Robust Allocations with Diversity Constraints

TL;DR

This paper investigates the impact of diversity constraints on resource allocation among agents, demonstrating that Nash Welfare provides robust and nearly optimal solutions that prevent negative externalities and ensure fairness.

Contribution

It introduces robustness criteria for allocations with diversity constraints and proves Nash Welfare's unique robustness and near-optimality among natural rules.

Findings

Nash Welfare is uniquely robust to diversity constraints.

Most natural allocation rules fail the robustness criteria.

Empirical simulations confirm Nash Welfare's superior performance in real-world data.

Abstract

We consider the problem of allocating divisible items among multiple agents, and consider the setting where any agent is allowed to introduce diversity constraints on the items they are allocated. We motivate this via settings where the items themselves correspond to user ad slots or task workers with attributes such as race and gender on which the principal seeks to achieve demographic parity. We consider the following question: When an agent expresses diversity constraints into an allocation rule, is the allocation of other agents hurt significantly? If this happens, the cost of introducing such constraints is disproportionately borne by agents who do not benefit from diversity. We codify this via two desiderata capturing robustness. These are no negative externality -- other agents are not hurt -- and monotonicity -- the agent enforcing the constraint does not see a large increase in value. We show in a formal sense that the Nash Welfare rule that maximizes product of agent values is uniquely positioned to be robust when diversity constraints are introduced, while almost all other natural allocation rules fail this criterion. We also show that the guarantees achieved by Nash Welfare are nearly optimal within a widely studied class of allocation rules. We finally perform an empirical simulation on real-world data that models ad allocations to show that this gap between Nash Welfare and other rules persists in the wild.