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In this paper we study the possibility of constructing satisfactory social choice mechanisms whose outcomes are determined by a combination of voting and chance. The following theorem is obtained: if a social choice mechanism does not leave too much to chance and satisfies a unanimity condition, then it is either uniformly manipulable or dictatorial. The result contributes to the program suggested by Gibbard [2] for the study of the extent to which social choice mechanisms in which chance plays a role can be freed from 2 strategic manipulation.

[This paper explores the possibilities opened up by combining preference aggregation and randomization in passing from individual to collective judgements about alternatives. We study the distribution of power under functions which assign to each profile of individual preferences a probabilistic judgement on each pair of alternatives x, y, that is, a probability of x being considered socially at least as good as y. Conditions are described under which the power of coalitions to guarantee that an alternative is not declared worse than another is subadditive, while their power to guarantee that one alternative is not declared better than another is superadditive. These results extend some of the main findings on the structure of decisive coalitions under deterministic social choice rules.]

We consider the allocation of goods in exchange economies with a finite number of agents who may have private information about their preferences. In such a setting, standard allocation rules such as Walrasian equilibria or rational expectations equilibria are not compatible with individual incentives. We characterize the set of allocation rules which are incentive compatible, or in other words, the set of strategy-proof social choice functions. Social choice functions which are strategy-proof are those which can be obtained from trading according to a finite number of pre-specified proportions. The number of proportions which can be accommodated is proportional to the number of agents. Such rules are necessarily inefficient, even in the limit as the economy grows

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.