Fairness through randomization: An operations research perspective

Incorporating a certain level of randomization is a prerequisite for designing fair processes in many applications. In this dissertation, we illustrate that intuitive methods to incorporate randomization, such as randomly ordering the agents, can often be improved upon from various perspectives. We study three distinct, yet related problem settings, and apply techniques from the field of operations research to find and compute alternative solutions with desirable properties. First, we propose a new egalitarian solution concept for the random assignment problem, which studies how to assign indivisible goods to agents who have preferences over these goods, without making use of monetary transfers. Second, for an extension of the random assignment problem, we study how to decompose probabilistic solutions as a lottery over deterministic outcomes while optimizing a worst-case measure of choice. Third, we propose methods to fairly control the selection probabilities of the (possibly many) optimal solutions of an integer linear program. For each of the three evaluated problem settings, we evaluate both the axiomatic and the computational properties of our proposed solutions. Our proposed methods can be applied to a wide range of practical problems, such as the assignment of apartments in housing cooperatives, the assignment of students to schools or universities, or kidney exchange programs.