Why Dempster´s rule doesn´t behave as Bayes rule with informative priors

In this paper, we analyze Bayes fusion rule in details from a fusion standpoint, as well as the emblematic Dempster´s rule of combination introduced by Shafer in his Mathematical Theory of evidence based on belief functions. We propose a new interesting formulation of Bayes rule and point out some of its properties. A deep analysis of the compatibility of Dempster´s fusion rule with Bayes fusion rule is done. Our analysis proves clearly that Dempster´s rule of combination does not behave as Bayes fusion rule in general, because these methods deal very differently with the prior information when it is really informative (not uniform). Only in the very particular case where the basic belief assignments to combine are Bayesian and when the prior information is uniform (or vacuous), Dempster´s rule remains consistent with Bayes fusion rule. In more general cases, Dempster´s rule is incompatible with Bayes rule and it is not a generalization of Bayes fusion rule.