We study how the design of admissions policies affects the ability of students admitted to universities. In our model, applicants have a multi-dimensional ability, which is a combination of a "type" and a "soft skill." Universities may differ in how they evaluate quality and have differing preferences on type and soft skills. Then, university admissions rely on a single noisy aggregate signal, such as a test score, that may not fully align with the university's preferences, and a university evaluates applicants through the posterior expectations of their preference metric given the observed signal. Our main results highlight that the design of good admission policies can be counter-intuitive. Under a single university, when holding the number of qualified applicants constant, increasing the usefulness of the signal (by aligning it more closely with the university preferences) leads to a worse type and soft skill for admitted students. Further, a university cannot affect the composition of students that are strong on type versus soft skills by changing their preferences. The picture becomes even more complicated under competition between as few as two universities: self-selection effects among students admitted to both universities can lead to part of the applicant pool switching which university they prefer, even under small changes in the design of the noisy signal. This can, in particular, lead to sudden and non-monotonic loss in the quality of admitted students when changing the alignment between signal and university preferences. Further, a university can get more students by increasing their selectivity. Finally, when admissions rely on separate noisy scores for type and for soft skills, we show that universities that put more emphasis on type (respectively soft skills) end up, counter-intuitively, admitting students with higher soft skills (respectively type).

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