Dempster's Rule as Seen by Little Colored Balls

Dempster’s rule is traditionally interpreted as an operator for fusing belief functions. While there are different types of belief fusion, there has been considerable confusion regarding the exact type of operation that Dempster’s rule performs. Many alternative operators for belief fusion have been proposed, where some are based on the same fundamental principle as Dempster’s rule, and others have a totally different basis, such as the cumulative and averaging fusion operators. In this article we analyze Dempster’s rule from a statistical and frequentist perspective and compare it with cumulative and averaging belief fusion. We prove, and illustrate by examples on colored balls, that Dempster’s rule in fact represents a method for serial combination of stochastic constraints. Consequently, Dempster’s rule is not a method for cumulative fusion of belief functions under the assumption that subjective beliefs are an extension of frequentist beliefs. Having identified the true nature of Dempster’s rule, appropriate applications of Dempster’s rule of combination are described such as the multiplication of orthogonal belief functions, and the combination of preferences dictated by different parties.