  Efficiency is a core concept of multi-objective optimization problems and
multi-attribute decision making. In the case of pairwise comparison matrices a
weight vector is called efficient if the approximations of the elements of the
pairwise comparison matrix made by the ratios of the weights cannot be improved
in any position without making it worse in some other position. A pairwise
comparison matrix is called double perturbed if it can be made consistent by
altering two elements and their reciprocals. The most frequently used weighting
method, the eigenvector method is analyzed in the paper, and it is shown that
it produces an efficient weight vector for double perturbed pairwise comparison
matrices.
