Coalitionally strategy-proof social choice correspondences and the Pareto rule

This paper studies coalitional strategy-proofness of social choice correspondences that map preference profiles into sets of alternatives. In particular, we focus on the Pareto rule, which associates the set of Pareto optimal alternatives with each preference profile, and examine whether or not there is a necessary connection between coalitional strategy-proofness and Pareto optimality. The definition of coalitional strategy-proofness is given on the basis of a max–min criterion. We show that the Pareto rule is coalitionally strategy-proof in this sense. Moreover, we prove that given an arbitrary social choice correspondence satisfying the coalitional strategy-proofness and nonimposition, all alternatives selected by the correspondence are Pareto optimal. These two results imply that the Pareto rule is the maximal correspondence in the class of coalitionally strategy-proof and nonimposed social choice correspondences.