Reducing the role of random numbers in matching algorithms for school admission

New methods for solving the college admissions problem with indifference are presented and characterised with a Monte Carlo simulation in a variety of simple scenarios. Based on a qualifier defined as the average rank, it is found that these methods are more efficient than the Boston and Deferred Acceptance algorithms. The improvement in efficiency is directly related to the reduced role of random tie-breakers. The strategy-proofness of the new methods is assessed as well.