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Causal Equal Protection as Algorithmic Fairness

Marcello Di Bello, Nicolò Cangiotti, Michele Loi

TL;DR

The paper tackles fairness in trial-based classifications by proposing causal equal protection, a criterion that combines classification parity with causal reasoning via do-calculus to require that protected traits not generate uneven misclassification risk in aggregate. It differentiates diagnostic and predictive evidence, analyzes direct and indirect causal influences, and uses stylized legal examples to show when parity alone is misleading and when causal mediation can justify or undermine evidence. The key contribution is a formal, process-level criterion, expressed as $P(C=1 \mid do[A=1] \& do[Y=0]) = P(C=1 \mid do[A=0] \& do[Y=0])$, that captures when risk imposition is fairly allocated across groups. This framework clarifies the fairness of legal evidence and informs broader judgments about algorithmic fairness in criminal justice and related domains, while acknowledging limitations and the need to model socially salient traits as causal structures rather than simple variables.

Abstract

By combining the philosophical literature on statistical evidence and the interdisciplinary literature on algorithmic fairness, we revisit recent objections against classification parity in light of causal analyses of algorithmic fairness and the distinction between predictive and diagnostic evidence. We focus on trial proceedings as a black-box classification algorithm in which defendants are sorted into two groups by convicting or acquitting them. We defend a novel principle, causal equal protection, that combines classification parity with the causal approach. In the do-calculus, causal equal protection requires that individuals should not be subject to uneven risks of classification error because of their protected or socially salient characteristics. The explicit use of protected characteristics, however, may be required if it equalizes these risks.

Causal Equal Protection as Algorithmic Fairness

TL;DR

The paper tackles fairness in trial-based classifications by proposing causal equal protection, a criterion that combines classification parity with causal reasoning via do-calculus to require that protected traits not generate uneven misclassification risk in aggregate. It differentiates diagnostic and predictive evidence, analyzes direct and indirect causal influences, and uses stylized legal examples to show when parity alone is misleading and when causal mediation can justify or undermine evidence. The key contribution is a formal, process-level criterion, expressed as , that captures when risk imposition is fairly allocated across groups. This framework clarifies the fairness of legal evidence and informs broader judgments about algorithmic fairness in criminal justice and related domains, while acknowledging limitations and the need to model socially salient traits as causal structures rather than simple variables.

Abstract

By combining the philosophical literature on statistical evidence and the interdisciplinary literature on algorithmic fairness, we revisit recent objections against classification parity in light of causal analyses of algorithmic fairness and the distinction between predictive and diagnostic evidence. We focus on trial proceedings as a black-box classification algorithm in which defendants are sorted into two groups by convicting or acquitting them. We defend a novel principle, causal equal protection, that combines classification parity with the causal approach. In the do-calculus, causal equal protection requires that individuals should not be subject to uneven risks of classification error because of their protected or socially salient characteristics. The explicit use of protected characteristics, however, may be required if it equalizes these risks.
Paper Structure (21 sections, 2 equations, 7 figures)

This paper contains 21 sections, 2 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Classification Parity
  3. An intuitive principle
  4. Hedden, Long and Beigang
  5. Neither necessary nor sufficient
  6. The Causal Analysis
  7. Correlation v. causal influence
  8. Direct v. indirect causal influence
  9. Causal paths and counterfactuals
  10. Diagnostic Fairness
  11. Diagnostic v. predictive evidence
  12. Biased diagnostic evidence
  13. Outcome-mediated paths
  14. Causal Equal Protection
  15. Subtly biased diagnostic evidence
  16. ...and 6 more sections

Figures (7)

  • Figure 1:
  • Figure 2: Algorithm based on predictive (a) v. diagnostic evidence (b).
  • Figure 3: Diagnostic evidence subject to two causal influences, from the outcome and the protected category.
  • Figure 4: The positive causal influence from the protected category onto the classification is neutralized.
  • Figure 5: Two unmediated causal influences balance each other out.
  • ...and 2 more figures