Respecting Evidence: Belief Functions not Imprecise
Probabilities
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The received model of degrees of belief represents them as
probabilities.  Over the last half century, many
philosophers have been convinced that this model fails
because it cannot make room for the idea that an agent's
degrees of belief should respect the available evidence.  In
its place they have advocated a model that represents
degrees of belief using imprecise probabilities (sets of
probability functions).  This paper presents a model of
degrees of belief based on Dempster-Shafer belief functions
and then presents arguments for belief functions over
imprecise probabilities as a model of evidence-respecting
degrees of belief.  The arguments cover three kinds of
issue: theoretical virtues (simplicity, interpretability and
flexibility); motivations; and problem cases (dilation and
belief inertia).