Interpreting Imprecise Probabilities
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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.