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Reconciling Predictive and Statistical Parity: A Causal Approach
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Derives a non-parametric causal decomposition of predictive parity and uses business necessity sets to reconcile statistical and predictive parity into a spectrum of fairness notions, validated on COMPAS and Census data.
Problem
The impossibility result showing statistical parity and predictive parity are mutually exclusive makes it hard for practitioners to choose a fairness measure; the paper asks how the two notions relate causally.
Approach
Decomposes the predictive parity measure into causal (term I) and reverse-causal spurious (term II) variations, defines causal predictive parity matching path-specific effects of the predictor to those of the true outcome along business-necessity pathways, and combines this with causal statistical parity in an algorithm ("Business Necessity Cookbook") so that SP and PP become endpoints of a spectr
Key results
- On COMPAS, Northpointe predictions show a direct effect of 6% ± 2.96% (violating disparate treatment), while the fair predictor's direct effect is -0.72% ± 1.11%.
- Varying the business necessity set (empty, Z, W, {Z,W}) traces a Pareto frontier: BN empty gives lowest SPM but largest iPPM; BN {Z,W} gives lowest iPPM but largest SPM.
- The decomposition of predictive parity (Term I + Term II) is verified empirically on a simulated SCM, with iTerm I and iTerm II canceling as predicted.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Remove the direct and indirect effects outside the business necessity set using fairadapt | Northpointe predictions on COMPAS · COMPAS | Ctf-DE: 6 % ± 2.96 % -> -0.72 % ± 1.11 % | Helped |
| Remove the direct and indirect effects outside the business necessity set using fairadapt | Northpointe predictions on COMPAS · COMPAS | Ctf-IE: -7.73 % ± 1.53 % -> -0.25 % ± 1.98 % | Helped |
| Use fairadapt-adjusted predictions instead of Northpointe predictions | COMPAS predictions · COMPAS | Ctf-SE: -3.75 % ± 1.58 % -> -2.75 % ± 1.22 % | No clear effect |
| Choose BN = ∅ rather than BN = {Z, W} (ablation) | fairadapt-adjusted predictor · COMPAS | SPM | Mixed |
| Choose BN = {Z, W} rather than BN = ∅ (ablation) | fairadapt-adjusted predictor · COMPAS | iPPM | Helped |
| Vary the business necessity set among ∅, Z, W, and {Z, W} (ablation) | fairadapt-adjusted predictor · COMPAS | SPM and iPPM | Mixed |
Surprising findings
- Northpointe's predictions are further from statistical parity yet better calibrated by iPPM than the fair predictor, illustrating the SP-PP trade-off.
Limitations
- Assumes the standard fairness model with no hidden confounding; partial identification needed to relax it.
- Finite-sample case requires hypothesis testing; the algorithm is presented in population-level form.
- Number of BN paths may scale unfavorably for larger causal graphs.
Experimental setup
Datasets: COMPAS Census 2018 (American Community Survey) simulated SCM data
Benchmarks: COMPAS Census 2018
Metrics: Ctf-DE Ctf-IE Ctf-SE statistical parity measure (SPM) integrated predictive parity measure (iPPM) AUC
Baselines: Northpointe COMPAS predictions group-specific threshold predictor (SP) random forest predictor (PP)
Builds on: statistical parity predictive parity impossibility result path-specific counterfactual fairness fairadapt structural causal models
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