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 at least 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.