Group strategy-proofness and voting between two alternatives

We study rules for choosing between two alternatives when people may be indifferent between them. We specify two strategic requirements for groups of people. The first, group strategy-proofness, says that manipulations by groups ought not make every member of the group better off. The second, strong group strategy-proofness, says that such manipulations ought not make even one member of the group better off without making another worse off. Our main result is a characterization of “consensus” rules and “constant” rules as the only strongly group strategy-proof rules when there are more than two people.