We consider the problem of actively eliciting preferences from a Decision Maker supervising a collective decision process in the context of fair multiagent combinatorial optimization. Individual preferences are supposed to be known and represented by linear utility functions defined on a combinatorial domain and the social utility is defined as a generalized Gini Social evaluation Function (GSF) for the sake of fairness. The GSF is a non-linear aggregation function parameterized by weighting coefficients which allow a fine control of the equity requirement in the aggregation of individual utilities. The paper focuses on the elicitation of these weights by active learning in the context of the fair multiagent knapsack problem. We introduce and compare several incremental decision procedures interleaving an adaptive preference elicitation procedure with a combinatorial optimization algorithm to determine a GSF-optimal solution. We establish an upper bound on the number of queries and provide numerical tests to show the efficiency of the proposed approach.

We introduce a new model-based incremental choice procedure for multicriteria decision support, that interleaves the analysis of the set of alternatives and the elicitation of weighting coefficients that specify the role of criteria in rank-dependent models such as ordered weighted averages (OWA) and Choquet integrals. Starting from a prior distribution on the set of weighting parameters, we propose an adaptive elicitation approach based on the minimization of the expected regret to iteratively generate preference queries. The answers of the Decision Maker are used to revise the current distribution until a solution can be recommended with sufficient confidence. We present numerical tests showing the interest of the proposed approach.