Why do both left and right political parties typically propose progressive income taxation schemes in political competition? Analysis of this problem has been hindered by the two‐dimensionality of the issue space. To give parties a choice over a domain that contains both progressive and regressive income tax policies requires an issue space that is at least two‐dimensional. Nash equilibrium in pure strategies of the standard two‐party game, whose players have complete preferences over a two‐dimensional policy space, generically fails to exist. 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.