We examine the relevance of an auction format in a competitive environment by comparing uniform and discriminatory price auctions with many bidders in a private values setting. We show that if the number of objects for sale is small relative to the number of bidders, then all equilibria of both auctions are approximately efficient and lead to approximately the same revenue. When the number of objects for sale is proportional to the number of bidders, then the particulars of the auction format matter. All equilibria of the uniform auction are efficient, while all of the equilibria of the discriminatory auction are inefficient. The relative revenue rankings of the auction formats can go in either direction, depending on the specifics of the environment. These conclusions regarding the efficiency and revenue ranking are in contrast to the previous literature, which focused on the case of independent information across agents.

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.