Sufficiency in Blackwell's theorem

If one information service is more informative than the other, then any agent values it more. In fact, the opposite implication (sufficiency) is also true, and this characterization is the celebrated Blackwell's theorem. We present here a short proof of sufficiency. Actually, we show a stronger result: it is enough to check whether the value of the service is greater than the value of the other for any fixed positive a priori probabilities and a set of terminal actions that has only two elements. (C) 2003 Elsevier Science B.V. All rights reserved.