Fairness and Utilization in Allocating Resources with Uncertain Demand

Abstract: 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.

• The paper establishes provable upper bounds on the utilization gap when fairness constraints are applied under uncertain demand.
• It demonstrates that exponential and Weibull demand distributions can achieve maximum utilization without sacrificing fairness, whereas power-law distributions exhibit a bounded gap.
• The research offers actionable insights for designing resource allocation policies that balance equitable access with system efficiency.

The paper "Fairness and Utilization in Allocating Resources with Uncertain Demand" explores the balance between fairness and utilization in the context of resource allocation when demands are uncertain and vary among different groups. Traditional resource allocation problems typically focus either on maximizing utilization (ensuring the resource is used as efficiently as possible) or on meeting fairness criteria (ensuring equitable access among different groups). This work investigates the trade-offs between these two goals within a probabilistic framework.

Key Points:

1. Fairness Condition: The paper considers a fairness condition where individuals across different groups should have approximately equal probabilities of receiving the resource. This equality of probabilities ensures that no particular group is disproportionately advantaged or disadvantaged.
2. Research Question: The central question addressed is quantifying the difference (gap) between the maximum possible utilization of the resource and the maximum achievable utilization when the fairness condition is imposed.
3. Upper Bounds on Utilization Gap:
   • The authors provide some of the first provable upper bounds on the utilization gap for arbitrary probability distributions of demand.
   • Specific Distributions: They derive much stronger bounds for specific families of distributions that are common in modeling demand, such as Exponential and Weibull distributions.
     • Exponential and Weibull Distributions: Interestingly, for these distributions, the authors show that it is indeed possible to achieve maximum utilization without compromising the fairness condition. This finding suggests that for certain types of demand models, the trade-off between fairness and utilization might not be as significant as previously thought.
     • Power-Law Distributions: For power-law distributions, which often illustrate heavy-tailed phenomena, the paper finds a non-trivial gap between achieving maximum utilization and meeting the fairness condition. However, the authors manage to bound this gap by a constant factor independent of the distribution parameters, offering insight into the extent of the trade-off.

Contributions:

• Provable Boundaries: By establishing upper bounds on the utilization gap, the paper provides a theoretical foundation for understanding how fairness constraints impact resource efficiency.
• Insights for Specific Demand Models: The results for exponential and Weibull distributions are particularly noteworthy because they challenge the prevailing notion that fairness always incurs a substantial cost in terms of utilization.
• Enabling Informed Policy: The findings of this paper can help policymakers and system designers make informed decisions about the trade-offs they might face when striving for fairness in resource allocation under uncertainty.

Overall, this paper makes significant contributions to the field of resource allocation by rigorously analyzing the interplay between fairness and utilization and providing actionable insights for various probabilistic models of demand.