Decision with belief functions and generalized independence: Two impossibility theorems1

Dempster-Shafer theory of evidence is a framework that is expressive enough to represent both ignorance and probabilistic information. However, decision models based on belief functions proposed in the literature face limitations in a sequential context: they either abandon the principle of dynamic consistency, restrict the combination of lotteries, or relax the requirement for transitive and complete comparisons. This work formally establishes that these requirements are indeed incompatible when any form of compensation is considered. It then demonstrates that these requirements can be satisfied in non-compensatory frameworks by introducting and characterizing a dynamically consistent rule based on first-order dominance.