An axiomatic analysis of concordance-discordance relations
Résumé
Outranking methods propose an original way to build a preference relation between alternatives evaluated on several attributes that has a definite ordi- nal avor. Indeed, most of them appeal the concordance / non-discordance principle that leads to declaring that an alternative is \superior" to another, if the coalition of attributes supporting this proposition is \sufficiently im- portant" (concordance condition) and if there is no attribute that \strongly rejects" it (non-discordance condition). Such a way of comparing alterna- tives is rather natural and does not require a detailed analysis of tradeoffs between the various attributes. However, it is well known that it may produce binary relations that do not possess any remarkable property of transitivity or completeness. This explains why the axiomatic foundations of outrank- ing methods have not been much investigated, which is often seen as one of their important weaknesses. This paper uses conjoint measurement tech- niques to obtain an axiomatic characterization of preference relations that can be obtained on the basis of the concordance / non-discordance principle. It emphasizes their main distinctive feature, i.e., their very crude way to dis- tinguish various levels of preference differences on each attribute. We focus on outranking methods, such as ELECTRE I, that produce a re exive rela- tion, interpreted as an \at least as good as" preference relation. The results in this paper may be seen as an attempt to give such outranking methods a sound axiomatic foundation based on conjoint measurement.
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