Demographic Parity

Demographic parity is satisfied when the probability of a positive prediction is identical for all groups. Formally: P(ŷ=1 | A=a) = P(ŷ=1 | A=b) for all groups a, b, where ŷ is the predicted outcome and A is the protected attribute. This metric is also known as statistical parity or group fairness. It is an independence criterion, meaning the prediction is statistically independent of the sensitive attribute.

A defining characteristic of demographic parity is that it does not consider the actual ground truth labels (Y). It only evaluates the distribution of predictions. This is both its primary strength and its most significant limitation. It can be achieved even if the base rates of the target variable differ substantially between groups, which may require systematically over-predicting positive outcomes for one group and under-predicting for another.

The most common implementation is the Disparate Impact Ratio, often defined as the 80% rule. It is calculated as:

• Ratio = P(ŷ=1 | unprivileged group) / P(ŷ=1 | privileged group)
• A perfectly fair model under this definition has a ratio of 1.0.
• A ratio below 0.8 (or above 1.25) is typically flagged as potential discrimination.

Demographic parity is mathematically incompatible with equalized odds and predictive parity unless the base rates of the target variable are identical across groups or the model is perfectly accurate. This is a fundamental impossibility theorem in algorithmic fairness. Pursuing demographic parity often requires sacrificing calibration, meaning the predicted probability of a positive outcome may no longer accurately reflect the true likelihood for a given individual.

Demographic parity aligns closely with disparate impact legal theory under U.S. employment law (Title VII of the Civil Rights Act), where a facially neutral policy that disproportionately harms a protected group is unlawful. It is a primary metric used in Algorithmic Impact Assessments under the EU AI Act to evaluate potential discrimination. However, strict demographic parity is not universally mandated by law, and its use as a binding constraint rather than a diagnostic tool remains legally debated.

Achieving demographic parity typically involves one of three intervention points:

• Pre-processing: Reweighing or transforming the training data to remove statistical dependence on the protected attribute.
• In-processing: Adding a fairness constraint or regularization term to the model's loss function during training.
• Post-processing: Adjusting decision thresholds independently for each group after prediction to equalize positive rates.

A stricter fairness criterion requiring that a model's true positive rate and false positive rate are equal across all protected groups. Unlike demographic parity, equalized odds accounts for the ground truth by ensuring the classifier is equally accurate for each group.

• True Positive Rate Parity: The model identifies actual positives at the same rate across groups.
• False Positive Rate Parity: The model makes the same proportion of mistaken positive predictions across groups.
• Trade-off: Satisfying both equalized odds and demographic parity simultaneously is mathematically impossible when base rates differ between groups.

A fairness metric defined as the ratio of the favorable outcome rate for a protected group to that of a reference group. A ratio below 0.8 (the four-fifths rule) is commonly used as a threshold for identifying potential indirect discrimination.

• Formula: (Selection rate of protected group) / (Selection rate of reference group)
• Origin: Derived from the U.S. Equal Employment Opportunity Commission's Uniform Guidelines on Employee Selection Procedures.
• Limitation: Does not account for legitimate business necessity or ground truth qualifications.

A causal fairness definition stating a prediction is fair if it remains the same in a counterfactual world where an individual's protected attribute was changed. This approach requires a structural causal model to determine which variables are descendants of the protected attribute.

• Causal Reasoning: Goes beyond correlation to model the data-generating process.
• Individual-Level: Assesses fairness for specific individuals rather than group-level statistics.
• Challenge: Requires strong assumptions about the causal graph, which may be difficult to validate in practice.

A proxy variable is a non-protected feature that inadvertently encodes a protected attribute, leading to masked discrimination. For example, zip code often correlates strongly with race, and credit card type may correlate with age.

• Detection Methods: Mutual information analysis, correlation testing, and adversarial removal techniques.
• Mitigation: Removing or transforming proxy variables during preprocessing, or applying fairness constraints during training.
• Regulatory Relevance: The EU AI Act requires high-risk systems to be tested for proxy discrimination.

A relaxed version of equalized odds that requires only true positive rate parity across groups. This ensures that qualified individuals from all groups have an equal chance of receiving a positive outcome, without constraining false positive rates.

• Focus: Protects against denying opportunities to qualified individuals.
• Application: Commonly used in hiring, lending, and college admissions contexts.
• Distinction: Does not address the harm of false positives, which may be acceptable in contexts where false negatives are the primary concern.

A fairness principle stating that similar individuals should receive similar predictions, regardless of group membership. This requires defining a task-specific distance metric that captures relevant similarity between individuals.

• Metric Learning: Requires a domain-expert-defined similarity function, which can be challenging to specify.
• Contrast with Group Fairness: Addresses fairness at the individual level rather than aggregating across demographic groups.
• Formalization: Introduced by Dwork et al. (2012) as a Lipschitz condition on the classifier with respect to the similarity metric.