Decision making under interval probabilities

If we know the probabilities p1; : : : ; pn of diierent situations s1; : : : ; sn, then we can choose a decision Ai for which the expected beneet Ci = p1 ci1 + : : : + pn cin takes the largest possible value, where cij denotes the beneet of decision Ai in situation sj. In many real life situations, however, we do not know the exact values of the probabilities pj; we only know the intervals pj = p ? j ; p + j ] of possible values of these probabilities. In order to make decisions under such interval probabilities, we would like to generalize the notion of expected beneets to interval probabilities. In this paper, we show that natural requirements lead to a unique (and easily computable) generalization. Thus, we have a natural way of decision making under interval probabilities.