The Ambiguity Dilemma for Imprecise Bayesians

Abstract

How should we make decisions when we do not know the relevant physical probabilities?In these ambiguous situations, we cannot use our knowledge to determine expected util-ities or payoffs. The traditional Bayesian answer is that we should create a probabilitydistribution using some mix of subjective intuition and objective constraints. ImpreciseBayesians argue that this approach is inadequate for modelling ambiguity. Instead, theyrepresent doxastic states using credal sets. Generally, insofar as we are more uncertainabout the physical probability of an event, there is more divergence in the credal set.Hence, their approach can represent these ambiguities via the extent of the divergence.Imprecise Bayesianism has mostly been advocated for its epistemological features. In thisarticle, we examine its properties for decision making. We develop a model for comparingstandard and imprecise Bayesianism by testing their performances in a classic decisionproblem. We find that the representational tools of imprecise Bayesianism also cause itto underperform in our tests. This issue has been overlooked, because previous researchon imprecise Bayesianism has not utilized agent-based modelling to provide informa-tion about its performance in the short-run. Overall, we reveal the ambiguity dilemmafor imprecise Bayesianism: To what extent should one value representational power ordecision-making performance?