From Concordance / Discordance to the Modelling of Positive and Negative Reasons in Decision Aiding

The principle of concordance/discordance was introduced by B. Roy in his very early work on Multiple Criteria Decision Analysis. Although such a principle is grounded by strong evidence from real life decision situations, the way in which it has been implemented in existing MCDA methods allows only for its partial and limited use. Indeed, the principle lacks a theoretical frame enabling a more general use in decision analysis. The paper presents a possible generalisation of this principle under the concepts of positive and negative reasons. For this purpose, a new formalism, (a four valued logic) is suggested. Under such a formalism the concordance test is seen as the evaluation of the existence of positive reasons supporting the sentence “x is at least as good as y”, while the discordance test can be viewed as the evaluation of the existence of negative reasons against the same sentence. A number of results obtained in preference modelling and aggregation shows the potentiality of this approach.