Discovering Opportunities in New York City's Discovery Program: an Analysis of Affirmative Action Mechanisms

Discovery program (DISC) is an affirmative action policy used by the New York City Department of Education (NYC DOE). It has been instrumental in increasing the number of admissions for disadvantaged students at specialized high schools. However, our empirical analysis of the student-school matches shows that about 950 in-group blocking pairs were created each year amongst the disadvantaged group of students, impacting about 650 disadvantaged students. Moreover, we find that this program usually benefits lower-performing disadvantaged students more than the top-performing ones, thus unintentionally creating an incentive to under-perform. In this work, we explore two affirmative action policies that can be used to minimally modify and improve the discovery program: minority reserve (MR) and joint-seat allocation (JSA). We show that (i) both MR and JSA result in no in-group blocking pairs, and (ii) JSA is weakly group strategy-proof, ensures that at least one disadvantaged is not worse off, and when reservation quotas are carefully chosen then no disadvantaged student is worse-off. In the general setting, we show that there is no clear winner in terms of the matchings provided by DISC, JSA and MR, from the perspective of disadvantaged students. We however characterize a condition for markets, that we term high competitiveness, where JSA dominates MR for disadvantaged students. This condition is verified in markets when there is a higher demand for seats than supply, and the performances of disadvantaged students are significantly lower than that of advantaged students. Data from NYC DOE satisfy the high competitiveness condition, and for this dataset our empirical results corroborate our theoretical predictions, showing the superiority of JSA. We believe that the discovery program, and more generally affirmative action mechanisms, can be changed for the better by implementing JSA.