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Individual Fairness In Strategic Classification

Zhiqun Zuo, Mohammad Mahdi Khalili

TL;DR

This work tackles fairness in strategic classification by showing that deterministic threshold rules fail individual fairness when individuals can manipulate features. It introduces a randomized threshold framework, where a threshold distribution $p(t)$ is optimized under Lipschitz-type constraints to achieve individual fairness with respect to both Best Response Cost and outcomes, and it reduces the optimization to a tractable linear program using a piecewise-constant approximation. The approach extends to group fairness by allowing group-specific threshold distributions and relaxing strict parity with a controllable margin, enabling concurrent improvement in both individual and group notions. Empirical results on real datasets demonstrate improved fairness metrics with minimal accuracy loss, highlighting the method’s practical relevance for fair decision-making under strategic behavior.

Abstract

Strategic classification, where individuals modify their features to influence machine learning (ML) decisions, presents critical fairness challenges. While group fairness in this setting has been widely studied, individual fairness remains underexplored. We analyze threshold-based classifiers and prove that deterministic thresholds violate individual fairness. Then, we investigate the possibility of using a randomized classifier to achieve individual fairness. We introduce conditions under which a randomized classifier ensures individual fairness and leverage these conditions to find an optimal and individually fair randomized classifier through a linear programming problem. Additionally, we demonstrate that our approach can be extended to group fairness notions. Experiments on real-world datasets confirm that our method effectively mitigates unfairness and improves the fairness-accuracy trade-off.

Individual Fairness In Strategic Classification

TL;DR

This work tackles fairness in strategic classification by showing that deterministic threshold rules fail individual fairness when individuals can manipulate features. It introduces a randomized threshold framework, where a threshold distribution is optimized under Lipschitz-type constraints to achieve individual fairness with respect to both Best Response Cost and outcomes, and it reduces the optimization to a tractable linear program using a piecewise-constant approximation. The approach extends to group fairness by allowing group-specific threshold distributions and relaxing strict parity with a controllable margin, enabling concurrent improvement in both individual and group notions. Empirical results on real datasets demonstrate improved fairness metrics with minimal accuracy loss, highlighting the method’s practical relevance for fair decision-making under strategic behavior.

Abstract

Strategic classification, where individuals modify their features to influence machine learning (ML) decisions, presents critical fairness challenges. While group fairness in this setting has been widely studied, individual fairness remains underexplored. We analyze threshold-based classifiers and prove that deterministic thresholds violate individual fairness. Then, we investigate the possibility of using a randomized classifier to achieve individual fairness. We introduce conditions under which a randomized classifier ensures individual fairness and leverage these conditions to find an optimal and individually fair randomized classifier through a linear programming problem. Additionally, we demonstrate that our approach can be extended to group fairness notions. Experiments on real-world datasets confirm that our method effectively mitigates unfairness and improves the fairness-accuracy trade-off.
Paper Structure (23 sections, 4 theorems, 44 equations, 1 figure, 9 tables, 2 algorithms)

This paper contains 23 sections, 4 theorems, 44 equations, 1 figure, 9 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Notations and Preliminaries
  3. Strategic Classification
  4. Randomized Classifier
  5. Best Response Cost
  6. Individual Fairness
  7. Individual Fairness with Repspect to BRC
  8. Fair Optimal Randomized Classifier
  9. Individual Fairness with Respect to Outcome
  10. Extension to Group Fairness
  11. Experiment
  12. Conclusion
  13. Limitations
  14. Acknowledgment
  15. Proofs
  16. ...and 8 more sections

Key Result

Theorem 3.1

Consider a $d$-dimensional binary classification problem with deterministic classifier $f(x; t_{0})$ with $t_{0} \in (C + \mathcal{C}, D)$. If $l(x)$ is reverse Lipschitz continuous, i.e. then for any constant $M_{c}$, there exist $x_{1}, x_{2} \in \mathcal{X}$ such that $\left|c_{f}(x_{1}) - c_{f}(x_{2})\right| > M_{c}\left\|x_{1} - x_{2}\right\|_{2}$.

Figures (1)

  • Figure 1: Estimated $\Pr\{\textit{bar\_pass} = 1|\textit{zgpa}\}$

Theorems & Definitions (10)

  • Definition 2.1: $d$-dimensional binary classification problem
  • Theorem 3.1
  • Theorem 3.2
  • Theorem 4.1
  • Theorem 4.2
  • Definition 5.1: Multi-group $d$-dimensional binary classification problem
  • proof
  • proof
  • proof
  • proof