Ties matter: improving efficiency in course allocation by introducing ties

We study the course allocation system at Nanyang Technological University, where students submit strict preferences for courses and courses have implicit preferences for students. This formulates a many-to-many matching problem. We show the inefficiencies of the current mechanism and propose new competing mechanisms called Pareto-improving draft and dictatorship mechanisms, which introduce ties into students' preferences. Our mechanisms generate (group) stable and Pareto-efficient allocations, and the dictatorship mechanism can be implemented truthfully. Simulations on real data show that introducing ties into students' preferences can significantly improve efficiency, and the draft mechanism outperforms the dictatorship mechanism despite that the former is non-strategyproof.