# Fair Grading Algorithms for Randomized Exams

arXiv: https://arxiv.org/abs/2304.06254 · HTML: https://mlsanity.com/paper/2304.06254/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 4 of 4)

- [Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation](https://mlsanity.com/paper/2005.14122/) (2020)
- [Best-of-Both-Worlds Fair-Share Allocations](https://mlsanity.com/paper/2102.04909/) (2021)
- [Simultaneously Achieving Ex-ante and Ex-post Fairness](https://mlsanity.com/paper/2004.02554/) (2020)
- [Peer Grading in a Course on Algorithms and Data Structures: Machine Learning Algorithms do not Improve over Simple Baselines](https://mlsanity.com/paper/1506.00852/) (2015)

## Abstract (arXiv)

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.