Title: Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method Show Chinese title

Title: 关于由特征值法和几何平均法得出的优先向量的相似性的一些注记

Abstract: This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings concerning the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index. Further on, we examine the relationship between differences in both rankings and Kendall's rank correlation coefficient $\tau$ and Spearman's rank coefficient $\rho$. Apart from theoretical results, intuitive numerical examples and Monte Carlo simulations are also provided. Show Chinese abstract

Abstract: 本文考察了使用特征值法和几何平均法从成对比较矩阵中获得的序排名之间的差异。 首先，我们介绍关于这两种排名相对于矩阵大小及其由Koczkodaj不一致性指数表示的不一致性的(不)相似性的一些命题。 进一步地，我们研究两种排名差异与Kendall秩相关系数$\tau$和Spearman秩系数$\rho$之间的关系。 除了理论结果外，还提供了直观的数值例子和蒙特卡洛模拟。