Selection of a representative sorting model in a preference disaggregation setting: a review of existing procedures, new proposals, and experimental comparison
This work addresses the challenge of model selection in decision-making systems for stakeholders like analysts or policymakers, but it is incremental as it builds on existing procedures with new robust variants.
The paper tackles the problem of selecting a representative sorting model from multiple compatible ones in preference disaggregation for multiple criteria sorting, reviewing existing procedures and proposing three new robust methods, with experimental results identifying the most efficient procedures in terms of classification accuracy, model reproduction, and robustness.
We consider preference disaggregation in the context of multiple criteria sorting. The value function parameters and thresholds separating the classes are inferred from the Decision Maker's (DM's) assignment examples. Given the multiplicity of sorting models compatible with indirect preferences, selecting a single, representative one can be conducted differently. We review several procedures for this purpose, aiming to identify the most discriminant, average, central, benevolent, aggressive, parsimonious, or robust models. Also, we present three novel procedures that implement the robust assignment rule in practice. They exploit stochastic acceptabilities and maximize the support given to the resulting assignments by all feasible sorting models. The performance of sixteen procedures is verified on problem instances with different complexities. The results of an experimental study indicate the most efficient procedure in terms of classification accuracy, reproducing the DM's model, and delivering the most robust assignments. These include approaches identifying differently interpreted centers of the feasible polyhedron and robust methods introduced in this paper. Moreover, we discuss how the performance of all procedures is affected by different numbers of classes, criteria, characteristic points, and reference assignments. Finally, we illustrate the use of all approaches in a study concerning the assessment of the green performance of European cities.