Ordinal aggregation and strict preferences for multi-attributed alternatives

This paper studies strict preference relations on product sets induced by “ordinal aggregation methods”. Such methods are interpreted here as performing paired comparisons of alternatives based on the “importance” of attributes favoring each element of the pair: alternative x will be preferred to alternative y if the attributes for which x is better than y are “more important” than the attributes for which y is better than x. Based on a general framework for conjoint measurement that allows for intransitive preferences, we propose a characterization of such preference relations. This characterization shows that the originality of these relations lies in their very crude way to distinguish various levels of “preference differences” on each attribute when compared to the preference relations usually studied in conjoint measurement. The relation between such preference relations and P. C. Fishburn’s noncompensatory preferences is investigated.