  A special class of preferences, given by a directed acyclic graph, is
considered. They are represented by incomplete pairwise comparison matrices as
only partial information is available: for some pairs no comparison is given in
the graph. A weighting method satisfies the linear order preservation property
if it always results in a ranking such that an alternative directly preferred
to another does not have a lower rank. We study whether two procedures, the
Eigenvector Method and the Logarithmic Least Squares Method meet this axiom.
Both weighting methods break linear order preservation, moreover, the ranking
according to the Eigenvector Method depends on the incomplete pairwise
comparison representation chosen.
