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The relative belief of singletons

In this paper we introduce the relative belief of singletons as a novel probability distribution associated with a belief function. We discuss its nature in terms of degrees of belief under several difierent angles, its rationale in terms of game theory and its applicability to difierent classes of belief functions. We prove that it commutes with Dempster’s orthogonal sum, and meets a number of properties which are the duals of those met by the relative plausibility of singletons. This highlights a classiflcation of Bayesian approximations in two families, according to the operator they relate to. Finally, we propose a natural extension of the relative belief transformation which exists for all belief functions and inherits its properties.