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, assigning every student to a weakly more preferred school. Nonetheless, it is unclear which and how many students do not improve their DA placement under EADA. We show that, despite all its merits, EADA never benefits pupils who are either assigned to their worst-ranked schools or unmatched under DA. It also limits the placement improvement of marginalized students, preserving school segregation. The placement of the worst-off student under EADA may be unreasonably bad, even though significantly more egalitarian allocations are possible. Finally, we provide a bound on the expected number of unimprovable students using a random market approach. Our results help to understand why EADA fails to reduce the inequality generated by DA in empirical evaluations of school choice mechanisms.