The standard Bowen model of political competition with single-peaked preferences (Bowen, 1943) predicts party convergence to the median voter's ideal policy, with the number of equilibrium policies not exceeding two. This result assumes majority rule and unidimensional policy space. We extend this model to static and dynamic political economies where the voting rule is a supermajority rule, and the policy space is totally ordered. Voters' strategic behavior is captured by the core in static environments and by the largest consistent set in dynamic environments. In these settings, we determine the exact number of equilibria and show that it is an increasing correspondence of the supermajority's size. This result has implications for the depth of policy diversity across structurally identical supermajoritarian political economies. We also examine the equilibrium effects of supermajority rules on utilitarian welfare and political compromise under uncertainty.