A rating system (RS) comprises a rating metric defined by a discrete set of integers contained in an interval (e.g., [0, N]), and an aggregation rule. RSs are widely used in various fields to capture and summarize individuals' opinions on alternatives. In this paper we argue that the multi-attribute additive value model (MAVM) should be used as a benchmark to analyze the reliability of RSs, and present some tight bounds on the parameter N and overall rating scores, which guarantee the consistency between the RS [0, N] and MAVM at the ranking and rating levels. Interestingly, the tight bounds at the rating level are twice as large as those at the ranking level. The results in this paper can provide new insights about the reliability analysis of RSs.

评级系统（RS）包括由间隔（例如，[0，N ]）中包含的离散整数集合定义的评级度量 ，以及聚合规则。RS广泛应用于各个领域，以捕获和总结个人对替代方案的看法。在本文中，我们认为应该使用多属性加价值模型（MAVM）作为分析RS可靠性的基准，并在参数N和总体评分上给出一些严格的界限，以确保RS之间的一致性。 [0，  N ]和MAVM在排名和等级级别。有趣的是，评级级别的紧迫边界是排名级别的紧迫边界的两倍。本文的结果可以为RS的可靠性分析提供新的见解。