Application of Linear Utility Theory to Belief Functions

Dempster-Shafer theory (Dempster[ 3 ], Sharer[ 9 ], [10] ) represents knowledge about events through the use of a generally non-additive set-function, termed a lower probability function (Dempster) or a belief function (Shafer). As shown in [3 ], there exists a wide class of uncertainty situations in which the objective information available naturally takes this form.[ 9 ]emphasizes the usefulness Of belief functions in the describing of subjective judgments. Dempster-Shafer theory is of little interest for decision analysts in the absence of a complementary decision model. This paper proposes that the mode] resulting from the application of von Neumann-Morgenstern linear utility theory to belief functions be adopted in such cases. The terminology and notations of Dempster-Shafer theory as they are presented in this paper are roughly those found in[ 9 ]. Proofs of the main properties of belief functions can be found in[ 3 ], [9 ], or in Chateauneuf and Jaffray[ 2 ]. For linear utility theory we have followed Fishburn [5 ].