Interpreting imprecise probabilities

Abstract It is essential that formal models come with interpretations: accounts of how the models relate to the phenomena. The traditional representation of degrees of belief as mathematical probabilities comes with a clear and simple interpretative story. This paper argues that the model of degrees of belief as imprecise probabilities (sets of probabilities) lacks a workable interpretation: The standard interpretative story given in the literature leads to unacceptable results—and there is no way for imprecise probabilists to restrict, replace, or finesse this story so as either to avoid or to be able to live with the consequences. Thus, the imprecise probabilist lacks a viable account of how a set of probability functions models a belief state: A story about which properties of the model correspond to facts about the thing modelled and how we are to extract information about an agent’s belief state from a set of probabilities.