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I introduce a new equilibrium concept for political games, based on the fact of factional conflict within parties. Each party is supposed to consist of reformists, militants, and opportunists: each faction has a complete preference order on policy space, but together they can only agree on a partial order. Nash equilibria of the two party game, where the policy space consists of all quadratic income tax functions, and each party is represented by its partial order, exist, and it is shown that, in such equilibria, both parties propose progressive income taxation.
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