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

TL;DR

This paper introduces new methods for college admissions that reduce reliance on random tie-breakers, improving efficiency over traditional algorithms like Boston and Deferred Acceptance, while also evaluating their strategy-proofness.

Contribution

The paper presents novel admission algorithms that decrease the use of randomness, demonstrating increased efficiency and analyzing their strategy-proofness compared to existing methods.

Findings

New methods outperform Boston and Deferred Acceptance algorithms in efficiency.

Reduced reliance on random tie-breakers leads to more effective matching.

Strategy-proofness of the new methods is thoroughly assessed.

Abstract

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.