A trade-off result for preference revelation

If the social choice rule g selects from one up to k alternatives (but not more), then there exists a coalition H of k individuals such that for each profile r, the choice set g(r) is the collection of the top-most alternativ es in the orderings of the individuals in H. Consequently, g is independent of the preferences of individuals not in H, forcing a disagreeable trade-o ff: Either some choice sets are very large, or most individuals never have any say in the social choice. (C) 2000 Elsevier Science S.A. All rights res erved.