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Classification Under Strategic Self-Selection
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Studies classification when candidates strategically choose whether to apply based on published group-level precision, and proposes a differentiable strategic-learning objective with smoothed application weights and a precision proxy, plus a statistical-parity variant.
Problem
Classifiers used for screening face self-selection: strategic candidates decide whether to apply based on published conditional precision, so the test-time applicant distribution depends on the learned classifier, and naive accuracy-based learning can mis-estimate performance.
Approach
Model user participation as a function of the classifier's group-conditional precision, and train against the induced self-selective distribution by replacing hard application decisions with a differentiable sigmoid surrogate and a bias-corrected differentiable precision proxy; add a statistical-parity penalty to restrict the firm's power and enable targeted subsidies.
Key results
- On adult with cost 0.7, the strategic method (strat_x) reaches 91.1% induced accuracy vs 85.2% for naive learning, with about 1.1 of 4 groups applying.
- On bank with cost 0.8, strat_x attains 88.7% induced accuracy vs 86.4% for semi-strategic tuning.
- Adding statistical parity (strat_indep) yields rank r^2 up to 0.85 on adult, approximately enforcing the base-rate ordering at some accuracy cost.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use strategic learning with all features instead of naive learning | Linear classifier · Adult (c=0.7) | induced accuracy: 85.2 -> 91.1 | Helped |
| Use strategic learning with all features instead of naive learning | Linear classifier · Adult (c=0.8) | induced accuracy: (87.8) -> 90.5 | Helped |
| Use strategic learning with all features instead of naive learning | Linear classifier · Bank (c=0.7) | induced accuracy: (80.9) -> 90.1 | Helped |
| Use strategic learning with all features instead of naive learning | Linear classifier · Bank (c=0.8) | induced accuracy | Helped |
| Discard group features from strategic learning (ablation) | Strategic_x · Adult (c=0.7) | induced accuracy: 91.1 -> 86.0 | Hurt |
| Discard group features from strategic learning (ablation) | Strategic_x · Adult (c=0.8) | induced accuracy: 90.5 -> 89.0 | Hurt |
| Discard group features from strategic learning (ablation) | Strategic_x · Bank (c=0.7) | induced accuracy: 90.1 -> 87.9 | Hurt |
| Discard group features from strategic learning (ablation) | Strategic_x · Bank (c=0.8) | induced accuracy: 88.7 -> 87.0 | Hurt |
| Add statistical-parity regularization to strategic learning (ablation) | Strategic_x · Adult (c=0.7) | induced accuracy: 91.1 -> 86.5 | Hurt |
| Add statistical-parity regularization to strategic learning (ablation) | Strategic_x · Adult (c=0.8) | induced accuracy: 90.5 -> 88.5 | Hurt |
| Add statistical-parity regularization to strategic learning (ablation) | Strategic_x · Bank (c=0.7) | induced accuracy: 90.1 -> 87.3 | Hurt |
| Add statistical-parity regularization to strategic learning (ablation) | Strategic_x · Bank (c=0.8) | induced accuracy: 88.7 -> 88.2 | Hurt |
Surprising findings
- Higher precision does not always imply higher utility for applicants.
- Naive accuracy-maximizing learning can result in no groups applying at all.
Limitations
- Assumes rational, strategic applicants with beliefs based only on published group-level precision.
- Experiments are limited to linear classifiers on two tabular datasets with semi-synthetic behavior.
- Statistical parity results on bank are highly variable across seeds and initializations.
Experimental setup
Datasets: adult bank
Benchmarks: adult bank
Metrics: induced accuracy number of applying groups rank r^2 social cost
Baselines: naive non-strategic learning semi-strategic threshold tuning
Builds on: strategic classification performative prediction
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