  This article proposes a characterization of admissions markets that can
predict the distribution of students at each school or college under both
centralized and decentralized admissions paradigms. The characterization builds
on recent research in stable assignment, which models students as a probability
distribution over the set of ordinal preferences and scores. Although stable
assignment mechanisms presuppose a centralized admissions process, I show that
stable assignments coincide with equilibria of a decentralized, iterative
market in which schools adjust their admissions standards in pursuit of a
target class size. Moreover, deferred acceptance algorithms for stable
assignment are a special case of a well-understood price dynamic called
t\^{a}tonnement. The second half of the article turns to a parametric
distribution of student types that enables explicit computation of the
equilibrium and is invertible in the schools' preferability parameters.
Applying this model to a public dataset produces an intuitive ranking of the
popularity of American universities and a realistic estimate of each school's
demand curve, and does so without imposing an equilibrium assumption or
requiring the granular student information used in conventional logistic
regressions.
