Assignment Mechanisms under Distributional Constraints

TL;DR

This paper introduces new assignment mechanisms that handle distributional constraints while maintaining key properties like strategyproofness and efficiency, improving allocation effectiveness under complex constraints.

Contribution

It generalizes serial dictatorship and probabilistic serial algorithms to satisfy distributional constraints with minimal error, preserving key desirable properties.

Findings

Mechanisms achieve near-optimal assignment sizes.

Serial dictatorship generalization maintains strategyproofness and efficiency.

Probabilistic serial generalization is ordinally efficient and envy-free.

Abstract

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.