Ties matter: Improving efficiency in course allocation by allowing ties

This paper studies course allocation as a multi-unit allocation problem with weak preferences under a homogeneous and weak priority structure. While ties are widespread in students’ preferences, most existing mechanisms either restrict students to rank courses in strict orderings or break ties in reported preferences as part of the mechanism, which leads to efficiency loss. To take weak preferences into account, we propose two new competing mechanisms, referred as the Pareto-improving draft and dictatorship mechanisms. Both mechanisms are stable and Pareto efficient, and the latter is strategyproof for students. With these proposed mechanisms, we document substantial efficiency improvement by allowing ties in preference revelation in a counterfactual calibration based on course allocation data at Nanyang Technological University in Singapore. Further numerical simulations in a random environment reconfirm our findings.