Explainer: What is Demographic Parity?

Equal outcomes, not equal treatment - and that distinction is everything.

The One-Sentence Definition

Demographic parity is a fairness metric that requires a model to produce positive predictions at equal rates across demographic groups - regardless of whether those groups have different underlying rates of the outcome being predicted.

Why This Matters

Demographic parity is the most widely used fairness metric in practice. It underlies US employment discrimination law (the EEOC's 80% rule), EU AI Act high-risk system audits, and most corporate fairness dashboards. When someone says an algorithm is "biased," they are usually - whether they know it or not - pointing at a demographic parity violation.

It matters because:

A model can be highly accurate overall and still produce systematically unequal outcomes for different groups - and demographic parity is the only metric that directly measures this
It is the legal threshold in hiring, lending, and admissions in most jurisdictions - violating it exposes organisations to disparate impact liability
It is the primary metric used throughout this repo - the fairness gaps in the COMPAS, Hiring, Credit, Insurance, and Benefits audits are all measured as demographic parity violations

But it also matters to understand what it doesn't catch - because a model can satisfy demographic parity while still being deeply unfair in other ways. See the Limitations section.

The Formal Definition

P(Ŷ = 1 | Group = A) = P(Ŷ = 1 | Group = B)

The model's positive prediction rate must be equal across groups. That's it. The metric makes no claim about whether the predictions are correct - only that the rate of positive predictions is equalised.

In practice, you rarely demand perfect equality. The EEOC's four-fifths rule treats any selection rate below 80% of the highest group's rate as evidence of adverse impact:

P(Ŷ = 1 | Group = B) / P(Ŷ = 1 | Group = A) ≥ 0.80

A ratio below 0.80 triggers scrutiny. A ratio above 0.80 passes. The 80% threshold is a legal convention, not a mathematical optimum.

Real-World Proof: Hiring Bias

The AI Fair Recruitment audit in this repo is a direct illustration of a demographic parity violation - and its fix.

A model trained with gender and age as features assigned hire recommendations at sharply different rates:

Group	Hire Rate
Male applicants	~71%
Female applicants	~50%
Fairness Gap	~20.9 percentage points

The model was not told to discriminate. It learned to - by treating age as a proxy for gender, because women in the dataset more often had career gaps. Age was correlated with gender, so including it smuggled the gender signal back in even without an explicit gender rule.

After dropping gender and age (the protected attribute and its proxy):

Group	Hire Rate
Male applicants	~67%
Female applicants	~67%
New Fairness Gap	~0.12 percentage points

97.3% reduction. The gap wasn't in the underlying merit of candidates - it was in which features the model was permitted to see.

Detection Code

Measure demographic parity gap

import pandas as pd

def demographic_parity_audit(df, prediction_col, group_col, positive_label=1):
    """
    Compute positive prediction rate per group and the parity gap.

    Returns a DataFrame with rates per group, plus the gap and
    the four-fifths ratio between the lowest and highest rate.
    """
    rates = (
        df.groupby(group_col)[prediction_col]
        .apply(lambda x: (x == positive_label).mean())
        .round(4)
        .rename('positive_rate')
        .reset_index()
        .sort_values('positive_rate', ascending=False)
    )

    max_rate = rates['positive_rate'].max()
    min_rate = rates['positive_rate'].min()
    gap = round(max_rate - min_rate, 4)
    ratio = round(min_rate / max_rate, 4) if max_rate > 0 else None

    print("Positive prediction rates by group:")
    print(rates.to_string(index=False))
    print(f"\nDemographic parity gap:   {gap:.4f} ({gap*100:.2f} pp)")
    print(f"Four-fifths ratio:        {ratio:.4f}  {'✓ passes' if ratio >= 0.8 else '✗ fails'} (threshold: 0.80)")

    return rates, gap, ratio

# Example - using the AI Fair Recruitment dataset
df = pd.read_csv('AI_Fair_Recruitment_Dataset.csv')
df['predicted_hire'] = model.predict(X_test)  # substitute your model

demographic_parity_audit(df_test, prediction_col='predicted_hire', group_col='Gender')

Compute across multiple protected attributes at once

def multi_group_parity_audit(y_pred, groups_df, positive_label=1):
    """
    Run demographic parity audit for every column in groups_df simultaneously.
    Useful when auditing for race, gender, and age in a single pass.
    """
    results = {}
    for col in groups_df.columns:
        temp = groups_df[[col]].copy()
        temp['y_pred'] = y_pred
        rates = temp.groupby(col)['y_pred'].apply(
            lambda x: (x == positive_label).mean()
        ).round(4)
        max_r, min_r = rates.max(), rates.min()
        results[col] = {
            'rates': rates.to_dict(),
            'gap': round(max_r - min_r, 4),
            'four_fifths_ratio': round(min_r / max_r, 4) if max_r > 0 else None,
            'passes_eeoc': (min_r / max_r) >= 0.8 if max_r > 0 else None,
        }
    return results

