A reference-dependent regret model for deterministic tradeoff studies

This communication focuses on a fundamental problem related to the recently introduced Reference-Dependent Regret Model (RDRM) [Kujawski, 2005] for deterministic multicriteria decision making. In [Kujawski, 2005] it was asserted that the RDRM model satisfies three properties. The first of these properties, referred to as the “independence of dominated alternatives”, seems to be an intuitive one. According to this property, the RDRM model preserves the ranking of two alternatives Ai and Aj with ranking Ai A f j when a new alternative dominated by Ai is introduced or an old alternative dominated by Aj is dropped. In this communication it is demonstrated algebraically and also by means of a numerical example that the RDRM model may fail to satisfy this property. The implication is that when the concepts of regret and/or rejoicing are considered and defined in terms of all the available alternatives in accordance with the RDRM, adding or dropping a dominated alternative can change the ranking of the alternatives and violate the independence of dominated alternatives property.