  This paper examines the relationship between Shafer's belief functions and
convex sets of probability distributions. Kyburg's (1986) result showed that
belief function models form a subset of the class of closed convex probability
distributions. This paper emphasizes the importance of Kyburg's result by
looking at simple examples involving Bernoulli trials. Furthermore, it is shown
that many convex sets of probability distributions generate the same belief
function in the sense that they support the same lower and upper values. This
has implications for a decision theoretic extension. Dempster's rule of
combination is also compared with Bayes' rule of conditioning.
