# Assigning Course Schedules: About Preference Elicitation, Fairness, and Truthfulness

## TL;DR

This paper compares the efficiency and fairness of the Probabilistic Serial mechanism to traditional methods in course scheduling, introduces tools for preference elicitation, and reports empirical results from implementation at a university.

## Contribution

It introduces a polynomial-time randomized mechanism (BPS) satisfying key economic properties and provides empirical metrics and tools for preference elicitation in large-scale course assignment.

## Key findings

- BPS outperforms FCFS in efficiency and fairness metrics.
- Preference elicitation tools reduce complexity for students.
- Empirical results demonstrate BPS's practical applicability.

## Abstract

Course assignment is a wide-spread problem in education and beyond. Often students have preferences for bundles of course seats or course schedules over the week, which need to be considered. The problem is a challenging distributed scheduling task requiring decision support. First-Come First-Served (FCFS) is simple and the most widely used assignment rule in practice, but it leads to inefficient outcomes and envy in the allocation. Recent theoretical results suggest alternatives with attractive economic and computational properties. Bundled Probabilistic Serial (BPS) is a randomized mechanism satisfying ordinal efficiency, envy-freeness, and weak strategy-proofness. This mechanism also runs in polynomial time, which is important for the large problem instances in the field. We report empirical results from a first implementation of BPS at the Technical University of Munich, which allows us to provide important empirical metrics such as the size of the resulting matching, the average rank, the profile, and the popularity of the assignments. These metrics were central for the adoption of BPS. In particular, we compare these metrics to Random Serial Dictatorship with bundle bids (BRSD). The BRSD mechanism is used to simulate the wide-spread First-Come First-Served (FCFS) mechanism and it allows us to compare FCFS (BRSD) and BPS. While theoretically appealing, preference elicitation is a major challenge when considering preferences over exponentially many packages. We introduce tools to elicit preferences which reduce the number of parameters a student needs to a manageable set. The approach together with BPS yields a computationally effective tool to solve course assignment problems with thousands of students, and possibly provides an approach for other distributed scheduling tasks in organizations.