Unimprovable Students and Inequality in School Choice

The Efficiency-Adjusted Deferred Acceptance (EADA) mechanism corrects the Pareto-inefficiency of the celebrated Deferred Acceptance (DA) algorithm by assigning every student to a weakly more preferred school. However, it remains uncertain which and how many students do not see an improvement in their DA placement under EADA. We show that, despite its advantages, EADA does not benefit students assigned to their worst-ranked schools or those who remain unmatched under DA. Additionally, it limits the placement improvement of marginalized students, thereby maintaining school segregation. The placement of worst-off students under EADA can be exceptionally poor, even though significantly more egalitarian allocations are possible. Lastly, we provide a bound on the expected number of unimproved students using a random market approach valid for small markets. Our findings shed light on why EADA fails to mitigate the inequality produced by DA in empirical evaluations.