This paper examines the design of rosters used to implement affirmative action in India’s public institutions. Unlike the U.S., India’s reservation policy mandates fixed proportions of seats or jobs for various beneficiary groups. Since positions are indivisible and arise over time, India uses publicly declared rosters—typically 200-item sequences—to allocate opportunities in proportion to these reservation quotas. These rosters ensure that groups take turns claiming seats over time, but while the overall number of turns per group is policy-determined, the specific order is not. Despite their importance, there has been no formal analysis or guidance on how to construct these rosters fairly and effectively. This study fills that gap.

We model the problem as a sequence of apportionment challenges. A roster assigns each position to a category such that, cumulatively, each group receives seats in line with its quota. This can be visualized as a staircase: each step represents an apportionment of seats up to that point.

To guide roster design, the study evaluates apportionment methods that meet essential principles. The focus is on divisor methods, which satisfy properties like anonymity, exactness, responsiveness, consistency, house-monotonicity, and balance. Among these, the Webster–Sainte-Laguë method emerges as uniquely suited to roster construction.

The method is shown to satisfy four critical fairness and practicality criteria:

Through comparative analysis, the paper highlights the shortcomings of the current Indian method, which uses a floor-based allocation approach. While it meets some basic principles (exactness, anonymity, and concatenation invariance), it fails on responsiveness, consistency, balance, and the fairness measures outlined above. Empirical evaluation reveals systematic biases: groups with smaller quotas experience longer delays in seat assignments. These biases are eliminated under the Webster–Sainte-Laguë method, which also cannot be replicated by any procedure outside the divisor framework.

In conclusion, the paper provides the first formal evaluation of India’s roster design and demonstrates that the Webster–Sainte-Laguë method is the only divisor method satisfying the full set of desired fairness and implementation properties. It offers a clear, principled alternative to the existing approach and sets a new standard for equitable affirmative action implementation.

About Manshu Khanna:

Manshu Khanna is an Assistant Professor of Economics at the Peking University HSBC Business School. He holds a Ph.D. in Economics from the Boston College. His research focuses on market design, microeconomics, and experimental economics.