Rawlsian Assignments

We study the assignment of indivisible objects to individuals when transfers are not allowed. Previous literature has mainly focused on efficiency (from ex-ante and ex-post perspectives), and individually fair assignments. Consequently, egalitarian concerns have been overlooked. We are inspired by the assignment of apartments in housing cooperatives where families regard the egalitarianism of the assignments as a first-order requirement. In particular, they want to avoid assignments where some families get their most preferred apartment, while others get options ranked very low in their preferences. Based on Rawls' idea of fairness, we introduce the notion of Rawlsian assignments. We prove that there always exists a unique Rawlsian assignment, which is efficient, and satisfies anonymity. We illustrate our analysis with preference data from housing cooperatives. Our results show that the Rawlsian assignment substantially improves, from an egalitarian perspective, both the probabilistic serial mechanism, and the mechanism currently in use.