Resource-constrained Fairness

TL;DR

Resource-constrained fairness reframes fair decision-making as a budgeted allocation problem where positive predictions are a scarce resource. The authors formalize harms per group $H_g[c_w]$ and show that under a fixed global selection rate $r$, optimal fairness enforces equal harm across groups (leveling up), with a measurable cost relative to the unconstrained optimum. They derive upper bounds on the cost of fairness via label swaps and demonstrate that costs are bell-shaped with respect to $r$, complemented by empirical results across diverse datasets showing how resource level and the chosen fairness metric influence trade-offs. The work unifies leveling up, cost-of-fairness, and resource constraints to enable practical deployment of fair decision systems and discusses policy levers such as adjusting selection rates or resources.

Abstract

Access to resources strongly constrains the decisions we make. While we might wish to offer every student a scholarship, or schedule every patient for follow-up meetings with a specialist, limited resources mean that this is not possible. When deploying machine learning systems, these resource constraints are simply enforced by varying the threshold of a classifier. However, these finite resource limitations are disregarded by most existing tools for fair machine learning, which do not allow the specification of resource limitations and do not remain fair when varying thresholds. This makes them ill-suited for real-world deployment. Our research introduces the concept of "resource-constrained fairness" and quantifies the cost of fairness within this framework. We demonstrate that the level of available resources significantly influences this cost, a factor overlooked in previous evaluations.

Figures (6)

• Figure 1: An illustration of how demographic parity varies with selection rate. We apply a range of classical bias mitigation methods from AIF360 bellamy2018ai and observe how fairness varies with selection rate. The dots indicate default thresholds. As the thresholds vary, fairness oscillates wildly (results on the Adult dataset, details Section \ref{['subsec:bias_mit_methods']}). Just as standard fairness methods fail to consider the selection rate, existing analyses of the cost of fairness corbett2017algorithmicfriedler2019comparativehaas2019pricevon2021cost also fail to take it into account.
• Figure 2: Impact of parameters on the cost of fairness, measured as the loss in precision (Adult Income dataset). We see that reducing the base rate disparity leads to a lower cost of fairness. Similarly, introducing more noise across all groups, also lowers the cost of fairness, but introducing more noise exclusively in the disadvantaged group, increases the cost of fairness. Finally, reducing the size of the disadvantaged group, results in a decrease in the cost of fairness as well.
• Figure 3: Cost of fairness (loss in precision) for all datasets when enforcing demographic parity (DP) and equal opportunity (EO). The cost of fairness for both metrics heavily depends on the available resource level and thus the used selection rate.
• Figure 4: Cost of fairness (loss in recall) for all datasets when enforcing demographic parity (DP) and equal opportunity (EO). The cost of fairness for both metrics heavily depends on the available resource level and thus the used selection rate.
• Figure 5: Cost of fairness (loss in accuracy) for all datasets when enforcing demographic parity (DP) and equal opportunity (EO). The cost of fairness for both metrics heavily depends on the available resource level and thus the used selection rate.

Theorems & Definitions (2)

• Proposition 1
• proof