An axiomatic analysis of concordance–discordance relations

Abstract

Outranking methods propose an original way to build a preference relation between alternatives evaluated on several attributes that has a denite ordinal 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 \suciently (concordance condition) and if there is no attribute that \strongly rejects it (non-discordance condition). Such a way of comparing alternatives is rather natural. 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 outranking methods have not been much investigated, which is often seen one of their important weaknesses. This paper uses conjoint measurement techniques 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 distinguish various levels of preference dierences on each attribute. We focus on outranking methods, such ELECTRE I, that produce a reexive relation, interpreted an \at least good as preference relation. The results in this paper may be seen an attempt to give such outranking methods a sound axiomatic foundation based on conjoint measurement.