In this paper, we consider the academic department ranking system of Italy, which is based on a performance index named Indice Standardizzato di Performance Dipartimentale (ISPD). While critiques to the ISPD have been moved for its marked tendency to polarization, we here formalize a yet unexplored determinant of this phenomenon, that is, the presence of within-department homogeneity among the standardized scores used to build the index. We account for this intra-departmental correlation by modeling it as a function of departments' size. The proposed model, estimated via Maximum Likelihood, allows to build a fairer ranking procedure via the definition of a properly adjusted version of the ISPD. The estimation framework is also adapted to fit publicly available data, which are coarsened by rounding and/or left-truncated. To this end, a novel probability distribution termed Betoidal is introduced. Empirical evidence in favor of the proposed model is found in the 2017 and 2022 data. Moreover, a simulation study shows that the adjusted index significantly overcomes not only the original ISPD, but also other more data-demanding competing proposals.

翻译：本文研究了基于“院系标准化表现指数”（ISPD）构建的意大利院系排名系统。针对ISPD因显著极化倾向而受到的批评，本文形式化了一种尚未被探索的极化决定因素，即用于构建该指数的标准化得分中存在系内同质性。我们通过将系内相关性建模为院系规模的函数来予以解释。该模型通过极大似然法进行估计，能够通过定义ISPD的适当调整版本构建更公平的排名程序。估计框架还适用于公开可用数据（该类数据因四舍五入和/或左截断而粗糙化）；为此，本文引入了一种名为“贝塔分布”（Betoidal）的新概率分布。2017年及2022年数据为所提模型提供了经验支持。此外，模拟研究表明，调整后的指数不仅显著优于原始ISPD，亦优于其他需更多数据的竞争性方案。