Fairness: three families

Fairness is not one measurement. It splits into three families, and the central fact about them is that they cannot all hold at once.

Family	Question	Check
Independence	Do selection rates match across groups?	disparate_impact
Separation	Do error rates match across groups?	equalised_odds
Sufficiency	Does a given score mean the same thing for every group?	subgroup_calibration

Before 0.5.0 this library measured only independence. That was not a neutral position — demographic parity ignores y_true entirely, so a model can achieve perfect parity by being wrong in compensating directions, and a reader seeing one green check had no way to know two other notions were never tested.

Independence — disparate_impact

Demographic parity: the share of each group predicted positive. It needs hard class labels, so continuous predictions are binarised at FairnessConfig.decision_threshold. For multiclass, "positive" means landing in context.favourable_classes.

Its weakness is that it never looks at the ground truth. A model that approves 50% of every group satisfies it perfectly, whether or not those are the right 50%.

Separation — equalised_odds

Conditions on the ground truth, which is what independence lacks. Two results per attribute:

• Equal opportunity — the true-positive-rate difference. Among applicants who should be approved, is every group equally likely to be? This is the notion lending regulators most often centre on.
• Equalised odds — the larger of the TPR and FPR differences. Stricter, and the one that matters when a false positive is costly too.

A model can satisfy the first and fail the second: equal opportunity ignores false positives entirely.

Sufficiency — subgroup_calibration

Does a score of 0.7 carry the same real risk for every group? A model can be well calibrated overall and badly miscalibrated for a minority, because the majority dominates the average and hides it.

This is a fairness failure, not merely a performance one — it means the same stated risk means something different depending on who the applicant is.

The regression analogue is calibration_parity, which compares mean residuals rather than binned frequencies.

The impossibility

You cannot satisfy all three

Calibration, TPR balance and FPR balance are mathematically incompatible whenever the base rate differs between groups, except in degenerate cases (Kleinberg–Mullainathan–Raghavan 2016; Chouldechova 2017).

This is not a limitation of the tool. It is a property of the problem, and it means choosing a fairness notion is a policy decision, not a technical one.

The gate's job is to stop that choice being made silently. It reports all three and names the trade-off; which one you gate on belongs to whoever signs the model off.

Notebook 01 demonstrates it rather than asserting it: rescaling each group's scores to equalise selection rates moves the parity gap from 0.365 to 0.010 while the calibration gap goes from 0.067 to 0.131. Independence bought, sufficiency spent.

A tool that reported only demographic parity would let you "fix" a model by making its scores mean different things for different people, and call that progress.

Intersections

Every check above treats each protected attribute independently. Harm concentrates where attributes meet, and marginal checks are blind to it by construction — a model can look acceptable on gender and on region while failing badly for women in one region.

config.fairness.intersectional = True

Turns on pairwise combinations, reported as gender × region. Off by default because joint groups are smaller and the reading needs more care; an intersection without two groups of at least min_group_size is skipped with a log line rather than scored.

Only pairs are generated. Three-way intersections fragment a validation set faster than any realistic min_group_size tolerates, and a disparity computed over four rows is worse than none.

Overall calibration — calibration

Distinct from fairness: do the stated probabilities match reality at all?

Discrimination and calibration are independent properties. A model can rank perfectly — AUC 1.0 — while every probability it emits is twice too high, which scores beautifully and misprices every policy.

Reported as Expected Calibration Error plus Murphy's decomposition:

Term	Meaning	Direction
reliability	distance from observed frequency	lower better — recalibration fixes this
resolution	how much predictions vary from the base rate	higher better
uncertainty	the base rate's own variance	a floor; a property of the problem

resolution is the one people forget. A model predicting the base rate for everyone is perfectly calibrated and completely useless — and neither ECE nor the Brier score says so alone.

This check is blocking, since it sits in the performance category, but max_ece defaults to a permissive 0.10. Plenty of good models are uncalibrated by construction, and a gate that blocks all of them gets switched off. Tighten it for pricing.

Skewed scores

Fraud and default scores cluster near zero, which leaves uniform bins nearly empty where it matters. Set config.performance.calibration_strategy = "quantile" for equal-count bins instead.