The Probabilistic Foundations of Surveillance Failure: From False Alerts to Structural Bias

Forensic statisticians have long debated whether searching large DNA databases undermines the evidential value of matches. Modern surveillance faces an exponentially harder problem: screening populations across thousands of attributes using threshold rules. Intuition suggests that requiring many coincidental matches should make false alerts astronomically unlikely. This intuition fails. Consider a system monitoring 1000 attributes, each with a 0.5 percent innocent match rate. Matching 15 pre-specified attributes has probability ${10}^{-35}$, 1 in 30 decillion, effectively impossible. But operational systems may flag anyone matching any 15 of the 1000. In a city of one million innocents, this produces about 226 false alerts. A seemingly impossible event becomes guaranteed. This is a mathematical consequence of high-dimensional screening, not implementation failure. We identify fundamental probabilistic limits on screening reliability. Systems undergo sharp transitions from reliable to unreliable with small data scale increases, a fragility worsened by data growth and correlations. As data accumulate and correlation collapses effective dimensionality, systems enter regimes where alerts lose evidential value even when individual coincidences remain vanishingly rare. This framework reframes the DNA database controversy as a regime shift. Unequal surveillance exposures magnify failure, making “structural bias’’ mathematically inevitable. Beyond a critical scale, failure cannot be prevented through threshold adjustment or algorithmic refinement.