  The eigenvalue method, suggested by the developer of the extensively used
Analytic Hierarchy Process methodology, exhibits right-left asymmetry: the
priorities derived from the right eigenvector do not necessarily coincide with
the priorities derived from the reciprocal left eigenvector. This paper offers
a comprehensive numerical experiment to compare the two eigenvector-based
weighting procedures and their reasonable alternative of the row geometric mean
with respect to four measures. The underlying pairwise comparison matrices are
constructed randomly with different dimensions and levels of inconsistency. The
disagreement between the two eigenvectors turns out to be not always a
monotonic function of these important characteristics of the matrix. The
ranking contradictions can affect alternatives with relatively distant
priorities. The row geometric mean is found to be almost at the midpoint
between the right and inverse left eigenvectors, making it a straightforward
compromise between them.
