Preference Aggregation with Graphical Utility Models

This paper deals with preference representation and aggregation in the context of multiattribute utility theory. We consider a set of alternatives having a combinatorial structure. We assume that preferences are compactly represented by graphical utility models derived from generalized additive decomposable (GAI) utility functions. Such functions enable to model interactions between attributes while preserving some decomposability property. We address the problem of finding a compromise solution from several GAI utilities representing different points of view on the alternatives. This scheme can be applied both to multicriteria decision problems and to collective decision making problems over combinatorial domains. We propose a procedure using graphical models for the fast determination of a Pareto-optimal solution achieving a good compromise between the conflicting utilities. The procedure relies on a ranking algorithm enumerating solutions according to the sum of all the GAI utilities until a boundary condition is reached. Numerical experiments are provided to highlight the practical efficiency of our procedure.