A Sophisticated Social Welfare Function (SSWF) is a mapping from profiles of individual preferences into a sophisticated preference which is a pairwise weighted comparison of alternatives. We characterize Pareto optimal and pairwise independent SSWFs in terms of oligarchies that are induced by some power distribution in the society. This is a fairly large class ranging from dictatoriality to anonymous aggregation rules. Our results generalize the impossibility theorem of Arrow (Social choice and individual values. Wiley, New York, 1951) and the oligarchy theorem of Gibbard (Intransitive social indifference and the Arrow dilemma, University of Chicago, unpublished manuscript, 1969).