Math in Justice and the Calculus of Truth
Thanks to Ptolemy's mismeasurement of the oceans, Columbus embarked on a trip to India that unexpectedly resulted in the discovery of America.1 So as long as there have been numbers, there have been miscalculations. Today, mathematical figuring, whether as evidence or analytics, plays a prominent role in cases relying on circumstantial proof and inferential reasoning. With progress in the revision of forensic science, it might be time also to renew acquaintance with the language of science.2
In criminal court, math can multiply mistakes and lead to injustice in several key ways: (1) the misuse of mathematics by prosecutors; (2) the failure of defense attorneys to recognize those errors; and (3) the courts' inability or unwillingness to correct them.3 Indeed, there is a body of case law and scholarship that has been addressing these issues for more than a generation.4
Math can supplement or establish proof of identification or likelihood of an occurrence. And it has raised concerns over the inflation of evidence, juror confusion, credibility assessment, shifting and lessening burdens of proof, and the fundamental quandary of distilling human nature to statistical probabilities.
Ever since Leonardo Fibonacci introduced Western society to Hindu-Arabic numerals, mathematics has become more accessible and widespread. And in the courtroom it is finding an important place in criminal prosecutions.5
Much of forensic identity matching science relies on statistics and probabilities. Thus, the improbability that two particular kinds of evidence would match has been introduced to create unique linkage between the accused and the crime scene or victim. But forensic conclusions are only as good as the data behind them.
There have been noteworthy cases where math of this kind had been introduced to bolster seemingly scientific proof of a match without any reliable data or foundation, e.g., hair follicles in United States v. Massey, 594 F. 2d 676 (8th Cir. 1979); eyewitness identification in People v. Collins, 68 Cal. 2d 319 (Sup. Ct. 1968) and Commonwealth v. Ferreira, 460 Mass. 781 (Mass. Sup. Jud. Ct. 2011); gun purchase in State v. Sneed, 414 P.2d 858 (N.M. Sup. Ct. 1966); soil samples in Miller v. State, 399 S.W. 2d 268 (Ark. Sup. Ct. 1966); and a typewritten note in People v. Risley, 214 N.Y. 75 (1915).
Even the suggestion that the nature of mathematical conclusions might inflate the credibility of evidence has led to reversal or at least criticism, e.g., conviction rates in Dorsey v. State, 350 A. 2d 665 (Md. Ct. App. 1976); likelihood of children fabricating testimony in State v. Hernandez, 531 N.W. 2d 348, 350 n.1 (Wis. Ct. App. 1995); overstating claims in closing argument in Meredith v. Com., 959 S.W. 2d 87 (Ky. Sup. Ct. 1997); and quantifying reasonable doubt in State v. Carlson, 267 N.W. 2d 170, 176 (Minn. Sup. Ct. 1978).
On the other hand, when there is some support in scientific studies or the evidence of guilt is otherwise overwhelming or the mathematics were not the linchpin of the case, the conviction has stood.6
Lastly, a new twist to forensic evidence is the potentiality of the CSI effect.7 Where the presence of the CSI influence is supportable, it can impact probability or relevance and might serve as a secondary explanation for the mis-assessment of mathematical proof.
The Human Equation
Before Harvard law professor and mathematician Laurence Tribe became a nationally known constitutional scholar, he clerked at the California Supreme Court when it was asked to decide People v. Collins, 68 Cal. 2d 319 (Sup. Ct. 1968).8
Collins and his wife had been convicted of robbery, stealing a woman's purse. The victim and other witnesses provided varying and unclear pictures of the culprits, certainly not enough to support a conviction in the state's view. So the prosecution called an expert.
A local college math professor testified about probabilities based on six factors including race, physical appearance, and the color of the getaway car—all of which were shards of evidence from eyewitnesses that did not add up. The prosecutor elicited fantastical odds all but eliminating the possibility that anyone other than the defendant and his wife had been responsible.