A scaling law to model the effectiveness of identification techniques

AI techniques are increasingly being used to identify individuals both offline and online. However, quantifying their effectiveness at scale and, by extension, the risks they pose remains a significant challenge. Here, we propose a two-parameter Bayesian model for exact matching techniques and derive an analytical expression for correctness (κ), the fraction of people accurately identified in a population. We then generalize the model to forecast how κ scales from small-scale experiments to the real world, for exact, sparse, and machine learning-based robust identification techniques. Despite having only two degrees of freedom, our method closely fits 476 correctness curves and strongly outperforms curve-fitting methods and entropy-based rules of thumb. Our work provides a principled framework for forecasting the privacy risks posed by identification techniques, while also supporting independent accountability efforts for AI-based biometric systems.