Algorithmic Loan-Approval Bias: Proxy Discrimination Lab

Historical Data Bias

Group B credit-record suppression 0.20

Classifier

Approval threshold P(qualified) ≥ 0.50

Outcomes

Group A approval

–

Group B approval

–

Group A false-reject

–

Group B false-reject

–

Demographic parity gap –
Overall accuracy vs. true qualification: –

How it works

Each of 200 synthetic applicants gets an income and a true creditworthiness drawn independently of group membership; their true label is qualified = (0.5·income + 0.5·trueCredit) > 0.5. But the recorded credit score fed to the model is suppressed for Group B by the slider amount — a stand-in for historically biased credit reporting, redlining, or under-sampled records.

A real logistic-regression classifier is trained in your browser by gradient descent on (income, recordedCredit) → qualified:

z = w0 + w1·income + w2·recordedCredit
p = 1 / (1 + e^-z)          (sigmoid)
loss = -mean[ y·ln(p) + (1-y)·ln(1-p) ]
w -= lr · ∂loss/∂w   (300 epochs)

Because recordedCredit is a group-correlated proxy, the model learns to penalize Group B even though group membership is never given to it directly — this is proxy discrimination, one of the main real-world mechanisms behind biased lending, hiring and risk-scoring algorithms.

The tilted plane is the decision boundary w0 + w1·income + w2·recordedCredit = logit(threshold). With a single shared threshold, raising the bias slider widens the gap between the two groups' approval rates and false-rejection rates even though both groups are equally qualified on average.

Fairness fix replaces the single global threshold with two group-specific thresholds, each chosen so both groups reach the same approval rate (demographic parity) — the classic post-processing fix, and its cost (accuracy vs. true qualification can drop) is shown live.

Group A applicant Group B applicant Approved Denied (dim)

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