Reference-dependent Qualitative Models for Decision Making under Uncertainty

The aim of this paper is to introduce and investigate a new family of purely qualitative models for decision making under uncertainty. Such models do not require any numerical representation and rely only on the definition of a preference relation over consequences and a relative likelihood relation on the set of events. Within this family, we focus on decision rules using reference levels in the comparison of acts. We investigate both the descriptive potential of such rules and their axiomatic foundations. We introduce in a Savage-like framework, a new axiom requiring that the Decision Maker’s preference between two acts depends on the respective positions of their consequences relatively to reference levels. Under this assumption we determine the only possible form of the decision rule and characterize some particular instances of this rule under transitivity constraints.