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Fairness and the set of optimal rankings for the linear ordering problem

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Abstract

The goals of this paper are: (1) to bring attention to the existence and utility of multiple optimal rankings for the linear ordering problem, (2) to make the case for finding some or all of these multiple optimal rankings, (3) to provide an efficient algorithm that determines the existence of multiple optimal rankings, (4) to provide algorithms that find a sample of all optimal rankings, and (5) to connect multiple optimal rankings to fairness in ranking. We create algorithms to find the two nearest optimal rankings, the two farthest optimal rankings, and a so-called centroid ranking nearest to the centroid, which summarizes the information in all optimal rankings.

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Notes

  1. https://github.com/IGARDS/fairness_optimal_rankings_lop_paper.

  2. https://github.com/IGARDS/lolib_study.

  3. The features of interest for the student dominance matrix and the parent dominance matrix were selected by our colleague Amanda Miller, College Planner, The Davidson Center.

  4. Because in nearly all cases the optimal ranking produced by Model (4) is indeed the optimal ranking closest to the true centroid, for ease in subsequent descriptions we use the term centroid, acknowledging that there are some cases for which approximate centroid is the more accurate phrase.

  5. An alternative model for finding a nearest pair across two datasets appears in Kondo (2014).

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Acknowledgements

We thank Linda LeFauve, Associate Vice President for Planning and Institutional Research, Davidson College, for sharing the US News and World Report college data and Amanda Miller, College Planner, The Davidson Center, for providing advice on a subset of colleges and features to analyze.

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Authors and Affiliations

  1. Department of Computer Science and Software Engineering, California Polytechnic State University, San Luis Obispo, CA, USA

    Paul E. Anderson

  2. Department of Mathematics and Computer Science, Davidson College, Davidson, NC, USA

    Timothy P. Chartier

  3. Department of Mathematics, College of Charleston, 175 Calhoun Street-RSS 339, Charleston, SC, 29401, USA

    Amy N. Langville & Kathryn E. Pedings-Behling

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  1. Paul E. Anderson
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  2. Timothy P. Chartier
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  3. Amy N. Langville
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  4. Kathryn E. Pedings-Behling
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Correspondence to Amy N. Langville.

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Anderson, P.E., Chartier, T.P., Langville, A.N. et al. Fairness and the set of optimal rankings for the linear ordering problem. Optim Eng 23, 1289–1317 (2022). https://doi.org/10.1007/s11081-021-09650-y

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