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Facets of Disparate Impact: Evaluating Legally Consistent Bias in Machine Learning

Jarren Briscoe, Assefaw Gebremedhin

TL;DR

Addressing gaps between legal concepts of bias and ML fairness metrics, the paper introduces the Objective Fairness Index ($OFI$) to quantify bias through marginal benefits under objective testing. It formalizes $b_q \in \{0,1\}$, group benefit $b = \frac{1}{n}\sum b_q$, expected benefit $\mathbb{E}[b] = \frac{TP+FN}{n}$, and marginal benefit $\mathcal{B} = b - \mathbb{E}[b] = \frac{FP-FN}{n}$, with $\text{OFI} = \mathcal{B}_i - \mathcal{B}_j$ and a theoretical range $[-2,2]$. The paper derives formal thresholds $OFI \in [-0.3,0.3]$ and demonstrates robustness to sampling, showing OFI aligns with Ricci v. DeStefano's emphasis on objective testing and discriminates cases where $DI$ is undefined or misleading. Through empirical analyses on $COMPAS$ and Folktables datasets, it shows OFI can reveal algorithmic bias beyond $DI$, while providing open-source code to reproduce results. These contributions advance legally coherent fairness assessment and point to future work in multi-class, regression, and debiasing techniques.

Abstract

Leveraging current legal standards, we define bias through the lens of marginal benefits and objective testing with the novel metric "Objective Fairness Index". This index combines the contextual nuances of objective testing with metric stability, providing a legally consistent and reliable measure. Utilizing the Objective Fairness Index, we provide fresh insights into sensitive machine learning applications, such as COMPAS (recidivism prediction), highlighting the metric's practical and theoretical significance. The Objective Fairness Index allows one to differentiate between discriminatory tests and systemic disparities.

Facets of Disparate Impact: Evaluating Legally Consistent Bias in Machine Learning

TL;DR

Addressing gaps between legal concepts of bias and ML fairness metrics, the paper introduces the Objective Fairness Index () to quantify bias through marginal benefits under objective testing. It formalizes , group benefit , expected benefit , and marginal benefit , with and a theoretical range . The paper derives formal thresholds and demonstrates robustness to sampling, showing OFI aligns with Ricci v. DeStefano's emphasis on objective testing and discriminates cases where is undefined or misleading. Through empirical analyses on and Folktables datasets, it shows OFI can reveal algorithmic bias beyond , while providing open-source code to reproduce results. These contributions advance legally coherent fairness assessment and point to future work in multi-class, regression, and debiasing techniques.

Abstract

Leveraging current legal standards, we define bias through the lens of marginal benefits and objective testing with the novel metric "Objective Fairness Index". This index combines the contextual nuances of objective testing with metric stability, providing a legally consistent and reliable measure. Utilizing the Objective Fairness Index, we provide fresh insights into sensitive machine learning applications, such as COMPAS (recidivism prediction), highlighting the metric's practical and theoretical significance. The Objective Fairness Index allows one to differentiate between discriminatory tests and systemic disparities.
Paper Structure (13 sections, 10 theorems, 18 equations, 8 figures, 1 table)

This paper contains 13 sections, 10 theorems, 18 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Limitations of Disparate Impact
  3. Legal Foundations of Disparate Impact
  4. Defining Benefit and Bias
  5. Improvement over Disparate Impact
  6. Establishing OFI Thresholds
  7. Applying OFI: Empirical Case Studies
  8. Conclusions and Future Directions
  9. Preliminaries
  10. Counting
  11. A Quasi-Triangular Distribution
  12. Standard Deviation and Mean of $\mathcal{B}$
  13. Empirical Studies

Key Result

Theorem B.1

Given the number of samples, $n$, the count of value $x\in[0,n]$, denoted as $C(x;n)$, appearing in $\mathcal{M}(n)$ is found by

Figures (8)

  • Figure 1: Objective Fairness Index's conceptual framework.
  • Figure 2: OFI shows that COMPAS manifests algorithmic bias in addition to manifesting disparate impact (DI). We use the predictions and labels published in propublica_compas.
  • Figure 3: DI conveys that Pacific Islanders have positive bias for 7/8 comparisons. However, OFI shows that Pacific Islanders suffer from algorithmic bias in 6/8 cases. Key: AI is American Indian, AN is Alaska Native, Pacific Isl. is Pacific Islander.
  • Figure 4: The number of times the value $x$ appears in $\mathcal{M}$.
  • Figure 5: Assessing COMPAS with results published by Propublicapropublica_compas.
  • ...and 3 more figures

Theorems & Definitions (19)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition A.1
  • Definition A.2
  • Theorem B.1
  • ...and 9 more