# Fairness and Utilization in Allocating Resources with Uncertain Demand

arXiv: https://arxiv.org/abs/1906.09050 · HTML: https://mlsanity.com/paper/1906.09050/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 16 of 16)

- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Learning to be Fair: A Consequentialist Approach to Equitable Decision-Making](https://mlsanity.com/paper/2109.08792/) (2021)
- [Algorithmic Fairness in Performative Policy Learning: Escaping the Impossibility of Group Fairness](https://mlsanity.com/paper/2405.20447/) (2024)
- [Fairer LP-based Online Allocation via Analytic Center](https://mlsanity.com/paper/2110.14621/) (2021)
- [Network Revenue Management with Demand Learning and Fair Resource-Consumption Balancing](https://mlsanity.com/paper/2207.11159/) (2022)
- [Sequential Fair Resource Allocation under a Markov Decision Process Framework](https://mlsanity.com/paper/2301.03758/) (2023)
- [Fairness in Contextual Resource Allocation Systems: Metrics and Incompatibility Results](https://mlsanity.com/paper/2212.01725/) (2022)
- [Fair Allocation in Dynamic Mechanism Design](https://mlsanity.com/paper/2406.00147/) (2024)
- [Resource-constrained Fairness](https://mlsanity.com/paper/2406.01290/) (2024)
- [Online Fair Allocation of Perishable Resources](https://mlsanity.com/paper/2406.02402/) (2024)
- [Fair and Welfare-Efficient Constrained Multi-matchings under Uncertainty](https://mlsanity.com/paper/2411.02654/) (2024)
- [Fair Resource Allocation for Demands with Sharp Lower Tail Inequalities](https://mlsanity.com/paper/2101.12403/) (2021)
- [Optimal Efficiency-Envy Trade-Off via Optimal Transport](https://mlsanity.com/paper/2209.15416/) (2022)
- [Modeling Access Differences to Reduce Disparity in Resource Allocation](https://mlsanity.com/paper/2402.00083/) (2024)
- [Price of Fairness in Short-Term and Long-Term Algorithmic Selections](https://mlsanity.com/paper/2605.06227/) (2026)
- [Fair Online Resource Allocation](https://mlsanity.com/paper/2606.18679/) (2026)

## Abstract (arXiv)

Resource allocation problems are a fundamental domain in which to evaluate the fairness properties of algorithms. The trade-offs between fairness and utilization have a long history in this domain. A recent line of work has considered fairness questions for resource allocation when the demands for the resource are distributed across multiple groups and drawn from probability distributions. In such cases, a natural fairness requirement is that individuals from different groups should have (approximately) equal probabilities of receiving the resource. A largely open question in this area has been to bound the gap between the maximum possible utilization of the resource and the maximum possible utilization subject to this fairness condition. Here, we obtain some of the first provable upper bounds on this gap. We obtain an upper bound for arbitrary distributions, as well as much stronger upper bounds for specific families of distributions that are typically used to model levels of demand. In particular, we find - somewhat surprisingly - that there are natural families of distributions (including Exponential and Weibull) for which the gap is non-existent: it is possible to simultaneously achieve maximum utilization and the given notion of fairness. Finally, we show that for power-law distributions, there is a non-trivial gap between the solutions, but this gap can be bounded by a constant factor independent of the parameters of the distribution.