Affirmative Action's Cumulative Fractional Assignments

Abstract

India's reservation policy entitles designated groups to fixed fractions of faculty positions. Positions are indivisible, arrive over time across departments, and appointments are irreversible. We show that no rule can keep cumulative reserved counts nondecreasing while rounding entitlements to adjacent integers at both the department and university levels; university-level compliance forces department-level errors that grow without bound. This impossibility explains why both solutions practiced in India provoked litigation and protests. A random-roster solution preserves irreversibility and department-level compliance, matches entitlements in expectation, and concentrates university-level errors. Dropping cumulative accounting restores exact rounding at both levels.

arXiv commentversion as accepted by The Review of Economics and Statistics