  The pairwise comparisons method is a convenient tool used when the relative
order among different concepts (alternatives) needs to be determined. One
popular implementation of the method is based on solving an eigenvalue problem
for the pairwise comparisons matrix. In such cases the ranking result the
principal eigenvector of the pairwise comparison matrix is adopted, whilst the
eigenvalue is used to determine the index of inconsistency. A lot of research
has been devoted to the critical analysis of the eigenvalue based approach. One
of them is the work (Bana e Costa and Vansnick, 2008). In their work authors
define the conditions of order preservation (COP) and show that even for a
sufficiently consistent pairwise comparisons matrices, this condition can not
be met. The present work defines a more precise criteria for determining when
the COP is met. To formulate the criteria a discrepancy factor is used
describing how far the input to the ranking procedure is from the ranking
result.
