Interpreting Imprecise Probabilities
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In formal modelling, it is essential that models be supplied
with an interpretative story: there must be a clear and
coherent account of how the formal model relates to the
phenomena it is supposed to model.  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 is shown to
lead to unacceptable results -- and, it is argued, 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
exactly we are to extract information about an agent's
belief state from a set of probabilities.