Ashlagi, Itai and Nikzad, Afshin and Romm, Assaf I, Assigning More Students to Their Top Choices: A Tiebreaking Rule Comparison (March 2015). Available for download at SSRN: http://ssrn.com/abstract=2585367

“School choice districts that implement stable matchings face various design issues that impact students’ assignments to schools. We study properties of the rank distribution of students with random preferences, when schools use different tiebreaking rules to rank equivalent students. Under a multiple tiebreaking rule a vanishing fraction of students match to one of their top choices, in contrast to a single tiebreaking rule under which a constant fraction of students are assigned to one of their top choices. When students can submit only a relatively short preference list, the multiple tiebreaking rule allows a constant fraction of students to match to one of their top choices, with only a ”small” fraction of students remaining unmatched.”