Computation of median orders: complexity results

Given a set of individual preferences defined on a same finite set, we consider the problem of aggregating them into a collective preference minimizing the number of disagreements with respect to the given set and verifying some structural properties like transitivity. We study the complexity of this problem when the individual preferences as well as the collective one must verify different properties, and we show that the aggregation problem is NP-hard for different types of collective preferences, even when the individual preferences are linear orders