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The standard Bowen (Bowen, 1943) model of political competition with single-peaked preferences predicts party convergence to the ideal point supported by the median voter, with the number of equilibrium policies not exceeding two. This fundamental result assumes majority rule and unidimensional policy space. Relaxing these two assumptions, 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, although it may not be unidimensional. 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 political economies governed by supermajority rules. We develop an application to immigration policies.

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