Robust Allocations with Diversity Constraints
This addresses fairness in resource allocation for domains like ad slots or task assignments, ensuring demographic parity without disproportionately burdening non-benefiting agents, though it is incremental as it builds on existing allocation rules.
The paper tackles the problem of allocating divisible items among agents with diversity constraints, showing that the Nash Welfare rule uniquely maintains robustness by minimizing harm to other agents and limiting gains for the constraint-enforcing agent, with empirical simulations confirming its superiority over other rules in real-world scenarios.
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.