Make evidence theory probabilistic again

In this paper we prove from a new angle that Dempster’s rule is inherently probabilistic, extends Bayes’ rule, and reduces to Bayes’ rule when precise probabilities are available, regardless of whether prior is uniform. We use examples to demonstrate this equivalence. Additionally, we explain that the Evidential Reasoning (ER) rule is also probabilistic and includes Bayes’ and Dempster’s rules as special cases. Furthermore, we address some criticisms of the behaviour of Dempster’s rule from a probabilistic perspective and explain the rationality of the behaviour. We also identify instances where such critiques were misapplied. Finally, we clarify vital differences between belief degrees in belief functions and basic probabilities and highlight the critical differences between Shafer’s discounting method and the ER rule. These differences make the latter probabilistic, while the former is not. Our motivation is to show that evidence theory has a probabilistic foundation and is possible to become probabilistic again.