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：特征值方法由广泛使用的层次分析法（AHP）的开发者提出，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互逆左特征向量导出的优先级一致。本文通过全面的数值实验，比较了这两种基于特征向量的赋权方法及其合理的替代方案——行几何均值，并考察了四种度量指标。底层成对比较矩阵随机生成，具有不同的维度和不一致性程度。结果表明，两个特征向量之间的差异并不总是矩阵这些重要特征的单调函数。排序矛盾可能影响优先级相对较远的备选方案。研究发现，行几何均值几乎位于右特征向量与逆左特征向量的中点，使其成为两者之间的直接折中方案。