A mathematical wall prevents algorithms from ever accurately predicting rare violent crimes in the legal system.
Pretrial risk tools fail to predict rare violence because of a fundamental structural limit in statistics. Legal experts often assume that better data or less biased algorithms will eventually fix the errors in these high-stakes tools. The math shows that predicting an event that rarely happens is impossible regardless of how much data a computer processes. This wall remains even after recalibrating the most advanced systems available today. Judges and policymakers cannot rely on technology to eliminate the uncertainty of human behavior in rare cases.
The Likelihood Ratio Wall: Structural Limits on Accurate Risk Assessment for Rare Violence
arXiv · 2604.27282
Pretrial risk assessment tools are used on over one million U.S. defendants each year, yet their use for predicting rare violent re-offense faces a basic statistical barrier. We derive a universal precision bound -- the Likelihood Ratio Wall -- showing that when violent re-arrest rates are low (2-5%), achieving even a 50% hit rate among people labeled "high risk" (positive predictive value, or PPV) would require tools far more discriminative than current instruments appear to be. For rare outcom