On the linear ordering problem and the rankability of data

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