Preference aggregation in combinatorial domains using GAI-nets

This paper deals with preference representation and aggregation in combinatorial domains. We assume that the set of alternatives is defined as the cartesian product of finite domains and that agents’ preferences are represented by generalized additive decomposable (GAI) utility functions. GAI functions allow an efficient representation of interactions between attributes while preserving some decomposability of the model. We address the preference aggregation problem and consider several criteria to define the notion of compromise solution (maxmin, minmaxregret, weighted Tchebycheff distance). For each of them, we propose a fast procedure for the exact determination of the optimal compromise solution in the product set. This procedure relies on a ranking algorithm enumerating solutions according to the sum of the agents individual utilities until a boundary condition is reached. We provide results of numerical experiments to highlight the practical efficiency of our procedure.