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AI Fairness Metrics: Demographic Parity to Equalized Odds
Group fairness metrics measure whether a model's decisions or errors differ across demographic groups.
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Résumé
Demographic parity compares selection rates, equal opportunity compares true positive rates, equalized odds compares both true and false positive rates, and predictive parity compares precision. These definitions matter because they can conflict mathematically, so choosing one is a value judgment about which kind of unfairness matters most in a particular use case.
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Take a loan model and two groups, A and B, of 100 applicants each. In A, 50 would repay; in B, 20 would. The model approves 40 in A (35 who would repay, 5 who would not) and 20 in B (14 who would repay, 6 who would not). Demographic parity compares selection rates: 40% versus 20%. The ratio of 0.5 falls below the four-fifths (0.8) threshold from US employment guidelines, so it fails. Equal opportunity compares true positive rates (TPR), the share of qualified people approved: 35/50 = 0.70 and 14/20 = 0.70. It is satisfied. Equalized odds (Hardt, Price and Srebro, 2016) also requires equal false positive rates (FPR): 5/50 = 0.10 versus 6/80 = 0.075. Close, but not equal. Predictive parity compares precision, or positive predictive value (PPV): 35/40 = 0.875 versus 14/20 = 0.70. It fails. When base rates differ, as here, an imperfect classifier generally cannot satisfy several definitions at once. Chouldechova (2017) and Kleinberg, Mullainathan and Raghavan (2016) proved versions of this: with unequal base rates, predictive parity or calibration cannot hold alongside equal false positive and false negative rates, except in degenerate cases such as perfect prediction. The COMPAS debate was exactly this conflict. Choosing a metric depends on context. Demographic parity suits cases where the labels themselves may be biased or where the goal is equal access. Equal opportunity suits cases where missing a qualified person is the main harm. Equalized odds adds concern about false accusations. Predictive parity or calibration matters when decision-makers read a score as a probability. A common misconception is that removing the protected attribute makes a model fair. Correlated proxies such as zip code can carry the same information.
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The Future of AI Fairness Metrics: Demographic Parity to Equalized Odds
Group metrics are increasingly written into audits and regulation. New York City's law on automated employment decision tools, for example, requires bias audits that report impact ratios. Research continues on individual fairness, causal fairness, and fairness for generative models, where outputs are text rather than yes-or-no decisions and the standard metrics do not apply directly. The impossibility results are mathematical and will not go away. Future progress is more likely to come from better labels, better documentation of which trade-offs were chosen and why, and stakeholder input than from a single universal metric.
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A hiring screen advances 40% of one group's applicants and 20% of another's. The ratio of 0.5 falls below the four-fifths rule of thumb used in US employment discrimination analysis, which flags a demographic parity concern.
A medical screening model catches 70% of true cases in both groups. It satisfies equal opportunity, even though the groups' selection rates differ.
ProPublica's 2016 analysis of the COMPAS recidivism tool found Black defendants had higher false positive rates. The vendor responded that its scores had similar predictive value across groups. The dispute showed two fairness metrics in direct conflict.
A data scientist uses Fairlearn's MetricFrame to break accuracy, selection rate and false positive rate down by group. She then applies ThresholdOptimizer to set group-specific thresholds that satisfy equalized odds.
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What is AI Fairness Metrics: Demographic Parity to Equalized Odds?
Group fairness metrics measure whether a model's decisions or errors differ across demographic groups. Demographic parity compares selection rates, equal opportunity compares true positive rates, equalized odds compares both true and false positive rates, and predictive parity compares precision. These definitions matter because they can conflict mathematically, so choosing one is a value judgment about which kind of unfairness matters most in a particular use case.
In the guide's loan example, group A has a 40% selection rate and group B has a 20% selection rate. Which metric does this violate?
Demographic parity compares selection rates. A ratio of 0.5 fails it and falls below the four-fifths threshold.
Equal opportunity requires which quantity to be equal across groups?
Equal opportunity asks that qualified people are approved at the same rate, which is the true positive rate.
What does equalized odds add on top of equal opportunity?
Equalized odds requires both equal true positive rates and equal false positive rates across groups.
In the example, group B's false positive rate is 6 of 80. Why is the denominator 80?
FPR equals false positives divided by all actual negatives. Group B has 100 applicants and 20 would repay, which leaves 80 actual negatives.
What do the impossibility results from Chouldechova and Kleinberg et al. say?
With unequal base rates, these criteria conflict except in degenerate cases such as a perfect predictor. The COMPAS debate showed this conflict in practice.
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