Weighted sets of probabilities and minimax weighted expected regret: a new approach for representing uncertainty and making decisions

We consider a setting where a decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision making, by modifying a standard approach to decision making—minimizing expected regret—to obtain minimax weighted expected regret (MWER). We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case. Copyright Springer Science+Business Media New York 2015