Problems of social choice frequently take the following form. There are n voters and a set K = {1, 2,..., k} of objects. The voters must choose a subset of K. We define a class of voting schemes called voting by committees. The main result of the paper is a characterization of voting by committees, which is the class of all voting schemes that satisfy voter sovereignty and nonmanipulability on the domain of separable preferences. This result is analogous to the literature on the Groves and Clarke scheme in that it characterizes all of the nonmanipulable voting schemes on an important domain.
Constitutional arrangements affect the decisions made by a society. We study how this effect leads to preferences of citizens over constitutions; and ultimately how this has a feedback that determines which constitutions can survive in a given society. Constitutions are stylized here, to consist of a voting rule for ordinary business and possibly a different voting rule for making changes to the constitution. We define an equilibrium notion for constitutions, called self-stability, whereby under the rules of a self-stable constitution, the society would not vote to change the constitution. We argue that only self-stable constitutions will endure. We prove that self-stable constitutions always exist, but that most constitutions (even very prominent ones) may not be self-stable for some societies. We show that constitutions where the voting rule used to amend the constitution is the same as the voting rule used for ordinary business are dangerously simplistic, and there are (many) societies for which no such constitution is self-stable. We conclude with a characterization of the set of self-stable constitutions that use majority rule for ordinary business.
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