This paper considers strategic voters who face an institutional structure in which there are two branches of the government: the executive, elected by plurality rule, and the legislature elected by proportional rule. Policy outcomes are described through a compromise between these two branches. I solve the game by relying only on purely non-cooperative behavior of individual voters. I prove the uniqueness of Nash equilibrium in the legislative subgame, where the election of the president is known. This equilibrium can be obtained by the process of iterated elimination of dominated strategies. I then solve the whole game by backward induction. The results suggest moderate behavior of voters, due to the desire to balance the plurality of a party in the presidential election by voting for the opposite party in the legislature. Similar results can be obtained in the case of reverse timing of the elections, as well as in the case where elections of the two branches of the government are simultaneous

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