Strategy-proof social choice correspondences

We study the possibilities of constructing strategy-proor rules that choose sets or alternatives as a function or agents' preferences over such sets. We consider two restrictions on the domain of individual preferences over sets. Assuming that all singletons are in the range of the rule, we show that only dictatorial rules can be strategy-proof on the larger domain. The smaller domain also allows for rules,which select the set of best elements of two fixed agents. (C) 2001 Academic Press.