# Reconciling Predictive and Statistical Parity: A Causal Approach

arXiv: https://arxiv.org/abs/2306.05059 · HTML: https://mlsanity.com/paper/2306.05059/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 8 Jun 2023.

## Builds on (most cited first, 13 of 13)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [PC-Fairness: A Unified Framework for Measuring Causality-based Fairness](https://mlsanity.com/paper/1910.12586/) (2019)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Counterfactual Risk Assessments, Evaluation, and Fairness](https://mlsanity.com/paper/1909.00066/) (2019)
- [Causal Fairness Analysis](https://mlsanity.com/paper/2207.11385/) (2022)
- [Fair Data Adaptation with Quantile Preservation](https://mlsanity.com/paper/1911.06685/) (2019)
- [fairadapt: Causal Reasoning for Fair Data Pre-processing](https://mlsanity.com/paper/2110.10200/) (2021)

## Built on by (most cited first, 7 of 7)

- [Fairness-Accuracy Trade-Offs: A Causal Perspective](https://mlsanity.com/paper/2405.15443/) (2024)
- [Investigating Bias and Fairness in Appearance-based Gaze Estimation](https://mlsanity.com/paper/2604.10707/) (2026)
- [Mind the Gap: A Causal Perspective on Bias Amplification in Prediction & Decision-Making](https://mlsanity.com/paper/2405.15446/) (2024)
- [Evaluating Causal Discovery Algorithms for Path-Specific Fairness and Utility in Healthcare](https://mlsanity.com/paper/2603.15926/) (2026)
- [Tuning Derivatives for Causal Fairness in Machine Learning](https://mlsanity.com/paper/2605.05882/) (2026)
- [Causal Bias Detection in Generative Artificial Intelligence](https://mlsanity.com/paper/2605.11365/) (2026)
- [GoT-CD: Graph-of-Thoughts Causal Discovery and the Fragility of Post-hoc Path-Specific Fairness Audits](https://mlsanity.com/paper/2608.02877/) (2026)

## Abstract (arXiv)

Since the rise of fair machine learning as a critical field of inquiry, many different notions on how to quantify and measure discrimination have been proposed in the literature. Some of these notions, however, were shown to be mutually incompatible. Such findings make it appear that numerous different kinds of fairness exist, thereby making a consensus on the appropriate measure of fairness harder to reach, hindering the applications of these tools in practice. In this paper, we investigate one of these key impossibility results that relates the notions of statistical and predictive parity. Specifically, we derive a new causal decomposition formula for the fairness measures associated with predictive parity, and obtain a novel insight into how this criterion is related to statistical parity through the legal doctrines of disparate treatment, disparate impact, and the notion of business necessity. Our results show that through a more careful causal analysis, the notions of statistical and predictive parity are not really mutually exclusive, but complementary and spanning a spectrum of fairness notions through the concept of business necessity. Finally, we demonstrate the importance of our findings on a real-world example.