Calibration with Equality of Opportunity

Description

A post-processing fairness technique that adjusts model predictions to achieve equal true positive rates across protected groups whilst maintaining calibration within each group. The method addresses fairness by ensuring that qualified individuals from different demographic groups have equal chances of receiving positive predictions, whilst preserving the meaning of probability scores within each group. This technique attempts to balance the competing objectives of group fairness and accurate probability estimation.

Example Use Cases

Fairness

Adjusting a loan approval model to ensure that qualified applicants from different ethnic backgrounds have equal approval rates, whilst maintaining that a 70% predicted repayment probability means the same thing for each ethnic group in practice.

Transparency

Post-processing a university admissions algorithm to equalise acceptance rates for qualified students across gender groups, whilst ensuring the predicted success scores remain well-calibrated within each gender to support transparent decision-making.

Reliability

Calibrating a medical diagnosis model to maintain equal detection rates for a disease across different age groups whilst preserving the reliability of risk scores, ensuring that a 30% risk prediction accurately reflects actual disease occurrence within each age group.

Limitations

Fundamental mathematical incompatibility exists between perfect calibration and exact equality of opportunity, except in highly constrained special cases.
May reduce overall model accuracy or calibration when forcing equal true positive rates across groups with genuinely different base rates.
Requires access to sensitive attributes during post-processing, which may not be available or legally permissible in all contexts.
The technique only addresses one aspect of fairness (true positive rates) and may allow disparities in false positive rates between groups.
Post-processing approaches cannot address biases inherent in the training data or model architecture, only adjust final predictions.

Resources

On Fairness and Calibration

Research Paper•Geoff Pleiss et al.•Sep 6, 2017

Foundational paper demonstrating the mathematical tension between calibration and equalised odds fairness constraints.

equalized_odds_and_calibration

Software Package

Python implementation of post-processing methods for achieving calibration with equality of opportunity constraints.

Equality of Opportunity in Supervised Learning

Research Paper•Moritz Hardt, Eric Price, and Nathan Srebro•Oct 7, 2016

Original paper introducing the equality of opportunity fairness criterion and post-processing algorithms.

Fairlearn: Postprocessing Methods

Documentation

Documentation for implementing threshold optimisation and calibration methods to achieve fairness constraints.

Related Techniques

Name	Description	Assurance Goals
Prototype and Criticism Models	Prototype and Criticism Models provide data understanding by identifying two complementary sets of examples: prototypes represent the most typical instances that best summarise common patterns in the data, whilst criticisms are outliers or edge cases that are poorly represented by the prototypes. For example, in a dataset of customer transactions, prototypes might be the most representative buying patterns (frequent small purchases, occasional large purchases), whilst criticisms could be unusual behaviors (bulk buyers, one-time high-value customers). This dual approach reveals both what is normal and what is exceptional, helping understand data coverage and model blind spots.	Explainability Fairness
Sobol Indices	Sobol Indices quantify how much each input feature contributes to the total variance in a model's predictions through global sensitivity analysis. The technique calculates first-order indices (individual feature contributions) and total-order indices (including all interaction effects involving that feature). By systematically sampling the input space and decomposing output variance, Sobol Indices reveal which features drive model uncertainty and which interactions between features are most important for predictions.	Explainability Fairness
Demographic Parity Assessment	Demographic Parity Assessment evaluates whether a model produces equal positive prediction rates across different demographic groups, regardless of underlying differences in qualifications or base rates. It quantifies fairness using metrics like Statistical Parity Difference (the absolute difference in positive outcome rates between groups) or Disparate Impact ratio (the ratio of positive rates). Unlike techniques that modify data or models, this is purely a measurement approach that highlights when protected groups receive favourable outcomes at different rates, helping organisations identify and document potential discrimination.	Fairness
Model Cards	Model cards are standardised documentation frameworks that systematically document machine learning models through structured templates. The templates cover intended use cases, performance metrics across different demographic groups and operating conditions, training data characteristics, evaluation procedures, limitations, and ethical considerations. They serve as comprehensive technical specifications that enable informed model selection, prevent inappropriate deployment, support regulatory compliance, and facilitate fair assessment by providing transparent reporting of model capabilities and constraints across diverse populations and scenarios.	Transparency Fairness Safety
Deep Ensembles	Deep ensembles combine predictions from multiple neural networks trained independently with different random initializations to capture epistemic uncertainty (model uncertainty). By training several models on the same data with different starting points, the ensemble reveals how much the model's predictions depend on training randomness. The disagreement between ensemble members naturally indicates prediction uncertainty - when models agree, confidence is high; when they disagree, uncertainty is revealed. This approach provides more reliable uncertainty estimates, better out-of-distribution detection, and improved calibration compared to single models.	Reliability Transparency Safety
SHapley Additive exPlanations	SHAP explains model predictions by quantifying how much each input feature contributes to the outcome. It assigns an importance score to every feature, indicating whether it pushes the prediction towards or away from the average. The method systematically evaluates how predictions change as features are included or excluded, drawing on game theory concepts to ensure a fair distribution of contributions.	Explainability Fairness Reliability