Representing knowledge and evidence for decision

Abstract

Our decisions reflect uncertainty in various ways. We take account of the uncertainty embodied in the roll of the die; we less often take account of the uncertainty of our belief that the die is fair. We need to take account of both uncertain knowledge and our knowledge of uncertainty.. “Evidence” itself has been regarded as uncertain. We argue that point-valued probabilities are a poor representation of uncertainty; that we need not be concerned with uncertain evidence; that interval-valued probabilities that result from knowledge of convex sets of distribution functions in reference classes (properly) include Shafer's mass functions as a special case; that these probabilities yield a plausible non-monotonic form of inference (uncertain inference, inductive inference, statistical inference); and finally that this framework provides a very nearly classical decision theory— so far as it goes. It is unclear how global the principles (such as minimax) that go beyond the principle of maximizing expected utility are.