The Ambiguity Dilemma for Imprecise Bayesians

How should we make decisions when we do not know the relevant physical probabilities? In these situations of ignorance, we cannot use our knowledge to determine expected utilities or payoffs. The traditional Bayesian answer is that we should create a probability distribution using some mix of subjective intuition and objective constraints. Imprecise Bayesians argue that this approach is inadequate for modelling states of ignorance. Instead, they represent doxastic states using sets of probability distributions. Generally, insofar as we are more ignorant about the physical probability of an event, the more its probabilities in this set will differ. Hence, the divergence of the probabilities provides an indication and even a measure of the extent to which the modelled reasoner is ignorant about that event. Imprecise Bayesianism has mostly been advocated for its epistemological features. In this article, we examine its properties for decision-making. We develop a model for contrasting standard and Imprecise Bayesianism by testing their performances in a classic decision problem. We find that the representational tools of Imprecise Bayesianism also cause it to underperform in our tests. This issue has been overlooked, because previous research on Imprecise Bayesianism has not utilised agent-based modelling to provide information about its performance in the short-run. Overall, we reveal the Ignorance Dilemma for Bayesianism: to what extent should one value representational power or decision-making performance?