under the proportional rule. These results are mostly consistent with the predictions of Duverger (1954)