What matters in school choice tie-breaking? How competition guides design
Many school districts apply the student-proposing deferred acceptance algorithm after ties among students are broken exogenously. We compare two common tie-breaking rules: one in which all schools use a single common lottery, and one in which every school uses a separate independent lottery. We identify the balance between supply and demand as the determining factor in this comparison.
First we analyze a two-sided matching 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 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.
Afshin Nikzad is an economic theorist with a particular focus on market and mechanism design. He is a graduate of Stanford (2018) with PhDs in Economics (advised by Al Roth and Paul Milgrom) and in Operations Research (advised by Itai Ashlagi and Al Roth). He is currently a postdoc in UC Berkeley. His work has a focus on matchings markets, including school choice and kidney exchange, and two-sided platforms.