  Pairwise comparison matrices are frequently applied in multi-criteria
decision making. A weight vector is called efficient if no other weight vector
is at least as good in approximating the elements of the pairwise comparison
matrix, and strictly better in at least one position. A weight vector is weakly
efficient if the pairwise ratios cannot be improved in all non-diagonal
positions. We show that the principal eigenvector is always weakly efficient,
but numerical examples show that it can be inefficient. The linear programs
proposed test whether a given weight vector is (weakly) efficient, and in case
of (strong) inefficiency, an efficient (strongly) dominating weight vector is
calculated. The proposed algorithms are implemented in Pairwise Comparison
Matrix Calculator, available at pcmc.online.
