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Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty
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Studies causal strategic classification with incomplete information, characterizing when rational agents invest effort in desirable features, showing non-convexity of designing desirable classifiers in general and tractable special cases.
Problem
Strategic classification where agents modify causally linked features; the principal wants agents to invest effort in desirable (lifestyle) features rather than undesirable ones, under complete and incomplete information about the classifier and causal graph.
Approach
Combines causal graph-based feature effects (contribution matrix) with Gaussian priors over the classifier and edge weights, introduces beta-desirability of effort profiles, and characterizes best responses for l_p costs; partial uncertainty yields convex agent problems and closed-form-like effort profiles.
Key results
- Under complete information, finding beta-desirable classifiers is non-convex in general but convex when there is a single desirable feature (p in [1,3]).
- Under partially incomplete information, the agent's problem is convex for delta <= 1/2, while full uncertainty over classifier and graph gives a non-convex problem.
- In the cardiovascular case study, higher uncertainty sigma reduces beta-desirability and the problem becomes infeasible beyond a threshold depending on delta.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the HPT classifier instead of the Obesity, DM, or HPL classifier | Agent response in the CVD risk study · CVD risk study | β-desirability | Helped |
| Increase classifier uncertainty σ | Agent response across the four classifiers · CVD risk study | β-desirability | Hurt |
| Increase failure probability δ | Agent response across the four classifiers · CVD risk study | β-desirability | Helped |
| Increase the distance α from the classification boundary | Agent response with ℓ2-norm costs · CVD risk study | β-desirability | No clear effect |
| Use causal links that let desirable features influence classifier-observed undesirable features | Agent response in the CVD risk study · CVD risk study | Effort on desirable features | Helped |
Surprising findings
- Desirable features can be incentivized even though the classifier places zero weight on them, because they causally affect observed undesirable features.
Limitations
- Agents' Gaussian priors are assumed; other uncertainty forms are not modeled.
- Causal graph topology is assumed common knowledge.
- Designing desirable classifiers is non-convex when more than one desirable feature exists; only heuristic convexification provided.
Experimental setup
Datasets: expert-survey causal graph for cardiovascular disease risk (Fuzzy Delphi)
Metrics: beta-desirability l2 norm of mean contribution
Builds on: causal strategic classification principal-agent models
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