DNA, Blue Bus, and phase changes

Abstract

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.

When statistical evidence is not specific enough

“…But a worry may linger here. Although they are highly discriminating across individu-25 Among forensic scientists and legal scholars, see NRC (1996); Balding & Donnely (1996); Stein (2005); Allen & Pardo (2007); Roth (2010); Cheng & Nunn (2016). Among philosophers, see De Macedo (2008); Enoch et al (2012); Pritchard (2015); Smith (2018); Mayo (2018).…”

Legal proof and statistical conjunctions

“…A final theory, which I call 'phase change' theory after a paper due to Cheng and Nunn (2016), argues that statistical evidence involving very high probabilities is different in kind from the much shorter odds found in the unadorned Prisoners, Gatecrasher, and Blue Bus cases.…”

Justice in Epistemic Gaps: The 'Proof Paradox' Revisited

“…There is also a legal literature which attempts to vindicate the aversion to bare statistics by offering new ways to understand the standard of proof (e.g Cheng 2013Sullivan 2019)…”

“…See Egglestone (1980) for an early rejection of the puzzle Hedden and Colyvan (2019). defend a probabilistic conception of the standard of proof against the idea that bare statistics are particularly paradoxical; Ross (2021a) argues against the supposed parallel between individualistic and legal epistemology; Krauss (2020) offers a legally-informed rebuttal of recent criticism of bare statistics.5 For example, seeCheng and Nunn (2016),Enoch and Fisher (2019), Di Bello (2019).6 SeeRoss (2021b) for an alternative criticism of this orthodoxy, appealing to cases involving conjunctions of different types of statistical evidence.…”