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：由广泛使用的层次分析法（AHP）开发者提出的特征值方法表现出左右不对称性：由右特征向量导出的优先级不一定与由倒数左特征向量导出的优先级一致。本文提供了一项全面的数值实验，比较了两种基于特征向量的加权程序及其合理的替代方案——行几何平均法，在四个测度上的表现。底层成对比较矩阵是随机构建的，具有不同的维度和不一致性水平。结果表明，两个特征向量之间的不一致并非总是这些重要矩阵特征的单调函数。排名矛盾可能影响优先级相对距离较远的备选方案。行几何平均法被发现几乎位于右特征向量和逆左特征向量的中点，使其成为两者之间直接的折衷方案。