An Axiomatic Utility Theory for DempsterShafer Belief Functions
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Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:145155, 2019.
Abstract
The main goal of this paper is to describe an axiomatic utility theory for DempsterShafer belief function lotteries. The axiomatic framework used is analogous to von NeumannMorgenstern’s utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to intervalvalued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray’s representation theorem for his linear utility theory for belief functions. We illustrate our framework using some examples discussed in the literature. Finally, we compare our decision theory with those proposed by Jaffray and Smets.
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