Coping with Imprecise Information : A Decision Theoretic Approach

We provide a model of decision making under uncertainty in which the decision maker reacts toimprecision of the available data. Data is represented by a set of probability distributions. Weaxiomatize a decision criterion of the maxmin expected utility type, in which the revealed setof priors explicitly depends on the available data. We then characterize notions of comparativeaversion to imprecision of the data as well as traditional notions of risk aversion. Interestingly,the study of comparative aversion to imprecision can be done independently of the utilityfunction, which embeds risk attitudes. We also give a more specific result, in which the functionalrepresenting the decision maker’s preferences is the convex combination of the minimumexpected utility with respect to the available data and expected utility with respect to a subjectiveprobability distribution, interpreted as a reference prior. This particular form is shown tobe equivalent to some form of constant aversion to imprecision. We finally provide examples ofapplications first to unanimity rankings of imprecision and risk and then to optimal risk sharingarrangements.