The most common school-choice mechanisms are variants of the deferred-acceptance algorithm and random serial dictatorship.
A major concern in designing a school-choice mechanism is that it should be strategyproof for the pupils (as they are considered to be strategic), so that they reveal their true preferences for schools.
This loss of efficiency might be substantial: a recent survey showed that around 2% of the pupils could receive a school that is more preferred by them, without harming any other student.
Moreover, in some cases, DA might assign each pupil to their second-worst or worst school.
[3] Interestingly, in lab experiments, more pupils report their true preferences to EADA than to DA (70% vs 35%).