Does Banning Affirmative Action Harm College Student Quality?

Banning affirmative action from college admissions decisions cannot prevent an admissions office that cares about diversity from achieving it through channels other than the explicit consideration of race. We construct a model of college admissions where candidates from two groups with different average qualifications compete for a fixed number of seats. When an admissions office that cares both about the quality and diversity of its entering class can use group identity as a criterion for admissions, its preferred admissions rule selects the best-qualified candidates from each group. When it cannot use affirmative action, the admissions office's preferred rule generally does not select the best-qualified candidates from either group: it randomizes over candidates to achieve diversity, at the expense of within-group selection. A ban always reduces diversity, and may also lower average quality. Moreover, even when a total ban on affirmative action raises average quality, a partial ban may raise average quality even more.