Affirmative action, critical mass, and a predictive model of undergraduate student body demographics

Black and Latinx students are underrepresented on most public university campuses. At the same time, affirmative action policies are controversial and legally fraught. The Supreme Court has ruled that affirmative action should help a minoritized group achieve a critical mass of representation. While the idea of critical mass is frequently invoked in law and in policy, the term remains ill-defined and hence difficult to operationalize. Motivated by these challenges, we build a mathematical model to forecast undergraduate student body racial/ethnic demographics on public university campuses. Our model takes the form of a Markov chain that tracks students through application, admission, matriculation, retention, and graduation. Using publicly available data, we calibrate our model for two different campuses within the University of California system, test it for accuracy, and make a 10-year prediction. We also propose a coarse definition of critical mass and use our model to assess progress towards it at the University of California-Berkeley. If no policy changes are made over the next decade, we predict that the Latinx population on campus will move towards critical mass but not achieve it, and that the Black student population will decrease, moving further below critical mass. Because affirmative action is banned in California and in nine other states, it is worthwhile to consider alternative policies for diversifying a campus, including targeted recruitment and retention efforts. Our modeling framework provides a setting in which to test the efficacy of affirmative action and of these alternative policies.