Formalising Anti-Discrimination Law in Automated Decision Systems

Algorithmic discrimination is a critical concern as machine learning models are used in high-stakes decision-making in legally protected contexts. Although substantial research on algorithmic bias and discrimination has led to the development of fairness metrics, several critical legal issues remain unaddressed in practice. To address these gaps, we introduce a novel decision-theoretic framework grounded in anti-discrimination law of the United Kingdom, which has global influence and aligns more closely with European and Commonwealth legal systems. We propose the 'conditional estimation parity' metric, which accounts for estimation error and the underlying data-generating process, aligning with legal standards. Through a real-world example based on an algorithmic credit discrimination case, we demonstrate the practical application of our formalism and provide insights for aligning fairness metrics with legal principles. Our approach bridges the divide between machine learning fairness metrics and anti-discrimination law, offering a legally grounded framework for developing non-discriminatory automated decision systems.