Demographic Parity

Demographic parity is an independence-based fairness metric. It requires that the probability of receiving a positive outcome is identical for all groups defined by a protected attribute (e.g., race, gender).

• Formal Definition: P(Ŷ=1 | A=a) = P(Ŷ=1 | A=b) for all groups a, b
• The model's prediction Ŷ is completely independent of the sensitive attribute A
• This is the strongest group fairness constraint, ignoring all other features
• Does not require access to ground truth labels, only predictions and group membership

The most common way to quantify demographic parity is through the Disparate Impact Ratio (DIR), often linked to the 80% rule in U.S. employment law.

• Formula: DIR = P(Ŷ=1 | unprivileged) / P(Ŷ=1 | privileged)
• A DIR of 1.0 indicates perfect demographic parity
• A DIR below 0.8 (or above 1.25) is conventionally flagged as potential disparate impact
• This ratio provides a single, interpretable scalar for auditing binary classifiers

A primary criticism of demographic parity is that it permits lazy solutions. A classifier can satisfy the criterion by randomly selecting a fixed quota of individuals from each group, ignoring actual qualifications.

• A lender could approve 50% of applicants from every group regardless of creditworthiness
• This violates equal opportunity for truly qualified individuals in the disadvantaged group
• It can incentivize selecting less-qualified individuals from advantaged groups to meet quotas
• The metric is blind to the base rate of true positive outcomes in each group

Demographic parity is often contrasted with Equalized Odds, a stricter separation-based metric. While demographic parity equalizes only the positive prediction rate, equalized odds requires equality of both true positive and false positive rates.

• Demographic Parity: Equal selection rates across groups
• Equalized Odds: Equal error rates (TPR and FPR) across groups
• A model can satisfy demographic parity while having wildly different false positive rates
• When base rates differ between groups, both criteria cannot be satisfied simultaneously except in trivial cases

Demographic parity is often enforced through pre-processing interventions that transform the training data before model fitting.

• Reweighing: Assigns weights to training examples to make the label distribution independent of the protected attribute
• Disparate Impact Remover: Edits feature values to obscure their correlation with the protected attribute while preserving rank ordering within groups
• Optimized Pre-Processing: Learns a probabilistic transformation of features and labels to satisfy fairness constraints with minimal information loss
• These methods modify the data distribution rather than the learning algorithm itself

Demographic parity aligns with the legal concept of disparate impact under Title VII of the U.S. Civil Rights Act of 1964, though the legal standard is more nuanced.

• The four-fifths rule from the Uniform Guidelines on Employee Selection Procedures (1978) operationalizes this
• In the EU, the AI Act classifies certain high-risk systems that exhibit statistical disparities as requiring conformity assessments
• Courts often require a showing of business necessity if a model exhibits disparate impact
• Demographic parity is a statistical proxy for legal compliance, not a complete legal defense

A separation-based fairness metric that is stricter than demographic parity. It requires a classifier to achieve equal True Positive Rates and equal False Positive Rates across all protected groups.

• Matches error rates for qualified and unqualified individuals
• Penalizes lazy classifiers that achieve parity by approving everyone
• Often trades off with demographic parity in practice

A relaxed version of equalized odds that only constrains the True Positive Rate to be equal across groups. This ensures that among individuals who should qualify, the same proportion actually receives a positive outcome.

• Focuses solely on qualified individuals
• Does not constrain false positive rates
• Preferred when the cost of a false negative is asymmetric across groups

A sufficiency-based criterion requiring that the Positive Predictive Value (precision) be equal across groups. If a model predicts a positive outcome, the probability that the prediction is correct must be the same regardless of group membership.

• Also called 'outcome test' in economics
• Ensures a positive decision means the same thing for everyone
• Mathematically incompatible with demographic parity unless base rates are equal

A legal doctrine originating from U.S. employment law, quantified by the 80% rule. A selection process exhibits disparate impact if the selection rate for a protected group is less than 80% of the rate for the group with the highest selection rate.

• Directly measures the ratio of positive prediction rates
• Closely related to demographic parity in practice
• Used by the U.S. Equal Employment Opportunity Commission

A causal definition of fairness. A prediction is counterfactually fair if it remains the same in the actual world and in a counterfactual world where the individual belonged to a different demographic group, given all other causally independent attributes.

• Requires a Structural Causal Model to define
• Captures intuition of 'what if' scenarios
• Addresses limitations of purely statistical definitions like demographic parity

The observed tension where enforcing strict fairness constraints like demographic parity can measurably reduce overall predictive accuracy. This trade-off is not universal and depends on:

• The quality and bias present in the training data
• Whether the protected attribute is causally relevant to the outcome
• The specific fairness metric being enforced

Key insight: Improving data collection and representation often mitigates this trade-off more effectively than post-hoc constraints.