Harmful Random Utility Models

Abstract

In many choice problems the evaluation of alternatives is determined by a mediation between opposite judgments. In these situations the decision maker (DM) may not maximize her true preference, but some compromise on it, in which the first i options are rated according to the adversarial ranking. Compromise-based Random Utility Models (compromise-based RUMs), which are RUMs whose support is limited to the compromises on some preference, naturally represent the consequences of the trade-off between antithetical criteria on choices. Compromise-based RUMs are characterized by the existence of a linear order that allows the experimenter to recover choice probabilities from selections over the ground set, or, alternatively, to verify three behavioral axioms. Necessary and sufficient conditions for a full identification of the DM's preference and her randomization over compromises are singled out. In all but two cases, there is a unique justification by compromise of data. Finally, a degree of compromise, which measures the extent of the mediation embraced by the DM in her decision, is characterized.