A number of unconventional formal approaches to decision making have been developed to provide mathematical foundations for rational choices under both aleatory and epistemic uncertainty. They challenge a central assumption of the Bayesian theory, that uncertainty should always be gauged by a single (additive) measure, and values should always be gauged by a precise utility function [3]. Decision-making theorists have presented approaches for arriving at rational decisions in spite of imprecision and indeterminacy [4-8, 10]. This paper introduces the theory of upper and lower previsions, provides examples, discusses how to account for unreliable statistical judgements, and reviews the relationships between the Precautionary Principle, indecision, and imprecise statistical reasoning.
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