Preferences for multi-attributed alternatives: Traces, dominance, and numerical representations

This paper analyzes conjoint measurement models allowing for intransitive and/or incomplete preferences. This analysis is based on the study of marginal traces induced on coordinates by the preference relation and uses conditions guaranteeing that these marginal traces are complete.Within the framework of these models, we propose a simple axiomatic characterization of preference relations compatible with the notion of dominance. We show that all such relations have a nontrivial numerical representation.Our results allow us to establish useful connections between two lines of thought in the area of decision analysis with multiple attributes that have largely remained unrelated: the one based on conjoint measurement and the one emphasizing the idea of dominance.