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We consider a setting where an agent's uncertainty is represented by a set ofprobability measures, rather than a single measure. Measure-bymeasure updatingof such a set of measures upon acquiring new information is well-known tosuffer from problems; agents are not always able to learn appropriately. Todeal with these problems, we propose using weighted sets of probabilities: arepresentation where each measure is associated with a weight, which denotesits significance. We describe a natural approach to updating in such asituation and a natural approach to determining the weights. We then show howthis representation can be used in decision-making, by modifying a standardapproach to decision making-minimizing expected regret-to obtain minimaxweighted expected regret (MWER).We provide an axiomatization that characterizespreferences induced by MWER both in the static and dynamic case.

Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions