Assigning more students to their top choices: A comparison of tie-breaking rules

School districts that implement stable matchings face various decisions that affect students’ assignments to schools. We study properties of the rank distribution of students with random preferences when schools use different tie-breaking rules to rank equivalent students. Under a single tie-breaking rule, where all schools use the same ranking, a constant fraction of students are assigned to one of their top choices. In contrast, under a multiple tie-breaking rule, where each school independently ranks students, a vanishing fraction of students are matched to one of their top choices. However, by restricting the students to submitting relatively short preference lists under a multiple tie-breaking rule, a constant fraction of students will be matched with one of their top choices, whereas only a “small” fraction of students will remain unmatched.