In his 1980 paper ‘A Subjectivist’s Guide to Objective Chance’, David Lewis argued that much of our reasoning about objective probabilities rests on an intuitively compelling rule of inference that Lewis dubbed the ‘Principal Principle’. In its simplest version, the Principal Principle states that one ought to set one’s subjective probabilities equal to the corresponding objective probabilities, provided that one has no ‘inadmissible’ evidence. (The principle will be explained at greater length below.) At the time, Lewis announced that he had one reservation about the Principal Principle: it seemed to be inconsistent with the philosophical doctrine of Humean supervenience concerning objective probabilities, or as they are sometimes called, chances. (Again, details will be found below.) In a recent triplet of articles (Lewis 1994, Thau 1994 and Hall 1994), Lewis and two of his associates have concluded that this ‘one reservation’, when examined more closely, is enough to undermine entirely the Principal Principle as we know it. Hall and Lewis claim that that principle—now deemed the ‘Old Principle’— 1 ought to be replaced with a new rule they call the ‘New Principle’. Thau seems to concur. What we are left with is “a revolutionary view”, according to Thau. The old, intuitive Principal Principle is dead; a new, unfamiliar, yet supposedly more rational principle has taken its place. It is notable, however, that none of the three authors is able to supply compelling reasons to think that the New Principle is legitimate. At best, the evidence is suggestive: the New Principle does not suffer from the problems of the old, and it supports approximately the same (intuitive) inferences as the old, in most situations. It is the aim of this paper to supply the necessary justification for the New Principle, though not quite in accordance with the wishes of Lewis, Hall and Thau...