Is Shafer General Bayes?

Abstract: 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.