School districts that implement stable matchings face various decisions that affect students' assignments to schools. We study the 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 with one of their top choices. However, if students are allowed to submit only relatively short preference lists under a multiple tie-breaking rule, a constant fraction of students will be matched with one of their top choices, while only a “small” fraction of students will remain unmatched.
Bibliographical noteFunding Information:
We thank Sergiu Hart, Avinatan Hassidim, Déborah Marciano, Parag Pathak, and Alvin Roth for helpful discussions. We also thank the editors and two referees in GEB for very useful comments. Ashlagi acknowledges the research support of National Science Foundation grant SES-1254768. Romm acknowledges the research support of the Maurice Falk Institute, Israel Science Foundation grant 1780/16, and the United States-Israel Binational Science Foundation grant 2016015.
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- Deferred acceptance
- School choice
- Stable matching
- Tie-breaking rule