Decision with Belief Functions and Generalized Independence: Two Impossibility Theorems

Hélène Fargier, Romain Guillaume

Abstract: Belief functions constitute a particular class of lower probability measures which is expressive enough to allow the representation of both ignorance and probabilistic information. Nevertheless, the decision models based on belief functions proposed in the literature are limited when considered in a dynamical context: either they drop the principle of dynamical consistency, or they limit the combination of lotteries, or relax the requirement for a transitive and complete comparison. The present work formally shows that these requirements are indeed incompatible as soon as a form of compensation is looked for. We then show that these requirement can be met in non compensative frameworks by exhibiting a dynamically consistent rule based on first order dominance.