Differential Parity: Relative Fairness Between Two Sets of Decisions

TL;DR

This work tackles the challenge of absolute fairness being subjective by introducing differential parity, a relative fairness criterion requiring that the difference between two decision sets, $R_0(x)-R_1(x)$, be independent of a sensitive attribute $A(x)$. It formalizes two binary-attribute metrics, DPT and DPD, and proposes two machine learning–based estimation strategies, Unbiased Bridge and Biased Bridge, to assess differential parity when the two decision sets are defined on different data. Through a case study on the SCUT-FBP5500 face-beauty dataset with multiple human raters, the authors demonstrate that Biased Bridge generally yields more accurate differential-parity estimates, while highlighting robustness to sampling bias for decisions made on the same data. The work discusses limitations (binary sensitive attributes, same-data requirement for true differential parity) and outlines future directions toward continuous attributes, multi-label decisions, and broader human–AI decision-making contexts.

Abstract

With AI systems widely applied to assist human in decision-making processes such as talent hiring, school admission, and loan approval; there is an increasing need to ensure that the decisions made are fair. One major challenge for analyzing fairness in decisions is that the standards are highly subjective and contextual -- there is no consensus for what absolute fairness means for every scenario. Not to say that different fairness standards often conflict with each other. To bypass this issue, this work aims to test relative fairness in decisions. That is, instead of defining what are ``absolutely'' fair decisions, we propose to test the relative fairness of one decision set against another with differential parity -- the difference between two sets of decisions should be independent from a certain sensitive attribute. This proposed differential parity fairness notion has the following benefits: (1) it avoids the ambiguous and contradictory definition of ``absolutely'' fair decisions; (2) it reveals the relative preference and bias between two decision sets; (3) differential parity can serve as a new group fairness notion when a reference set of decisions (ground truths) is provided. One limitation for differential parity is that, it requires the two sets of decisions under comparison to 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 decisions sets made on difference data and estimate the differential parity.

Figures (1)

• Figure 1: Illustration of how relative fairness is tested with differential parity.

Theorems & Definitions (4)

• Definition 1
• Definition 2
• Definition 3
• Definition 4