Fairness Under Feature Constraints: When Gender and Income Are Entangled

> Paper: Fairness of Classifiers in the Presence of Constraints between Features > Authors: Martin C. Cooper, Imane Bousdira > arXiv: 2605.00592 | 2026-04-30

The Myth of "Just Remove Gender"

Imagine a loan-approval AI. The fairness requirement says decisions must not depend on protected features like gender. The naive fix is to drop the gender column during training. But the model can still infer gender through other features:

• Occupation type correlates strongly with gender (imbalanced gender ratios in certain professions)
• Working hours correlate with gender (differences in childcare responsibilities)
• Income level correlates with gender (the gender pay gap)

Even with gender removed, the model can reconstruct it from other inputs. This is called proxy discrimination.

Feature Constraints: The Hidden Killer of Fairness

Real-world features are bound by constraints:

1. Statistical correlations

• Gender → occupation choice → income level
• Race → educational opportunity → credit history
• Age → health status → insurance risk

2. Structural constraints

• Gender ratios in some industries result from historical and social structures
• They are not individual choices but systemic constraints
• When a model exploits these constraints, it exploits structural discrimination

3. Causal confounding

• Low income may be the *result* of discrimination
• A model using "low income" to predict "bad credit" can amplify existing discrimination

Blind spot of existing fairness methods: they only check whether protected features are used directly, ignore inter-feature constraints, and end up producing systems that are "fair on the surface, discriminatory in practice."

Explanation-Based Fairness

The paper proposes a new framework with a core idea:

> A decision is fair if it has a fair explanation.

What counts as a fair explanation?

1. Prime-Implicant Reasons — the "minimal sufficient conditions" behind a decision: which combination of features is enough to trigger it, such that removing any one changes the outcome. 2. Fairness constraints — a fair explanation must not contain protected features; and if feature A implies protected feature B, then A is excluded as well. 3. Constraint awareness — the search for explanations accounts for inter-feature constraints, so proxy features cannot sneak past the fairness check.

Example:

• Decision: loan rejected
• Unfair explanation: "because the applicant is a woman" (direct discrimination)
• Unfair explanation: "because the occupation is nurse" (proxy discrimination — nurses are predominantly female)
• Fair explanation: "because credit score is below threshold AND income is unstable" (independent of gender)

It resembles the legal standard: you must examine not only whether illegal evidence was used on the surface, but whether the reasoning behind the verdict contains discrimination.

Why Explanation-Level Fairness Beats Feature-Level Fairness

Problems with feature-level fairness:

• Surface compliance: protected features removed, compliance checks passed, yet discrimination persists
• Proxy loophole: countless proxy features can be exploited; banning them one by one is a whack-a-mole game

Advantages of explanation-level fairness:

• Deeper scrutiny: examines how features *combine* to produce a decision, not just which features were used
• Theoretical guarantees: the paper proves results on the existence of fair explanations when constraints are present
• Auditability: explanations are human-understandable and usable in legal review — "explain why this applicant was rejected"

A Feynman-Style Judgment: Fairness Is Causal, Not Just Technical

Feynman noted that knowing the name of something is different from understanding it. In AI fairness:

> Removing the "gender" feature does not eliminate gender discrimination, because gender's influence seeps in through countless other features. Real fairness requires understanding causal relationships between features, not just statistical ones.

This reminds us that fairness is not merely a technical problem. It touches sociology, economics, and law; AI systems are embedded in social structures, and technical solutions must account for social context.

Takeaways

If you build AI systems that require fairness, ask yourself:

1. Do feature constraints exist in my system? 2. Does removing protected features eliminate discrimination — or merely hide it? 3. Have I examined the *explanations* of decisions, not just the features used? 4. Does my fairness definition account for proxy discrimination?

The paper's core lesson: fairness is not "not looking at the unfair thing," but "not using unfair reasons." In a world where features constrain one another, surface-level fairness can mask deep discrimination. Only through explanations — asking *why* a decision was made — can we genuinely ensure AI fairness. In the era of algorithmic decisions, fairness is not just a statistical property but a moral requirement, and morality begins with asking why.