Algorithmic Fairness: Not a Purely Technical but Socio-Technical Property

The rapid trend of deploying artificial intelligence (AI) and machine learning (ML) systems in socially consequential domains has raised growing concerns about their trustworthiness, including potential discriminatory behaviours. Research in algorithmic fairness has generated a proliferation of mathematical definitions and metrics, yet persistent misconceptions and limitations -- both within and beyond the fairness community -- limit their effectiveness, such as an unreached consensus on its understanding, prevailing measures primarily tailored to binary group settings, and superficial handling for intersectional contexts. Here we critically remark on these misconceptions and argue that fairness cannot be reduced to purely technical constraints on models; we also examine the limitations of existing fairness measures through conceptual analysis and empirical illustrations, showing their limited applicability in the face of complex real-world scenarios, challenging prevailing views on the incompatibility between accuracy and fairness as well as that among fairness measures themselves, and outlining three worth-considering principles in the design of fairness measures. We believe these findings will help bridge the gap between technical formalisation and social realities and meet the challenges of real-world AI/ML deployment.