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.

翻译：特征值法由广泛使用的层次分析法开发者提出，表现出左右不对称性：由右特征向量得出的优先级不一定与由倒数左特征向量得出的优先级一致。本文通过全面的数值实验，比较了两种基于特征向量的加权方法及其合理的替代方案——行几何平均法，涉及四个衡量指标。基础的两两比较矩阵以不同维度和不一致性水平随机生成。研究发现，两个特征向量之间的不一致性并非始终是这些重要矩阵特征的单调函数。排序矛盾可能影响优先级相对接近的备选方案。行几何平均法几乎处于右特征向量与倒数左特征向量之间的中点，成为两者之间直接的折中方案。