Divided government and dominance solvability

Using the spatial theory of voting, this paper describes an institutional structure where there are two branches of the government: the executive, elected by plurality rule, and the legislative elected by proportional rule. The resulting policy outcome is described through a compromise between these two branches. The parties announce their position on a policy issue and then voters vote. We prove the uniqueness of Nash equilibrium in the subgame, where the election of the president is known. Moreover, this equilibrium can be obtained by the process of iterated elimination of dominated strategies. We then solve the whole game by backward induction. Furthermore, the policy outcome at equilibrium of the two-stage game is the same of the simultaneous game, where voters simultaneously choose the two branches. The results suggest a moderate behavior of the voters, basically due to the will to balance the policy outcome.