  We use majorization to model comparative diversity in school choice. A
population of agents is more diverse than another population of agents if its
distribution over groups is less concentrated: being less concentrated takes a
specific mathematical meaning borrowed from the theory of majorization. We
adapt the standard notion of majorization in order to favor arbitrary
distributional objectives, such as population-level distributions over
race/ethnicity or socioeconomic status. With school admissions in mind, we
axiomatically characterize choice rules that are consistent with modified
majorization, and constitute a principled method for admitting a diverse
population of students into a school. Two important advantages of our approach
is that majorization provides a natural notion of diversity, and that our
axioms are independent of any exogenous priority ordering. We compare our
choice rule to the leading proposal in the literature, ``reserves and quotas,''
and find ours to be more flexible.
