One of the fundamental problems of the positive theory of income taxation is explaining why the statutory income tax schedules in all industrialized democracies are marginal-rate progressive. While it is commonly believed that this is but a simple consequence of the fact that the number of relatively poor voters exceeds that of richer voters in such societies, putting this contention in a voting equilibrium context proves to be a nontrivial task. We study the Downsian model in the context of nonlinear taxation and inquire about the possibility of providing a formal argument in support of the aforementioned intuition. We first show existence of mixed strategy equilibria and then ask qualitative questions about the nature of these equilibria. Our positive results show that there are cases where marginal-rate progressive taxes are chosen with probability one by the political parties. Our negative results show that, if the tax policy space is not artificially constrained, equilibria exist whose support does not lie within the set of all marginal-rate progressive taxes.