# Quantifying Infra-Marginality and Its Trade-off with Group Fairness

arXiv: https://arxiv.org/abs/1909.00982 · HTML: https://mlsanity.com/paper/1909.00982/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Being Right for Whose Right Reasons?](https://mlsanity.com/paper/2306.00639/) (2023)
- [How Far Can Fairness Constraints Help Recover From Biased Data?](https://mlsanity.com/paper/2312.10396/) (2023)

## Abstract (arXiv)

In critical decision-making scenarios, optimizing accuracy can lead to a biased classifier, hence past work recommends enforcing group-based fairness metrics in addition to maximizing accuracy. However, doing so exposes the classifier to another kind of bias called infra-marginality. This refers to individual-level bias where some individuals/subgroups can be worse off than under simply optimizing for accuracy. For instance, a classifier implementing race-based parity may significantly disadvantage women of the advantaged race. To quantify this bias, we propose a general notion of η-infra-marginality that can be used to evaluate the extent of this bias. We prove theoretically that, unlike other fairness metrics, infra-marginality does not have a trade-off with accuracy: high accuracy directly leads to low infra-marginality. This observation is confirmed through empirical analysis on multiple simulated and real-world datasets. Further, we find that maximizing group fairness often increases infra-marginality, suggesting the consideration of both group-level fairness and individual-level infra-marginality. However, measuring infra-marginality requires knowledge of the true distribution of individual-level outcomes correctly and explicitly. We propose a practical method to measure infra-marginality, and a simple algorithm to maximize group-wise accuracy and avoid infra-marginality.