A stochastic method for exploiting outranking relations in multicriteria choice problems

The multicriteria decision aiding field offers many methods to support decision makers in comparing a list of alternatives. Among these, outranking methods such as ELECTRE are appreciated for avoiding full compensation among criteria, but outranking relations are difficult to exploit due to incompleteness and lack of transitivity. This work focuses on choice problems, proposing a stochastic exploitation method to select the most preferred alternative. It builds on the concept of Markov solution, which has become popular to select a winner in tournaments and voting problems. The proposed method can be used to exploit crisp outranking relations, valued outranking relations, or stochastic outranking relations. This can be a valuable addition to the toolbox for exploiting outranking relations as this work shows that solutions can be computed without much effort and guarantee some essential properties.