Intransitivities of preferences, lexicographic shifts and the transitive dimension of oriented graphs

Intransitivities in preference relations are usually explained by shifts in choice criteria, i.e. shifts in points of view. This paper is concerned with the following problem: assume that a preference relation R on a finite set of alternatives is observed and that no information about choice criteria is provided, how many shifts of point of view are needed, at a minimum, to explain all the intransitivities of R? A model is proposed that takes into account lexicographic shifts in point of view, and some bounds are computed for the minimal number required. One of the results of this paper is that this number is relatively small: if p binary preferences are expressed, then it is bounded by a function in O(log p).