Essays on Apportionment Methods for Affirmative Action

Abstract

This collection of two essays in market design examines the designs of affirmative action policies. In the first chapter, “Affirmative Action in Two Dimensions: A Multi-Period Apportionment Problem”, we study affirmative action policies that take the form of reserved seats or positions and apply at two levels simultaneously. For instance, in India, beneficiary groups are entitled to their proportion of reserved seats in public universities at both university and at department levels. We theoretically and empirically document the shortcomings of existing solutions. We propose a method with appealing theoretical properties and empirically demonstrate advantages over the existing solutions using recruitment advertisement data from India. Our problem also suggests possible extensions in the theory of apportionment (translating electoral votes into parliamentary seats). In the second chapter, “Impartial Rosters for Affirmative Action’’, we present an answer to this question for the case where all positions are homogeneous. Devising methods is particularly necessary when the number of seats is small. For instance, a university appoints at most one assistant professor of economics every year, while the country’s affirmative action policy has more than one beneficiary group. To ensure that, over a period of time, each beneficiary group respects the spirit of an affirmative action policy, India devised a tool called roster. We present a theory of designing rosters to argue that only a few rosters can be considered impartial in that they do not favor some beneficiaries over others. We provide a method that constructs the set of impartial rosters. We show that the existing roster of India is not one of them and favors categories with a larger proportion of seats relative to the smaller ones.