On the relation between accuracy and fairness in binary classification

Our study revisits the problem of accuracy-fairness tradeoff in binary classification. We argue that comparison of non-discriminatory classifiers needs to account for different rates of positive predictions, otherwise conclusions about performance may be misleading, because accuracy and discrimination of naive baselines on the same dataset vary with different rates of positive predictions. We provide methodological recommendations for sound comparison of non-discriminatory classifiers, and present a brief theoretical and empirical analysis of tradeoffs between accuracy and non-discrimination.

💡 Research Summary

The paper revisits the widely discussed accuracy‑fairness trade‑off in binary classification and shows that many conclusions drawn in the literature are confounded by differences in the positive prediction rate (acceptance rate, π). The authors argue that comparing non‑discriminatory classifiers without controlling for π can be misleading because both raw accuracy and raw discrimination depend on π. To address this, they propose two normalized performance measures. Accuracy is measured by Cohen’s Kappa (κ = (A − R)/(1 − R)), where R is the expected accuracy of a random classifier that predicts positives with probability π. Discrimination is measured by δ = d/d_max, where d is the difference in positive rates between the favored and protected groups and d_max = min{π/α, (1 − π)/(1 − α)} is the maximum possible discrimination at the given acceptance rate (α is the proportion of the favored group). κ ranges from 0 (random) to 1 (perfect), while δ ranges from –1 (full reverse discrimination) through 0 (no discrimination) to 1 (worst possible discrimination).

The authors conduct experiments on the UCI Adult dataset using logistic regression, Naïve Bayes, and a J48 decision tree. By varying the classification threshold they generate classifiers with a wide range of π values. The raw accuracy and raw discrimination curves change dramatically with π, but the κ‑δ plots remain stable, demonstrating that κ and δ capture the intrinsic trade‑off independent of acceptance rate. They also evaluate a “massaging” pre‑processing technique that flips a small number of labels to achieve zero discrimination in the training data. While massaging reduces nominal discrimination, the normalized δ shows that discrimination can remain high at many π values, and sometimes reverse discrimination appears.

Theoretical analysis introduces two baselines: an “oracle” that knows the true labels and a random classifier. When π is fixed, the relationship between κ and δ is linear: κ₀ − κ = min{απ₀, 1 − α 1 − π₀}(δ₀ − δ). If π can be adjusted, the optimal strategy to eliminate discrimination is either to lower the acceptance rate for the favored group or to raise it for the protected group, depending on α, the original acceptance rate π₀, and the target δ*. The authors provide simulated results confirming that the upper bound on accuracy declines linearly with the reduction in normalized discrimination.

In conclusion, the paper recommends that researchers compare non‑discriminatory classifiers using κ and δ when acceptance rates differ, or restrict comparisons to classifiers with identical π if raw accuracy and raw discrimination are used. This normalization prevents misleading claims about fairness improvements and clarifies the true cost of achieving non‑discrimination under realistic resource constraints.