  We study the assignment of indivisible goods to individuals when monetary
transfers are not allowed. Previous literature has mainly focused on efficiency
(from both ex-ante and ex-post perspectives) and individually fair assignments.
As a result, egalitarian concerns have been overlooked. We draw inspiration
from the assignment of apartments in housing cooperatives, where families
consider egalitarianism of assignments as a first-order requirement.
Specifically, they aim to avoid situations where some families receive their
most preferred apartments while others are assigned options ranked very low in
their preferences. Building on Rawls' concept of fairness, we introduce the
notion of Rawlsian assignment. We prove that a unique Rawlsian assignment
always exists. Furthermore, the Rawlsian rule is efficient and anonymous. To
illustrate our analysis, we use preference data from housing cooperatives. We
show that the Rawlsian rule substantially improves, from an egalitarian
perspective, both the probabilistic serial rule, and the rule currently used to
assign apartments in the housing cooperatives.
