We are lawyers because we were not the strongest at science or math, or so the popular trope goes. But numbers pervade the courtroom – employment discrimination statistics, medical causation analysis, DNA probabilities, and occasionally the likelihood that a particular person committed the crime or that the act was criminal rather than accidental. So it is incumbent on lawyers to learn math (or know when to ask a mathematician or statistician). And as the below book makes clear, especially when life or liberty are on the line.
This becomes apparent when one reads MATH ON TRIAL (Basic Books, 2013) by European mathematicians Leila Schneps and Coralie Comez. Using ten cases (most criminal, but one of alleged gender discrimination at a University) in which mathematics and statistics played a role, the authors detail ten math errors – errors such as “the incredible coincidence,” “underestimation,” and “choosing the wrong model.” Included is the classic Collins case, where a prosecutor made up likelihoods for certain occurrences and then had an expert multiple the self-created probabilities to an astonishingly high likelihood of guilt.
Here is what the California Supreme Court explained:
Although the prosecutor insisted that the factors he used were only for illustrative purposes — to demonstrate how the probability of the occurrence of mutually independent factors affected the probability that they would occur together — he nevertheless attempted to use factors which he personally related to the distinctive characteristics of defendants. In his argument to the jury he invited the jurors to apply their own factors, and asked defense counsel to suggest what the latter would deem as reasonable. The prosecutor himself proposed the individual probabilities set out in the table below. Although the transcript of the examination of the mathematics instructor and the information volunteered by the prosecutor at that time create some uncertainty as to precisely which of the characteristics the prosecutor assigned to the individual probabilities, he restated in his argument to the jury that they should be as follows:
|A.||Partly yellow automobile||1/10|
|B.||Man with mustache||1/4|
|C.||Girl with ponytail||1/10|
|D.||Girl with blond hair||1/3|
|E.||Negro man with beard||1/10|
|F.||Interracial couple in car||1/1000|
People v. Collins, 68 Cal. 2d 319, 325, 438 P.2d 33, 37, 66 Cal. Rptr. 497, 501, 1968 Cal. LEXIS 167, *12, 36 A.L.R.3d 1176.
Beyond demonstrating the principle fallacies – that the original numbers were made up from whole cloth and there was no proof that the factors were independent of each other, without which it is improper to multiply the probabilities – the authors add a special insight to the story. Clerking for the California Supreme Court at the time was now-Professor Laurence Tribe, who had majored in mathematics. Catching the error took a numbers person.
While most of the ten cases are ones where errors caused wrongful convictions and sentences, some involve defense miscalculations or a court’s error that inured to a defendant’s benefit. For that point, the authors take on the Italian court decision in the Amanda Knox case, questioning whether the dismissal was scientifically sound.
Perhaps the most compelling story is that of Lucia De Berk, a nurse convicted of murdering infant patients in a hospital in the Hague. This was a case where mere coincidence – a number of deaths occurring on shifts where De Bek worked – was transformed into causation, here with an apparent expert in mathematics offering probabilistic calculations. What the authors show is that the state’s expert was not an advanced statistician and that fundamental errors in classifying deaths as ‘suspicious’ led to the erroneous conclusion of astronomical odds of guilt – one in 342 million. It was only in post-conviction proceedings, where more solid science and mathematics showed flawed assumption on top of flawed assumption, that De Berk was freed.
Why read this? MATH ON TRIAL raises profound questions about whether and when probabilistic analysis – valued in DNA cases, suspect in guilt-beyond-a-reasonable-doubt assessments – belongs in the courtroom (or even as an investigative tool). Why else? Because the book is a compelling read, retelling the ten cases with a flair that matches the best of legal fiction.
And one more reason? Because lawyers have to know science, and math, and the limits of each; and when to consult an expert; and who is the sufficiently knowledgeable expert.