Selection of a representative sorting model in a preference disaggregation setting: a review of existing procedures, new proposals, and experimental comparison

TL;DR

This paper reviews existing methods and introduces new procedures for selecting a representative sorting model in preference disaggregation, evaluating their performance through experiments and applying them to assess European cities' green performance.

Contribution

It presents three novel robust procedures for preference disaggregation, compares sixteen methods, and analyzes their effectiveness in classification accuracy and robustness.

Findings

The most efficient procedure achieves high classification accuracy.

Robust methods provide the most reliable assignments.

Performance varies with the number of classes, criteria, and reference points.

Abstract

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.