Technical Summary: Individual Fairness-aware Strategic Classification with Peer Imitation

1. Problem Statement

Strategic Classification (SC) addresses scenarios where agents manipulate their observable features to obtain favorable decisions from predictive models. While existing fairness-aware SC approaches primarily focus on group fairness (e.g., demographic parity) and assume agents respond independently, this paper identifies a critical gap when individual fairness is required.

Individual fairness mandates that similar individuals receive similar decisions. The authors argue that under this constraint, the assumption of independent manipulation breaks down. Instead, agents engage in peer imitation: an agent's optimal manipulation strategy depends on the outcomes of their "neighborhood" (similar peers). Specifically, agents observe positively decided peers within their similarity radius and strategically manipulate their features to imitate these peers, thereby entering a favorable decision region.

This creates a fundamental mismatch:

1. Classical SC assumes manipulation is a function of the agent's features and the classifier alone: $x' = b(x; f)$.
2. Individual Fairness (IF) SC induces population-dependent manipulation: $x' = b_{IF}(x; f, \{x_j\})$, where the manipulation depends on the set of visible, positively decided peers $\{x_j\}$.

The paper posits that standard SC models fail to capture this interdependence, leading to suboptimal classifiers and potential fairness violations in strategic environments.

2. Methodology: Individual Fairness-aware Strategic Classification (IFSC)

To address the interdependence of strategic manipulation, the authors propose IFSC, a framework that models peer-driven manipulation and learns classifiers robust to this behavior.

2.1 Modeling Peer-Driven Manipulation

The framework formalizes the manipulation process through a visibility-driven mechanism:

• Visible Peer Set ($S^{vis}_i$): Agents do not observe the entire population. They observe a subset of positively decided peers within a visibility radius $R_{vis}$ or based on salient features.
• Strategic Utility: An agent $i$ evaluates the utility of manipulating their features to fall within the $\delta$-similarity neighborhood of a visible peer $j$. The utility balances the benefit of a positive decision against the manipulation cost.
• Manipulation Rule: If visible peers exist, the agent chooses the manipulation that maximizes utility by moving toward a specific peer's neighborhood. If no peers are visible, the agent defaults to no manipulation.

2.2 Robust Learning with Stochastic Perturbation

Recognizing that the set of visible peers is uncertain and may vary across environments, IFSC employs a robust learning process:

• Stochastic Perturbation: During training, the visible peer set $S^{vis}_i$ is randomly perturbed (e.g., removing some peers and introducing others) to simulate uncertainty in observability.
• Simulation: The classifier is trained on the resulting post-manipulation distributions generated by these perturbed peer sets, rather than a fixed visibility realization.

2.3 Unified Optimization Objective

The classifier is learned by minimizing a unified objective that combines:

1. Post-Manipulation Accuracy Risk ($R_{acc}$): The expected classification loss on the simulated manipulated features.
2. Individual Fairness Regularization ($V_{IF}$): A penalty term enforcing that similar manipulated individuals receive similar decisions.

The optimization problem is formulated as:
$$f^*_{IF} \in \arg \min_{f \in \mathcal{F}} \left[ R_{acc}(f) + \lambda V_{IF}(f) \right]$$
where both terms are evaluated on the simulated post-manipulation features.

3. Key Contributions

The paper outlines three primary contributions:

1. Identification of a Structural Limitation: The authors demonstrate that the standard assumption of agent-independent manipulation in classical SC is invalid under individual fairness constraints. They prove that individual fairness induces interdependent strategic manipulation via peer imitation, a phenomenon not captured by existing models.
2. Proposal of the IFSC Framework: They introduce a strategic framework that explicitly models peer-driven manipulation. This includes a principled training objective that optimizes classifiers over simulated post-manipulation distributions with stochastic perturbations to align learning with the induced strategic distribution.
3. Empirical Validation: Extensive experiments on synthetic and real-world datasets show that IFSC consistently preserves individual fairness consistency and improves post-manipulation accuracy compared to standard SC baselines, particularly when agents exhibit peer imitation behaviors.

4. Experimental Results

The authors evaluated IFSC on seven datasets (six real-world, one synthetic) across three manipulation regimes: Classical (independent), Peer Imitation, and Mixed.

• Manipulation Effectiveness: Figure 3 shows that under individual fairness constraints, peer-driven manipulation yields significantly higher "cheatment rates" (the rate at which initially rejected agents become accepted) compared to independent manipulation. This advantage grows as the similarity threshold $\delta$ increases.
• Accuracy and Fairness:
  • Standard SC trained on independent assumptions suffers a performance drop (2–4% accuracy loss) and increased fairness gaps when agents actually perform peer imitation.
  • IFSC consistently achieves higher post-manipulation accuracy and lower Individual Fairness Gaps (IF-Gap) across all datasets and manipulation regimes.
• Robustness to Visibility Mismatch: Experiments varying the visibility regimes (Local, kNN, Probabilistic) between training and testing demonstrate that IFSC maintains stable performance. In contrast, classifiers trained on fixed visibility assumptions degrade significantly when the test-time visibility differs.
• Stochastic Perturbation: Introducing stochastic perturbations during training enhances robustness to visibility variations without compromising individual fairness.

5. Significance and Claims

The paper claims that its work addresses a fundamental mismatch between classical strategic classification formulations and fairness-aware decision settings. By shifting the focus from group-level statistics to individual-level consistency, the authors reveal that fairness constraints can fundamentally alter strategic behavior, transforming independent responses into interdependent, peer-driven imitation.

The significance of the work lies in:

• Theoretical Insight: Establishing that individual fairness necessitates a reformulation of strategic classification to account for population-dependent manipulations.
• Practical Robustness: Providing a learning framework that remains effective even when the specific visibility conditions of agents are uncertain or mismatched between training and deployment.
• Fairness Preservation: Demonstrating that accounting for fairness-induced strategic dependence leads to more robust decisions that better satisfy individual fairness requirements in the presence of strategic agents.

The authors conclude that future work should extend this framework to more complex strategic interaction models and investigate long-term population dynamics.