We study efficient, Bayes-Nash incentive compatible mechanisms in a general social choice setting that allows for informationally interdependent valuations and for allocative externalities. We show that such mechanisms exist only if a congruence condition relating private and social rates of information substitution is satisfied. If signals are multi-dimensional, the congruence condition is determined by a complex integrability constraint, and it can hold only in non-generic cases such as the private value case or the symmetric case. If signals are one-dimensional, the congruence condition reduces to a monotonicity constraint and it can be generically satisfied. We apply the results to the study of multi-object auctions, and we discuss why such auctions cannot be reduced to one-dimensional models without loss of generality.