🧪 Fairness–Accuracy Trade-off

The data model

Every individual has a latent "true merit" m ~ N(0,1), drawn from the same distribution for both groups — underneath, group A and group B are equally qualified. The true label is Y = 1 if m + ε_y > 0 (outcome noise ε_y ~ N(0,0.6)).

The classifier never sees m directly — it sees a score S = m − bias·[group=B] + ε_s, with ε_s ~ N(0,0.5). The bias slider is the historical bias: it shifts group B's recorded scores down even though their true merit distribution is identical to A's — a simplified model of biased training data.

The metrics

Decision D = 1 if S > threshold_group

• Accuracy = (TP+TN) / N, over both groups combined.
• Demographic parity gap = |P(D=1 | A) − P(D=1 | B)| — the difference in approval rate between groups, ignoring whether the decision was correct.
• TPR (recall) = TP/(TP+FN); FPR = FP/(FP+TN), computed separately per group.
• Equalized odds gap = average of |TPR_A−TPR_B| and |FPR_A−FPR_B| — zero only when both groups get the same error rates, not just the same approval rate.

Why they fight each other

Because group B's scores are shifted down by bias, a shared threshold approves fewer of them — a demographic parity violation. Lowering B's threshold to restore equal approval rates raises B's FPR (more unqualified people approved) while barely moving A's — an equalized odds violation. With one threshold per group you generally cannot close both gaps to zero at once except in the degenerate case where bias = 0; the "auto-equalize" buttons solve for the closest achievable setting given the current bias, so you can see the residual gap that remains.

Reading the scene

• Left: two point clouds, one row per group, points shaped into their score distribution. Green = truly qualified, red = truly not — the classifier can't see this color, only the score.
• The vertical wall in each row is that group's decision threshold; everything past it (toward +score) is approved.
• Right: two 3D ROC curves (FPR on one axis, TPR on the other), one per group, each with a marker at the current threshold's operating point. Pulling a threshold slides its marker along its own curve.

Controls

• Drag the cyan / magenta knob above a cloud (or use the matching slider) to move that group's threshold.
• Historical bias slider controls how far group B's true score distribution is shifted down.
• Auto-equalize demographic parity moves B's threshold to the score quantile that makes both approval rates equal.
• Auto-equalize equalized odds searches B's threshold for the value that minimizes the combined TPR/FPR gap — usually not zero, which is the point.
• 🎲 Resample draws a fresh population from the same distributions; ↺ Reset also restores bias and thresholds to their defaults.