Fair by Which Measure? The Mathematics of Fairness Trade-Offs in Rural–Urban Credit Scoring in India

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Machine-learning systems can support decisions that affect access to financial services, making the mathematical meaning of fairness an important research question. This paper studies three competing fairness criteria—Statistical Parity, Equalized Odds and Predictive Parity—using a Rural–Urban subset of the Dream Housing Finance loan-approval dataset. The analysis uses 381 observations: 179 Rural and 202 Urban. The observed positive-outcome rates are 61.45% and 65.84%, respectively, a difference of 4.39 percentage points. A logistic regression model is fitted to ten applicant-level features, with Property_Area retained as a grouping variable rather than a predictor. Using the supplied author-run Python/scikit-learn implementation, the baseline model at a common threshold of 0.50 achieves 77.95% accuracy. Group-specific threshold searches then maximize accuracy subject to fairness tolerances of 0.02 for Statistical Parity, 0.05 for Equalized Odds and 0.02 for Predictive Parity. The resulting accuracies are 78.22%, 77.43% and 77.69%, respectively. Statistical Parity reduces the positive-rate gap to 0.0069; Equalized Odds reduces the combined TPR/FPR gap to 0.0435; and Predictive Parity reduces the PPV gap to 0.0200. The results demonstrate that satisfying one fairness criterion can leave another gap unchanged or increase it. The paper therefore does not claim that one metric is universally fairer. Instead, it argues that fairness is a modelling choice: researchers must specify which equality is relevant, quantify the resulting trade-offs, and test whether the target variable represents the real-world outcome of interest. Because Loan_Status records historical approval rather than verified repayment, the experiment should be interpreted as a study of fairness in predicting a historical decision label, not as evidence that Rural or Urban applicants are inherently more or less creditworthy.