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Explainable Disparity Compensation for Efficient Fair Ranking

Abraham Gale, Amélie Marian

TL;DR

This work tackles bias-induced disparities in ranking outcomes by introducing an explainable, data-driven disparity compensation framework that uses compensatory bonus points. The core contribution is the Disparity Compensation Algorithm (DCA), a sampling-based optimization that adjusts ranking scores through a nonnegative bonus vector applied to fairness attributes, enabling interpretable, intersectional fairness adjustments. The method is extended to handle multiple top-k values via logarithmic discounting and validated on NYC school admissions and COMPAS data, showing substantial disparity reduction with minimal utility loss and favorable comparisons to quotas and other fairness approaches. The results demonstrate that DCA offers a practical, scalable path to fair ranking with transparent explanations for stakeholders, while supporting applicability to various fairness metrics and real-world decision systems.

Abstract

Ranking functions that are used in decision systems often produce disparate results for different populations because of bias in the underlying data. Addressing, and compensating for, these disparate outcomes is a critical problem for fair decision-making. Recent compensatory measures have mostly focused on opaque transformations of the ranking functions to satisfy fairness guarantees or on the use of quotas or set-asides to guarantee a minimum number of positive outcomes to members of underrepresented groups. In this paper we propose easily explainable data-driven compensatory measures for ranking functions. Our measures rely on the generation of bonus points given to members of underrepresented groups to address disparity in the ranking function. The bonus points can be set in advance, and can be combined, allowing for considering the intersections of representations and giving better transparency to stakeholders. We propose efficient sampling-based algorithms to calculate the number of bonus points to minimize disparity. We validate our algorithms using real-world school admissions and recidivism datasets, and compare our results with that of existing fair ranking algorithms.

Explainable Disparity Compensation for Efficient Fair Ranking

TL;DR

This work tackles bias-induced disparities in ranking outcomes by introducing an explainable, data-driven disparity compensation framework that uses compensatory bonus points. The core contribution is the Disparity Compensation Algorithm (DCA), a sampling-based optimization that adjusts ranking scores through a nonnegative bonus vector applied to fairness attributes, enabling interpretable, intersectional fairness adjustments. The method is extended to handle multiple top-k values via logarithmic discounting and validated on NYC school admissions and COMPAS data, showing substantial disparity reduction with minimal utility loss and favorable comparisons to quotas and other fairness approaches. The results demonstrate that DCA offers a practical, scalable path to fair ranking with transparent explanations for stakeholders, while supporting applicability to various fairness metrics and real-world decision systems.

Abstract

Ranking functions that are used in decision systems often produce disparate results for different populations because of bias in the underlying data. Addressing, and compensating for, these disparate outcomes is a critical problem for fair decision-making. Recent compensatory measures have mostly focused on opaque transformations of the ranking functions to satisfy fairness guarantees or on the use of quotas or set-asides to guarantee a minimum number of positive outcomes to members of underrepresented groups. In this paper we propose easily explainable data-driven compensatory measures for ranking functions. Our measures rely on the generation of bonus points given to members of underrepresented groups to address disparity in the ranking function. The bonus points can be set in advance, and can be combined, allowing for considering the intersections of representations and giving better transparency to stakeholders. We propose efficient sampling-based algorithms to calculate the number of bonus points to minimize disparity. We validate our algorithms using real-world school admissions and recidivism datasets, and compare our results with that of existing fair ranking algorithms.
Paper Structure (41 sections, 5 theorems, 16 equations, 10 figures, 2 tables, 2 algorithms)

This paper contains 41 sections, 5 theorems, 16 equations, 10 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Motivating Examples
  5. NYC High School Admissions
  6. COMPAS Recidivism Data
  7. Definitions
  8. Ranking Functions
  9. Bonus Points
  10. Disparity
  11. Disparity Compensation Methods
  12. Challenges
  13. Disparity Compensation Algorithm
  14. Accuracy of DCA
  15. Time Complexity of DCA
  16. ...and 26 more sections

Key Result

Theorem 4.1

At every step of Full DCA, if removing object $q$ from the top-k and replacing it with object $p$ would reduce the overall disparity, Full DCA will allocate more bonus points at that step to $p$ than to $q$.

Figures (10)

  • Figure 1: $nDCG@k$ on the school data (Test dataset) for varying $k$
  • Figure 2: $nDCG@k$ and disparity norm on the school data (Test dataset) for varying proportions of total recommended bonus points
  • Figure 3: Disparity on the school data (Test dataset) for varying proportions of total recommended bonus points
  • Figure 4: Experiments using DCA on the School dataset
  • Figure 5: Log-Discounted disparity when there is a maximum number of bonus points
  • ...and 5 more figures

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 4.1
  • Lemma 4.2
  • Lemma 4.3
  • Lemma 4.4
  • Theorem 4.5