Nonmanipulable voting schemes when participants' interests are partially decomposable

Recent papers by Barberá and Peleg and by Zhou have established that the Gibbard-Satterthwaite Theorem remains valid when individuals are restricted to reporting only "reasonable" preferences. We present a theorem that covers situations in which, as in Barberá-and-Peleg and Zhou, preferences may be restricted to reasonable ones, but in which, additionally, it may be known in advance that some dimensions of the social decision do not affect all the participants - i.e., in which the social decisions are partially decomposable into decisions that affect only subsets of the participants. As in the previous theorems, the conclusion of this new theorem is that nonmanipulable voting schemes must be dictatorial.