Designing and computing explanations for comparisons inferred from an additive value model

Many decision models are based on an additive representation of preferences. Recommendations obtained from such additive decision models are sometimes considered as self-evident. On the contrary, we claim that these recommendations deserve an explanation so as to be fully understood by the user/decision-maker and to foster her trust. We propose to explain a preference statement x preferred to y by decomposing this statement into simpler ones. Arguments in favor of x (Pros), and arguments in favor of y (Cons) are decomposed using a covering scheme in which each Con is covered by a Pro. We use a decomposition language in which elementary self-evident statements involve (i) one Pro against one Con, (ii) one pro against several Cons, or (iii) several Pros against one Con. We prove that computing such explanations is computationally difficult in case (ii) and (iii), and propose a mathematical programming formulation to solve it. Numerical experiments provide insights on the actual behavior of our algorithm. We also illustrate the usefulness of our approach in the context of multicriteria decision aid but also for machine learning approaches.