# Example
protected = test_df[['Gender', 'Race', 'AgeGroup']]
audit = multi_group_parity_audit(y_pred, protected)
for attr, result in audit.items():
    status = '✓' if result['passes_eeoc'] else '✗'
    print(f"{attr}: gap={result['gap']:.4f}, 4/5 ratio={result['four_fifths_ratio']:.4f} {status}")

Visualise the gap

import matplotlib.pyplot as plt

def plot_parity_gap(rates_df, group_col, rate_col='positive_rate', title='Demographic Parity'):
    fig, ax = plt.subplots(figsize=(8, 4))
    fig.patch.set_facecolor('#0f1117')
    ax.set_facecolor('#1a1d27')

    colors = ['#e05c5c' if i == 0 else '#5c9ee0' for i in range(len(rates_df))]
    bars = ax.barh(rates_df[group_col], rates_df[rate_col], color=colors)
    ax.axvline(x=rates_df[rate_col].max() * 0.8, color='#f0c040',
               linestyle='--', linewidth=1.2, label='80% threshold (EEOC)')

    ax.set_xlabel('Positive Prediction Rate', color='#aaaaaa')
    ax.set_title(title, color='white')
    ax.tick_params(colors='#aaaaaa')
    for spine in ax.spines.values():
        spine.set_edgecolor('#333344')
    ax.legend(facecolor='#1a1d27', labelcolor='white', fontsize=9)

    plt.tight_layout()
    plt.savefig('demographic-parity-gap.png', dpi=150, bbox_inches='tight',
                facecolor='#0f1117')
    print("Saved: demographic-parity-gap.png")

What Demographic Parity Catches - and What It Doesn't

What it catches

Models that assign positive outcomes (loans, hires, parole, insurance approvals) at lower rates to protected groups
Cases where a protected attribute or its proxies are driving the disparity - even if accuracy looks fine overall
Legal violations under disparate impact law without requiring evidence of intent

What it misses

1. Parity in mediocrity. A model achieves demographic parity by reducing the positive rate for the advantaged group rather than raising it for the disadvantaged group. The gap closes - but no one benefits. Always inspect absolute rates, not just the gap.

2. Error rate disparities. A model can satisfy demographic parity while making systematically different types of errors for different groups. It might approve loans at equal rates but deny creditworthy applicants from one group at a higher rate (a false negative disparity) while approving uncreditworthy applicants from another at a higher rate (a false positive disparity). Equalized odds catches this; demographic parity does not.

3. Calibration failures. A model can predict at equal rates across groups while its predictions mean different things for each group. If a risk score of 0.7 corresponds to 70% true risk for Group A but only 50% for Group B, the model is miscalibrated - but demographic parity will not flag it.

4. The impossibility result. When base rates differ between groups - which they almost always do - demographic parity cannot be satisfied simultaneously with equalized odds and predictive parity. Satisfying demographic parity will necessarily force one of the other two metrics to fail. This is not a flaw in the metric; it is a mathematical fact. See fairness-metric-conflicts.md for the proof.

Limitations

Demographic parity ignores the ground truth. It does not ask whether the groups should receive different rates, given the actual distribution of the outcome. A perfectly accurate model trained on data where Group A has a genuinely higher rate of the positive outcome will violate demographic parity - not because it is biased, but because it is accurate. This is the core tension between parity-based and accuracy-based fairness.

The 80% rule is a legal convention, not a scientific threshold. The EEOC chose 80% pragmatically in 1978. There is no statistical basis for treating 79% as discriminatory and 81% as fair. Courts have found discrimination below and above this threshold. Treat it as a trigger for scrutiny, not a verdict.

Intersectionality is not captured. Auditing by race alone and by gender alone can pass demographic parity while Black women face a combined disparity that neither single-attribute audit would surface. Disaggregate by all relevant combinations when the data supports it.

The baseline can be corrupted. If the positive prediction rate you are equalising is itself built on biased historical data - arrest rates instead of actual crime rates, for example - equalising it embeds the historical bias into the fair model. See proxy-variables.md and sampling-bias.md.

All five audits (COMPAS/, AI Fair Recruitment/, German Credit Lending/, Insurance Denial/, Benefits Denial/) - demographic parity gap is the primary fairness metric in every one
explainers/fairness-metric-conflicts.md - why demographic parity cannot coexist with equalized odds and predictive parity when base rates differ
explainers/equalized-odds.md - the error-rate alternative to demographic parity
explainers/disparate-impact.md - how demographic parity maps onto the legal four-fifths rule
explainers/proxy-variables.md - how to find and remove features that smuggle protected attributes back into the model

Demographic Parity