What matters in school choice tie-breaking? How competition guides design
Abstract Many school districts apply the student-proposing deferred acceptance algorithm after ties among students are resolved exogenously. This paper compares two common tie-breaking rules: one in which all schools use a common lottery, and one in which each school uses a separate independent lottery. We identify the balance between supply and demand as the determining factor in this comparison. We analyze a two-sided assignment model with random preferences in over-demanded and under-demanded markets. In a market with a surplus of seats, a common lottery is less equitable, and there are efficiency tradeoffs between the two tie-breaking rules. However, a common lottery is always preferable when there is a shortage of seats in the sense of stochastic dominance of the rank distribution. The theory suggests that popular schools should use a common lottery to resolve ties. We run numerical experiments with New York City school choice data after partitioning the market into popular and non-popular schools. The experiments support our findings.