  Efficiency, the basic concept of multi-objective optimization is investigated
for the class of pairwise comparison matrices. A weight vector is called
efficient if no alternative weight vector exists such that every pairwise ratio
of the latter's components is at least as close to the corresponding element of
the pairwise comparison matrix as the one of the former's components is, and
the latter's approximation is strictly better in at least one position. A
pairwise comparison matrix is called simple perturbed if it differs from a
consistent pairwise comparison matrix in one element and its reciprocal. One of
the classical weighting methods, the eigenvector method is analyzed. It is
shown in the paper that the principal right eigenvector of a simple perturbed
pairwise comparison matrix is efficient.

Optimization and Control