Abstract
Combinatorial allocation involves assigning bundles of items to agents when the use of money is not allowed. Course allocation is one common application of combinatorial allocation, in which the bundles are schedules of courses and the assignees are students. Existing mechanisms used in practice have been shown to have serious flaws, which lead to allocations that are inefficient, unfair, or both. A new mechanism proposed by Budish [2011] is attractive in theory, but has several features that limit its feasibility for practice: reporting complexity, computational complexity, and approximations that can lead to violations of capacity constraints. This paper reports on the design and implementation of a new course allocation mechanism, Course Match, that enhances the Budish [2011] mechanism in various ways to make it suitable for practice. To find allocations, Course Match performs a massive parallel heuristic search that solves billions of Mixed-Integer Programs to output an approximate competitive equilibrium in a fake-money economy for courses. Quantitative summary statistics for two semesters of full-scale use at a large business school (Wharton, which has about 1,700 students and up to 350 courses in each semester) demonstrate that Course Match is both fair and efficient, a finding reinforced by student surveys showing large gains in satisfaction and perceived fairness.
Highlights
There are numerous settings in which resources must be allocated but markets with money are not permitted
This paper reports on the design and implementation of a new course allocation mechanism, Course Match, that is suitable in practice
Quantitative summary statistics for two semesters of full-scale use at a large business school demonstrate that Course Match is both fair and efficient, a finding reinforced by student surveys showing large gains in satisfaction and perceived fairness
Summary
There are numerous settings in which resources must be allocated but markets with money are not permitted. To solve the course allocation problem, this paper describes a new mechanism, Course Match, and reports on its successful implementation at the Wharton School of Business at the University of Pennsylvania (“Wharton”), a large business school with approximately 1,700 students and up to 350 courses in each semester. The lucky first student is ensured her best schedule while the unlucky last student is relegated to select seats from a limited set of the least popular courses While this mechanism is efficient, it scores poorly in terms of fairness. The draft mechanism used by the Harvard Business School, in which students take turns choosing courses one at a time rather than all at once (as in the drafting of professional sports teams), improves on the fairness of the dictatorship but has efficiency problems because of incentives to misreport preferences strategically (Budish and Cantillon 2012). Course Match includes a rich preference reporting language and user interface to assist students in reporting preferences
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