英文标题：
《On the monotonicity of the eigenvector method》
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作者：
L\\\'aszl\\\'o Csat\\\'o and D\\\'ora Gr\\\'eta Petr\\\'oczy
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最新提交年份：
2020
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英文摘要：
  Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a multiplicative pairwise comparison matrix. We consider two monotonicity axioms in this setting. First, increasing an arbitrary entry of a pairwise comparison matrix is not allowed to result in a counter-intuitive rank reversal, that is, the favoured alternative in the corresponding row cannot be ranked lower than any other alternative if this was not the case before the change (rank monotonicity). Second, the same modification should not decrease the normalised weight of the favoured alternative (weight monotonicity). Both properties are satisfied by the geometric mean method but violated by the eigenvector method. The axioms do not uniquely determine the geometric mean. The relationship between the two monotonicity properties and the Saaty inconsistency index are investigated for the eigenvector method via simulations. Even though their violation turns out not to be a usual problem even for heavily inconsistent matrices, all decision-makers should be informed about the possible occurrence of such unexpected consequences of increasing a matrix entry.
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中文摘要：
两两比较用于各种各样的决策情况，其中应在数字尺度上衡量备选方案的重要性。推导优先级的一种常用方法是基于乘法成对比较矩阵的右特征向量。在这种情况下，我们考虑两个单调性公理。首先，不允许增加成对比较矩阵的任意条目来导致违反直觉的排名反转，即，如果在更改之前不是这种情况（排名单调性），则相应行中的首选备选方案的排名不能低于任何其他备选方案。第二，同样的修改不应减少所选方案的归一化权重（权重单调性）。几何平均法满足这两个性质，但特征向量法违反了这两个性质。公理不能唯一地确定几何平均数。通过仿真研究了特征向量法的两个单调性与Saaty不一致性指数之间的关系。即使事实证明，即使对于严重不一致的矩阵，它们的违反也不是一个常见问题，但应告知所有决策者增加矩阵条目可能会产生的意外后果。
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics        经济学
二级分类：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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