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Affirmative Action as a Large Contest

We develop a model of affirmative action as a large contest wherein students with heterogeneous underlying abilities compete for seats at vertically differentiated colleges that use color-sighted affirmative action policies to evaluate applicants. Students make costly human capital investments before applying, and these investments are both intrinsically productive and serve as signals of ability to colleges. We use a continuum model to approximate the outcomes of a game with large, but finite, sets of colleges and students. First, we show that (legal) admissions preference schemes and (illegal) quotas are, in fact, outcome equivalent. Second, we design affirmative action systems that maximize welfare, close the black-white test gap, and achieve fair outcomes.