In 2019, Anderson et al. proposed the concept of rankability, which refers to a dataset's inherent ability to be meaningfully ranked. In this article, we give an expository review of the linear ordering problem (LOP) and then use it to analyze the rankability of data. Specifically, the degree of linearity is used to quantify what percentage of the data aligns with an optimal ranking. In a sports context, this is analogous to the number of games that a ranking can correctly predict in hindsight. In fact, under the appropriate objective function, we show that the optimal rankings computed via the LOP maximize the hindsight accuracy of a ranking. Moreover, we develop a binary program to compute the maximal Kendall tau ranking distance between two optimal rankings, which can be used to measure the diversity among optimal rankings without having to enumerate all optima. Finally, we provide several examples from the world of sports and college rankings to illustrate these concepts and demonstrate our results.

翻译：2019年, Anderson 等人提出了等级概念, 指数据集固有的有意义排序能力。 在本条中, 我们给出了线性定序问题( LOP) 的解释性审查, 然后用它来分析数据的等级性。 具体地说, 直线性程度用于量化数据中与最佳排名一致的百分比。 在体育方面, 这类似于排序能够正确预测后视力的游戏数量。 事实上, 在适当的客观功能下, 我们显示通过 LOP 计算的最佳排行顺序的精度最大化。 此外, 我们开发了一个二进制程序, 在两种最佳排名之间计算最大 Kendall Tau 的距离, 它可以用来测量最佳排名的多样性, 而不必列举所有opima 。 最后, 我们提供了几个来自体育和大学排名世界的例子来说明这些概念, 并展示我们的成果 。