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Fairness on Principal Stratum: A New Perspective on Counterfactual Fairness
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Proposes principal counterfactual fairness, which requires counterfactual fairness only for principal strata where the protected attribute has no individual effect on the outcome, with bounds, an optimization-based test, and a DR-based post-processing method.
Problem
Standard counterfactual fairness requires decisions to be invariant to the protected attribute for all individuals, which ignores that a protected attribute may causally affect the outcome of interest (e.g., disability and athlete performance), so it is unclear which attributes and individuals shoul
Approach
Restrict counterfactual fairness to the principal stratum where the protected attribute has no individual causal effect on the outcome (Y(0)=Y(1)), derive sharp bounds on the stratum-level decision disparities under ignorability, test feasibility via optimization, and post-process decisions with minimal flips using doubly robust estimates.
Key results
- On synthetic data, post-processing raised PCF by roughly 5.2% to 9.3% across LR, SVM, RF, and NB estimators, with PCF gains larger than CF gains for all models.
- On OULAD, the whole-population test found the algorithm already satisfies principal counterfactual fairness, so no post-processing was needed.
- On OULAD subgroups, post-processing raised PCF by up to 9.59% (X1 < 120, X2 > 0) and CF by up to 5.22% for unsolvable subgroups.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply principal counterfactual fairness post-processing | LR + OR · Synthetic | PCF: +6.68% | Helped |
| Apply principal counterfactual fairness post-processing | LR + IPS · Synthetic | PCF: +6.89% | Helped |
| Apply principal counterfactual fairness post-processing | LR + DR · Synthetic | PCF: +6.09% | Helped |
| Apply principal counterfactual fairness post-processing | SVM + OR · Synthetic | PCF: +5.15% | Helped |
| Apply principal counterfactual fairness post-processing | SVM + IPS · Synthetic | PCF: +8.98% | Helped |
| Apply principal counterfactual fairness post-processing | SVM + DR · Synthetic | PCF: +8.30% | Helped |
| Apply principal counterfactual fairness post-processing | RF + OR · Synthetic | PCF: +6.67% | Helped |
| Apply principal counterfactual fairness post-processing | RF + IPS · Synthetic | PCF: +8.35% | Helped |
| Apply principal counterfactual fairness post-processing | RF + DR · Synthetic | PCF: +9.02% | Helped |
| Apply principal counterfactual fairness post-processing | NB + OR · Synthetic | PCF: +8.31% | Helped |
| Apply principal counterfactual fairness post-processing | NB + IPS · Synthetic | PCF: +9.31% | Helped |
| Apply principal counterfactual fairness post-processing | NB + DR · Synthetic | PCF: +9.16% | Helped |
Surprising findings
- On the whole OULAD population the test found no violation, but subgroup analysis revealed violations in several subgroups, indicating violations grow with more subgrouping.
Limitations
- Principal counterfactual fairness is only partially identified, so unbiased point estimates cannot be obtained, only bounds and falsification tests.
- Experiments are limited to simple synthetic data and one real dataset with binary variables and linear/simple classifiers.
- Necessary but not sufficient conditions; the test can only falsify fairness.
Experimental setup
Datasets: OULAD STUDENTINFO (Open University Learning Analytics Dataset) synthetic SEM data on random 10-node DAG
Benchmarks: OULAD
Metrics: counterfactual fairness (CF) principal counterfactual fairness (PCF) percentage change of CF and PCF after post-processing
Baselines: LR + OR LR + IPS LR + DR SVM Random Forest Naive Bayes
Builds on: counterfactual fairness principal fairness counterfactual equalized odds path-specific counterfactual fairness
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