An Axiomatic Utility Theory for Dempster-Shafer Belief Functions

International audienceThe main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for proba-bilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued 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

Models for pessimistic or optimistic decisions under different uncertain scenarios

In many decision problems under uncertainty, agents are only able to provide a possibly incomplete preference relation on gambles, that can be “irrational” according to the classical expected utility paradigm. Furthermore, agents can find it easier to express their preference relation taking one or more specific scenarios as hypothesis. In order to handle these situations two betting scheme rationality conditions are introduced, which characterize those preference relations representable by a conditional Choquet expected value with respect to a conditional belief or plausibility function. Such conditions encode a pessimistic or an optimistic attitude towards uncertainty, respectively, and allow to take into account (possible) “null” scenarios by means of a weak ordering of “unexpectation”. Moreover, they are the basis of a completion technique for enlarging the set of preferences by preserving rationality