Assignment Mechanisms Under Distributional Constraints

We generalize the serial dictatorship (SD) and probabilistic serial (PS) mechanism for assigning indivisible objects (seats in a school) to agents (students) to accommodate distributional constraints. Such constraints are motivated by equity considerations. Our generalization of SD maintains several of its desirable properties, including strategyproofness, Pareto optimality, and computational tractability, while satisfying the distributional constraints with a small error. Our generalization of the PS mechanism finds an ordinally efficient and envy-free assignment while satisfying the distributional constraint 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.