License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FORC.2023.7
URN: urn:nbn:de:0030-drops-179282
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17928/
Chen, Jiale ;
Hartline, Jason ;
Zoeter, Onno
Fair Grading Algorithms for Randomized Exams
Abstract
This paper studies grading algorithms for randomized exams. In a randomized exam, each student is asked a small number of random questions from a large question bank. The predominant grading rule is simple averaging, i.e., calculating grades by averaging scores on the questions each student is asked, which is fair ex-ante, over the randomized questions, but not fair ex-post, on the realized questions. The fair grading problem is to estimate the average grade of each student on the full question bank. The maximum-likelihood estimator for the Bradley-Terry-Luce model on the bipartite student-question graph is shown to be consistent with high probability when the number of questions asked to each student is at least the cubed-logarithm of the number of students. In an empirical study on exam data and in simulations, our algorithm based on the maximum-likelihood estimator significantly outperforms simple averaging in prediction accuracy and ex-post fairness even with a small class and exam size.
BibTeX - Entry
@InProceedings{chen_et_al:LIPIcs.FORC.2023.7,
author = {Chen, Jiale and Hartline, Jason and Zoeter, Onno},
title = {{Fair Grading Algorithms for Randomized Exams}},
booktitle = {4th Symposium on Foundations of Responsible Computing (FORC 2023)},
pages = {7:1--7:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-272-3},
ISSN = {1868-8969},
year = {2023},
volume = {256},
editor = {Talwar, Kunal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17928},
URN = {urn:nbn:de:0030-drops-179282},
doi = {10.4230/LIPIcs.FORC.2023.7},
annote = {Keywords: Ex-ante and Ex-post Fairness, Item Response Theory, Algorithmic Fairness in Education}
}
Keywords: |
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Ex-ante and Ex-post Fairness, Item Response Theory, Algorithmic Fairness in Education |
Collection: |
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4th Symposium on Foundations of Responsible Computing (FORC 2023) |
Issue Date: |
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2023 |
Date of publication: |
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04.06.2023 |