On the complexity of achieving proportional representation

We demonstrate that winner selection in two prominent proportional representation voting systems is a computationally intractable problem—implying that these systems are impractical when the assembly is large. On a different note, in settings where the size of the assembly is constant, we show that the problem can be solved in polynomial time.     

Super Majoritarianism and the Endowment Effect

The American and some other constitutions entrench property rights by requiring super majoritarian voting as a condition for amending or revoking their own provisions. Following Buchanan and Tullock [The Calculus of Consent, Logical Foundations of Constitutional Democracy (University of Michigan Press, Ann Arbor), 1962], this paper analyzes individuals' interests behind a veil of ignorance, and shows that under some standard assumptions, a (simple) majoritarian rule should be adopted. This result changes if one assumes that preferences are consistent with the behavioral phenomenon known as the endowment effect. It then follows that (at least some) property rights are best defended by super majoritarian protection. The paper then shows that its theoretical results are consistent with a number of doctrines underlying American Constitutional Law.