DNA, Blue Bus, and phase changes

• Published in: The international journal of evidence & proof Vol. 20; no. 2; pp. 112 - 120
• Main Authors: Cheng, Edward K., Nunn, G. Alexander
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.04.2016
• Subjects: probabilistic evidence; evidence; Bayesian statistics; proof paradoxes; DNA; Blue Bus problem
• ISSN: 1365-7127; 1740-5572
• DOI: 10.1177/1365712715623556

In ‘Exploring the Proof Paradoxes’, Mike Redmayne comprehensively surveyed the puzzles at the intersection of law and statistics, the most famous of which is the Blue Bus problem, which prohibits legal actors from ascribing liability purely on the basis of probabilistic evidence. DNA evidence, however, is a longstanding exception to Blue Bus. Like Blue Bus, DNA presents probabilistic evidence of identity. Unlike Blue Bus, DNA is widely accepted as legitimate, even when it stands alone as so-called ‘naked’ statistical evidence. Observers often explain such DNA exceptionalism in two ways: either that people break down in extreme cases, or relatedly, that modern DNA testing generates effectively unique (as opposed to probabilistic) identifications. While both explanations are understandable, they are unsatisfying in certain ways. Breakdown theory seems unprincipled and falls victim to slippery slopes. Uniqueness theory rests on a fiction and fails to delineate a threshold for when probabilities are sufficiently small to be considered ‘unique’. In this paper inspired by our reading of Professor Redmayne’s piece, we propose a quantitative explanation for DNA exceptionalism. Specifically, we argue that as random match probabilities become smaller, the probability of error (i.e. mistaken identification) sharply transitions from high to low. This sharp change in probability, which we label a ‘phase change’, explains why legal actors can treat DNA as non-probabilistic evidence. The phase change further avoids slippery slope problems and helps define when one can legitimately treat DNA—or any similarly qualified forensic identification method for that matter—as a form of direct evidence.