# Robust Allocations with Diversity Constraints

arXiv: https://arxiv.org/abs/2109.15015 · HTML: https://mlsanity.com/paper/2109.15015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 53 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 12 of 12)

- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Fairness-Aware Ranking in Search & Recommendation Systems with Application to LinkedIn Talent Search](https://mlsanity.com/paper/1905.01989/) (2019)
- [Ranking with Fairness Constraints](https://mlsanity.com/paper/1704.06840/) (2017)
- [Fast Algorithms for Online Stochastic Convex Programming](https://mlsanity.com/paper/1410.7596/) (2014)
- [Fair Allocation of Indivisible Public Goods](https://mlsanity.com/paper/1805.03164/) (2018)
- [Regularized Online Allocation Problems: Fairness and Beyond](https://mlsanity.com/paper/2007.00514/) (2020)
- [Proportionality and the Limits of Welfarism](https://mlsanity.com/paper/1911.11747/) (2019)
- [Balanced Ranking with Diversity Constraints](https://mlsanity.com/paper/1906.01747/) (2019)
- [Fair Knapsack](https://mlsanity.com/paper/1711.04520/) (2017)
- [Diverse Weighted Bipartite b-Matching](https://mlsanity.com/paper/1702.07134/) (2017)
- [Efficiency Guarantees in Auctions with Budgets](https://mlsanity.com/paper/1304.7048/) (2013)
- [Advertising for Demographically Fair Outcomes](https://mlsanity.com/paper/2006.03983/) (2020)

## Built on by (most cited first, 1 of 1)

- [Intuitions of Compromise: Utilitarianism vs. Contractualism](https://mlsanity.com/paper/2410.05496/) (2024)

## Abstract (arXiv)

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.