We study indirect democracy in which countries, states, or districts each elect a representative who later votes at a union level on their behalf. We show that the voting rule that maximizes the total expected utility of all agents in the union involves assigning a weight to each district’s vote and then sticking with the status quo unless at least a threshold of weighted votes is cast for change. We analyze how the weights relate to the population size of a country and the correlation structure of agents’ preferences, and then we compare the voting weights in the Council of the European Union under the Nice Treaty and the recently proposed Constitution.

Many salient rules to allocate private goods are not only strategy-proof, but also group strategy-proof, in appropriate domains of definition, hence diminishing the traditional conflict between incentives and efficiency. That is so for solutions to matching, division, cost sharing, house allocation, and auctions, in spite of the substantive disparity between these cases. In a general framework encompassing all of them, we prove that the equivalence between the two forms of strategy-proofness is due to an underlying common structure that transcends the many differences between the contexts and the mechanisms for which it holds.