Strategic party formation on a circle and Duverger's Law

Duverger’s law states that plurality rule tends to favor a two-party system. We study the game-theoretic foundations of this law in a spatial model of party formation and electoral competition. The standard spatial model assumes a linear agenda space. However, when voters vote sincerely, electoral competition on the line under plurality rule gravitates towards a single party located at the median. We therefore depart from the linear space and instead adopt the unit circle as the space of agendas. We characterize pure-strategy (subgame-perfect) nash equilibria under both sincere and strategic voting. Under both voting behaviors, multiple configurations of parties are possible in equilibrium. We refine our predictions using a new notion called defection-proof (subgame-perfect) nash equilibrium. Under sincere voting, either two or three parties are effective in defection-proof nash equilibria, whereas under strategic voting, either one or two parties are effective in defection-proof subgame-perfect nash equilibria. These results are partially consistent with duverger’s law.