Given a tournament T, Slater's problem consists in determining a linear order (i.e. a complete directed graph without directed cycles) at minimum distance from T, the distance between T and a linear order O being the number of directed edges with different orientations in T and in O. This paper...

This article surveys seven directions of consensus theories : Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly –...

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T. While Woeginger shows that recognizing whether a given vertex of T is a Banks winner is NP-complete, the computation of a Banks winner of T is polynomial, and...

In this paper we present the notions of median useful for the aggregation of preferences and, more generally, in problems of consensus. After the introduction on the general notion of median, the first section studies the median relations of a profile of arbitrary or particular (tournaments,...