Differential Parity: Relative Fairness Between Two Sets of Decisions

Abstract

Background: With AI systems increasingly being applied to assist humans in decision-making processes such as talent hiring, school admissions, and loan approvals, there is a growing need to ensure that the resulting decisions are fair. A major challenge in analyzing fairness is that standards are highly subjective and context-dependent —- there is no consensus on what absolute fairness means in every scenario. Moreover, different standards of fairness often conflict with each other.

Objectives: To address this issue, this work aims to evaluate the relative fairness between decisions.

Methods: Instead of defining what constitutes “absolutely” fair decisions, we propose assessing the relative fairness of one decision set against another using differential parity —- two sets of decisions are considered relatively fair with respect to each other if and only if the difference between them is independent of a given sensitive attribute. The proposed notion of differential parity fairness offers three key benefits: (1) it avoids the ambiguity and contradictions inherent in defining “absolutely” fair decisions; (2) it reveals relative preferences and biases between two decision sets; and (3) it can serve as a new notion of group fairness when a reference set of decisions (e.g., ground truth) is available. One limitation of differential parity is that the two sets of decisions being compared must be made on the same data subjects. To overcome this limitation, we propose to utilize a machine learning model to bridge the gap between the two sets of decisions made on different data and approximate the differential parity metrics. In addition to differential parity and inspired by the statistical parity fairness notion, we also define relative statistical parity – the difference between the means of two sets of decisions is required to be independent of the sensitive attribute – as a weaker notion of relative fairness compared to differential parity.

Results: Theoretically, we show how the proposed metrics statistically evaluate differential parity and relative statistical parity. We also proved the feasibility of using the proposed biased bridge algorithm to approximate differential parity metrics between decisions made on different data. Empirically, we evaluated the Type I and Type II error rates of differential parity and relative statistical parity both between decisions made on the same data and on different data. Experimental results suggest that differential parity outperforms relative statistical parity by having a much lower Type II error rate in both scenarios.

Conclusions: With lower than 0.1 Type I and Type II error rates in both scenarios, the effectiveness of differential parity demonstrated in this article suggests that it is feasible and beneficial to evaluate relative bias between decisions made by different entities. We expect this to pave the way for the analysis of relative fairness in AI and beyond.