Ranking by rating
研究了通过外部评分函数对项目进行排序的方法，证明了可分离性和一致性等公理性质，并指出在向量绩效下需按加权几何平均排序。
Ranking by rating consists in evaluating the performances of items using exogenous rating functions and ranking these items according to their performance ratings. Any such method is separable: the ordering of two items does not depend on the performances of the remaining items. When performances belong to a finite set, ranking by rating is characterized by separability and a property of consistency; this characterization generalizes to the infinite case under a continuity axiom. Consistency follows from separability and symmetry or from monotonicity alone. When performances are vectors in R m + , a separable, symmetric, monotonic, continuous, and invariant method must rank items according to a weighted geometric mean of their performances along the m dimensions.