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.

The authors consider the problem of allocating a bundle of commodities among a group of agents who are collectively entitled to them. It is proved that, for an atomless economy with possibly satiated preferences, any solution that is efficient, equitable, and consistent must select allocations that are supported by equal-budget Walrasian equilibria with slack.

According to this paper, the analysis of the Nash bargaining problem with risky outcomes must include the cases where the disagreement outcome itself is risky as well. Thus, one generalizes the Roth and Rothblum results to models with risky disagreement outcome as well. It turns out that their result will depend, in some cases, upon the «degree of change» in risk aversion. Particularly, when the potential agreement, has an outcome which makes player 2 worse off compared to the disagreement, and if the disagreement does not dominate that outcome (i.e., its support contains a worse outcome), then when player 2 becomes «sufficiently» more risk averse player 1 becomes better off. Thus one obotains that increase in risk aversion may be disadvantageous to player 2 even if the risky disagreement is preferred to some outcome of the (risky) agreement

In a nontransferable utility exchange economy with a continuum of agents, the Mas-Collel bargaining set coincides with the set of Walrasian equilibria. In this paper, we show that the Mas-Colell bargaining set, as well as a smaller bargaining set due to Zhou, may fail to converge to competitive outcomes in large finite NTU exchange economies.