An allocation for an exchange economy with smooth preferences is shown to be Walrasian if there is a set of net trades that is closed under addition, contains the negations of net trades that would improve any agent's final bundle, and is such that each agent's final bundle is weakly preferred to the sum of the initial endowment and any allowed net trade. These conditions characterize the sets of net trades available in equilibria of market games in which randomly paired agents bargain repeatedly and imply that steady state equilibria are Walrasian.

The main result of this paper characterizes voting by committees. There are n voters and K objects. Voters must choose a subset of K. Voting by committees is defined by one monotone family of winning coalitions for each object; an object is chosen if it is supported by one of its winning coalitions. This is proven to be the class of all voting schemes satisfying voter sovereignty and nonmanipulability on the domain of separable preferences. The result is analogous to the characterization of Clarke-Groves schemes in that it exhibits the class of all nonmanipulable schemes on an important domain.