Diversity in Choice as Majorization

The paper presented in this ZEW Research Seminar uses 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. The authors 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, the authors also 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 the approach is that majorization provides a natural notion of diversity, and that the axioms are independent of any exogenous priority ordering. The authors compare their choice rule to the leading proposal in the literature, "reserves and quotas," and find theirs to be more flexible.