Rosters and connected apportionments

Abstract

Affirmative action in India reserves explicit proportions of seats and jobs in publicly funded institutions for various beneficiary groups. Because seats are indivisible and arise in small numbers over time, implementation of this policy requires that beneficiary groups take turns claiming seats, for which purpose India relies on a device called a roster. We study the problem of constructing a roster, which involves addressing a series of connected apportionment problems. To identify suitable apportionment methods, six essential requirements direct our search to a large class of divisor methods. We show that the Webster–Sainte-Laguë method is the unique divisor method that satisfies several practical properties and fairness criteria. Comparative analysis between an existing Indian roster and the application of the Webster–Sainte-Laguë method highlights that method’s benefits.