Deploying Fair and Efficient Course Allocation Mechanisms

TL;DR

This work tackles fair and efficient large-scale course allocation by recasting it as a fair allocation problem with indivisible items and constraints, and evaluating mechanisms under formal justice criteria. It combines a large real-world dataset of student preferences from University of Massachusetts Amherst with synthetic data to enable scalable analysis, encodes preferences via linear inequalities, and compares four mechanisms: Serial Dictatorship, Round Robin, an ILP, and Yankee Swap. Yankee Swap, particularly with multiplicity-aware adaptations, delivers leximin welfare and strong fairness guarantees (EF-X and PMMS) while maintaining high utilitarian welfare, outperforming the other mechanisms in both welfare and fairness in large-scale tests. The work provides publicly available data and implementations, offering a practical, scalable benchmark for course allocation research and highlighting Yankee Swap as a robust, fair, and efficient option for large universities.

Abstract

Universities regularly face the challenging task of assigning classes to thousands of students while considering their preferences, along with course schedules and capacities. Ensuring the effectiveness and fairness of course allocation mechanisms is crucial to guaranteeing student satisfaction and optimizing resource utilization. We approach this problem from an economic perspective, using formal justice criteria to evaluate different algorithmic frameworks. To evaluate our frameworks, we conduct a large scale survey of university students at University of Massachusetts Amherst, collecting over 1,000 student preferences. This is, to our knowledge, the largest publicly available dataset of student preferences. We develop software for generating synthetic student preferences over courses, and implement four allocation algorithms: the serial dictatorship algorithm used by University of Massachusetts Amherst; Round Robin; an Integer Linear Program; and the Yankee Swap algorithm. We propose improvements to the Yankee Swap framework to handle scenarios with item multiplicities. Through experimentation with the Fall 2024 Computer Science course schedule at University of Massachusetts Amherst, we evaluate each algorithm's performance relative to standard justice criteria, providing insights into fair course allocation in large university settings.

Figures (11)

• Figure 1: Percentage of students who include each course in their set of preferred courses, grouped by student status. Thick colored lines represent real student data, while the shaded regions indicate the range of percentages observed across 100 synthetic student simulations.
• Figure 2: Runtime of the four allocation algorithms as a function of the number of students. Boxplots represent the distribution of runtime values across 10 runs with different random seeds for each instance.
• Figure 3: Welfare metrics for the reduced student instance. \ref{['fig:num-seats-reduced']} compares % of allocated seats (USW), \ref{['fig:nash-welfare-reduced']} compares the Nash welfare, and \ref{['fig:zeros-reduced']} presents the number of empty bundles.
• Figure 4: Fairness metrics for the reduced student instance. \ref{['fig:PMMS-reduced']} shows the number of PMMS violations, \ref{['fig:EF-reduced']} shows the number of envious agents, and \ref{['fig:EF1-reduced']} shows the number of EF-1 violations.
• Figure 5: Histogram of the number of seats assigned to students under the four algorithmic benchmarks, for reduced student instances. We also report the mean $\mu$ number of seats assigned, as well as the standard deviation $\sigma$ of the assignment distribution for each allocation mechanism.

Theorems & Definitions (3)

• Theorem 1
• Example 5.1
• Proposition 1