Review and experimental comparison of ranking and choice procedures for constructing a univocal recommendation in a preference disaggregation setting

Abstract

We account for the preference disaggregation setting given multiple criteria ranking and choice problems. An assumed preference model is a set of additive value functions compatible with the Decision Maker’s pairwise comparisons of reference alternatives. The incompleteness of such indirect preferences implies the multiplicity of feasible functions and the ambiguity in indicating the most preferred alternative or ordering alternatives from the best to the worst. We review approaches that construct a univocal recommendation under such scenarios. They represent four groups of methods: procedures selecting a representative value function, decision rules, scoring methods, and mathematical models for constructing a robust ranking. The use of all thirty-five approaches is illustrated on a simple decision problem. Then, they are compared in an extensive computational study in terms of their abilities to reconstruct the DMs’ true preferences and robustness of delivered recommendations given the support they are given in the set of all compatible models. The results are quantified in terms of seven performance measures. Their analysis indicates that in the context of choice, it is beneficial to consider the rank acceptabilities for the best ranks. For ranking problems, the most advantageous outcomes are attained by procedures that emphasize the most frequent relations or positions in the feasible polyhedron. Apart from the average results, we discuss how the performance of all approaches changes for different parameterizations of the decision problem and preference model.