Essays on Behavioral Matching and Apportionment Methods for Affirmative Action

Abstract

This thesis is a collection of three essays in market design concerning designs of matching markets, affirmative action schemes, and COVID-19 testing policies. In Chapter 1, we explore the possibility of designing matching mechanisms that can accommodate non-standard choice behavior. In the standard model of matching markets, preferences over potential assignments encode participants' choice behavior. Our contribution to this literature is introducing behavioral participants to matching theory's setup. We pin down the necessary and sufficient conditions on participants' choice behavior for the existence of stable and incentive compatible matching mechanisms. Our results imply that well-functioning matching markets can be designed to adequately accommodate a plethora of non-standard (and standard) choice behaviors. We illustrate the applicability of our results by demonstrating that a simple modification in a commonly used matching mechanism enables it to accommodate non-standard choice behavior. In Chapter 2, we show that commonly used methods in reserving positions for beneficiaries of affirmative action are often inadequate in settings where affirmative action policies apply at two levels simultaneously, for instance, at university and itsdepartments. We present a comprehensive evaluation of existing procedures and formally and empirically document their shortcomings. We propose a new solution with appealing theoretical properties and quantify the benefits of adopting it using recruitment advertisement data from India. Our theoretical analysis hints at new possibilities for future work in the literature on the theory of apportionment (of parliamentary seats). Chapter 3 delves into the designs of the commonly used and advocated COVID-19 testing policies to resolve a conflict between their allocative efficiency and the ability to identify the infection rates. We present a novel comparison of various COVID-19 testing policies that allows us to pin down ordinally efficient testing policies that generate reliable estimates of infection rates while prioritizing testing of persons suspected of having the disease.