Stochastic Ordinal Regression for Multiple Criteria Decision Support



We consider the two problems of (1) ranking decision alternatives and (2) sorting them in predefined, ordered categories based on deterministic evaluations on multiple criteria. We apply additive value theory and assume the Decision Maker's (DM) per-criterion preferences to be representable with general monotonic marginal value functions. The DM provides indirect preference information in form of (1) pair-wise comparisons of reference alternatives, or (2) assignment of reference alternatives to categories. We use the indirect preferences to derive the set of compatible value functions. In (1), this set is analyzed to describe possible and necessary preference relations, probabilities of the possible relations, the ranges of ranks the alternatives may obtain and the distributions of these ranks. In (2) we derive necessary and possible assignment-based weak preference relations and the assignment probabilities. Our work combines previous results from Robust Ordinal regression (ROR), Extreme Ranking Analysis (ERA) and Stochastic Multicriteria Acceptability Analysis (SMAA) under a unified decision support framework. We show how the different results complement each other, discuss extensions of the main proposals, and demonstrate practical use of the approaches by considering two problems: (i) ranking of 20 European countries in terms of 4 criteria reflecting the quality of their universities, and (ii) sorting of 28 Asian countries in 4 regimes based on 4 indicators of democracy.
Contact information:
Remy Spliet