Partially efficient voting by committees

On the separable preference domain, voting by committees is the only class of voting rules that satisfy strategy-proofness and unanimity, and dictatorial rules are the only ones that are strategy-proof and Pareto efficient. To fill the gap, we define a sequence of efficiency conditions. We prove that for strategy-proof rules on the separable preference domain, the various notions of efficiency reduce to three: unanimity, partial efficiency, and Pareto efficiency. We also show that on the domain, strategy-proofness and partial efficiency characterize the class of voting rules represented as simple games which are independent of objects, proper and strong. We call such rules voting by stable committee.The author is deeply indebted to William Thomson for many helpful discussions on an earlier draft. The current version is greatly benefited from detailed comments of an anonymous referee. Thanks are also due to Jeffrey Banks, Salvador Barberà, Marcus Berliant, Ryo-ichi Nagahisa, Takehiko Yamato, and participants in a seminar at Rochester in 1992, the 1992 Midwest Conference at Michigan State, and the 1993 Summer Meeting of Econometric Society at Boston University for conversations and suggestions.