Math on Trial: How Numbers Get Used and Abused in the Courtroom — New Book Review

Math on Trial/Leila Schneps and Coralie Colmez, Basic Books 2013
K 2290 .S73 S36 2013

…Or Prosecution by Ponytail

Ignore math and statistics at you and your client’s peril! Math On Trial is a study of mostly criminal cases where flaws in mathematical, statistical and probability calculations and their analyses led judges and juries to incorrect findings of guilt or innocence. The book is an enjoyable read and you don’t need to be a math whiz to do so. I will not attempt to explain the math problems solutions as the authors do so very thoroughly and understandably in the book. The authors connect ten “math errors” including the “birthday problem”, “Simpson’s paradox” and others to ten specific trials.
The notorious Amanda Knox case involved the “double experiment” problem. Amanda Knox is an American who was studying in the Italian town of Perugia and living with roommates including British student Meredith Kercher. However, she spent most of her time at the apartment of a shy Italian student she called her “lover”, Raffaele Sollecito. When Meredith was viciously abused and murdered, the two went from witnesses to suspects and were eventually convicted of the murder. After a massive publicity campaign by Amanda’s family, the appeal judge overturned the conviction. At the heart of the controversy was a knife found in Raffaele’s kitchen with Meredith’s blood on it. Meredith had never been to Raffaele’s apartment. On appeal, her attorneys questioned the validity of the DNA testing. The appeal judge accepted their faulty reasoning. He also refused the prosecution request for a second test to confirm the DNA matching believing in error that a second test would add no new evidence nor confirm the first test. He fell victim to the “double experiment “problem. Amanda and Raffaele remain free although at the time of the book’s publication there was some chance they might be retried in Italy.
The “evidence” against blonde haired Janet Collins included her “ponytail”, a hairstyle fairly common in 1964. Not so common was her interracial marriage to a black man. The case illustrates “unjustified estimates” of the occurrence of separate probabilities. For example, factoring in a hairstyle as a probability is absurd since a hairstyle may be altered instantaneously and at will. And yet that is what the prosecution did along with using numerous other dubious probabilities. Despite her fairly solid alibi and the prosecution’s shaky evidence, both Janet and her husband were, the authors say, convicted by math not evidence. Indeed, the prosecutor extolled this new type of mathematical proof declaring that it would soon replace the “hackneyed, stereotyped, trite, [and] misunderstood” concept of proof beyond a reasonable doubt. The husband decided to appeal and had the great good fortune of having a judge whose law clerk was Laurence Tribe. Tribe, who had excelled as a math major at Harvard before receiving his law degree wrote a memo to the judge systematically destroying the analysis of the prosecution’s expert witness. The judgment was reversed and Malcolm Collins free to join his wife who by then had finished her sentence. The authors point out that Tribe’s unsigned memo appears below the opinion at People v. Collins, 68 Cal.2d 319 available at: (
Tribe later wrote a very famous and influential article “Trial by Mathematics: Precision and Ritual in the Legal Process” . He concluded that mathematics cannot replace the intuitive approach that must be taken by juries in evaluating evidence, that the two approaches cannot properly be combined and that the dangers of the misapplication, misunderstanding and the psychological threat (of the accepted superiority of math) to the jury found in the kinds of cases he saw throughout his career and studied in this later book are too profound to be allowed in the courtroom. His influence held sway for many years but recently with the increase of DNA evidence, there has been increasing use of probability theory in other situations as well.

Concern with the potential miscarriage of justice in criminal trials using probability theories, an international consortium of leading mathematicians and statisticians involved in criminal trials as experts and so forth has begun work on a research project to create a standardized set of criteria and analytics tools to ensure that probability studies at trial be “used correctly, [and] applied only to situations in which it can give a meaningful result…”

Other cases analyzed include the Berkeley sex bias case (illustrating Simpson’s Paradox), the case of Charles Ponzi (underestimation) and the Dreyfus Affair (Mathematical Madness).

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