Reference‐based preferences aggregation procedures in multi‐criteria decision making

This paper aims at introducing and investigating a new family of merely qualitative models for multicriteria decision making. Such models do not require any numerical representation. Within this family, we will focus on decision rules using reference levels in order to help comparing several alternatives. We will investigate both the descriptive potential of such rules and their axiomatic foundations. After recalling the descriptive and prescriptive limitations of merely ordinal rules that do not use reference points, we will introduce a new axiom requiring that the Decision Maker’s preference between two alternatives depends on the respective positions of their consequences relatively to reference levels. Under this assumption we will determine the only possible form for the decision rule and characterize some particular instances of this rule under transitivity constraints. Our results show that introducing reference points overcomes the usual limitations of purely ordinal aggregation methods, by moving the application point of Arrow’s theorem.