Inducing probability distributions on the set of value functions by Subjective Stochastic Ordinal Regression

Abstract

Multiple criteria ranking problem is approached using Subjective Stochastic Ordinal Regression (SSOR).Preferences of the decision maker are expressed through pairwise comparisons of some reference alternatives.A part of pairwise comparisons is certain, and another part is uncertain.Uncertain pairwise comparisons are used to build a probability distribution over the space of all preference models compatible with certain pairwise comparisons.From sampling of this distribution, one learns a probability with which a is ranked on the rth position (rank acceptability index), and probability that a is preferred to b (pairwise winning index). Ordinal regression methods of Multiple Criteria Decision Aiding (MCDA) take into account one, several, or all value functions compatible with the indirect preference information provided by the Decision Maker (DM). When dealing with multiple criteria ranking problems, typically, this information is a series of holistic and certain judgments having the form of pairwise comparisons of some reference alternatives, indicating that alternative a is certainly either preferred to or indifferent with alternative b. In some decision situations, it might be useful, however, to additionally account for uncertain pairwise comparisons interpreted in the following way: although the preference of a over b is not certain, it is more credible than preference of b over a. To handle certain and uncertain preference information, we propose a new approach that builds a probability distribution over the space of all value functions compatible with the DM's certain holistic judgments. A didactic example shows the applicability of the proposed approach.