ON THE LINEAR ORDERING PROBLEM AND THE RANKABILITY OF DATA

Thomas R. Cameron, Sebastian Charmot, Jonad Pulaj

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)133-149
Number of pages17
JournalFoundations of Data Science
Volume3
Issue number2
DOIs
StatePublished - Jun 2021

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Analysis
  • Statistics and Probability
  • Applied Mathematics

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