  We study the assignment problem of objects to agents with heterogeneous
preferences under distributional constraints. Each agent is associated with a
publicly known type and has a private ordinal ranking over objects. We are
interested in assigning as many agents as possible. Our first contribution is a
generalization of the well-known and widely used serial dictatorship. Our
mechanism maintains several desirable properties of serial dictatorship,
including strategyproofness, Pareto efficiency, and computational tractability
while satisfying the distributional constraints with a small error. We also
propose a generalization of the probabilistic serial algorithm, which finds an
ordinally efficient and envy-free assignment, and also satisfies the
distributional constraints with a small error. We show, however, that no
ordinally efficient and envy-free mechanism is also weakly strategyproof. Both
of our algorithms assign at least the same number of students as the optimum
fractional assignment.
