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Collective Counterfactual Explanations: Balancing Individual Goals and Collective Dynamics
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Proposes Collective Counterfactual Explanations (CCE), which add a population-dynamics (mean-field) equilibrium penalty based on chi-squared divergence to counterfactual explanations and relax the problem to unbalanced optimal transport with solvers and guarantees.
Problem
Standard counterfactual explanations are individual-centric: when many individuals seek similar changes they compete for the same favorable regions, creating externalities and ignoring the data distribution, so recommendations may be unrealistic or crowded.
Approach
Model competition via a mean-field population dynamics model with resource distribution, penalize deviation of the post-recourse distribution from equilibrium (chi-squared divergence to the current positive-region density), and reformulate CE as an unbalanced optimal transport problem that yields collective recourse plans.
Key results
- Across 100 random-seed experiments, CCE achieves lower competition cost than all baselines but not the lowest modification cost.
- On the combined modification-plus-competition metric, CCE outperforms the six baselines (Wachter, Growing Spheres, CLUE, FOCUS, C-CHVAE, ROAR).
- Increasing the competition weight lambda_2 in [0.01, 0.3] shows a clear trade-off between modification cost and competition cost.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CCE instead of the baseline recourse methods | Recourse methods on Adult, COMPAS, HELOC, and Moons · Adult, COMPAS, HELOC, and Moons | competition cost | Helped |
| Use CCE instead of the baseline recourse methods | Recourse methods on Adult, COMPAS, HELOC, and Moons · Adult, COMPAS, HELOC, and Moons | modification cost | Mixed |
| Use CCE instead of the baseline recourse methods | Recourse methods on Adult, COMPAS, HELOC, and Moons · Adult, COMPAS, HELOC, and Moons | combined modification and competition cost | Helped |
| Increase the competition-cost weight λ₂ (ablation) | CCE · Simulation varying λ₂ from 0.01 to 0.3 | modification cost | Mixed |
Surprising findings
- CCE does not achieve the lowest modification cost; it trades individual cost for lower competition cost by moving points toward higher-density regions.
Limitations
- Choice of competition weight lambda_2 is application-specific and non-trivial.
- Assumes population starts at equilibrium and resources remain fixed; does not model strategic deviation from recommendations.
- Causal recourse is only sketched without technical details; experiments use only two continuous actionable features.
Experimental setup
Datasets: Adult COMPAS HELOC Moons
Benchmarks: Adult COMPAS HELOC Moons
Metrics: modification cost competition cost (chi-squared based) combined modification plus competition cost
Baselines: Wachter Growing Spheres CLUE FOCUS C-CHVAE ROAR
Builds on: counterfactual explanations (Wachter et al.) unbalanced optimal transport Sinkhorn algorithm mean-field game theory back-and-forth dynamic OT
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