Laurence Tribe: Maths on Trial (3)

Tribe’s reaction to probability at trial

The other main theme of Laurence Tribe’s article “Trial by Mathematics: Precision and Ritual in the Legal Process” (84 Harvard Law Review 1338 1970-71) is, to use his own words, “cases in which mathematical methods are turned to the task of deciding what occurred on a particular, unique occasion, as opposed to cases in which the very task defined by the applicable law is that of measuring the statistical characteristics or likely effects of some process or the statistical features of some population of people or events”.

This part of the article is divided into four main sections:

Firstly, a description of the kind of use of mathematics at trial that he is specifically going to discuss, with examples;

Secondly, a review of the traditional arguments that judges have used against mathematics at trial, together with Tribe’s reaction to these arguments;

Thirdly, a sketch of the introduction of Bayes’ theorem at trial as introduced by Finkelstein and Fairley;

Fourthly, the very heart of the article: an emotional and deeply human explanation of his final decision to recommend the avoidance of mathematical methods altogether in the area of criminal law.

Tribe’s opinions held such sway in the world of legal thinking that it has been said by those who strongly favour the properly thought out and properly controlled use of mathematics at trial that Tribe alone held back the development of that area of research for a good 30 years. If this is the case, then it seems worth exploring Tribe’s objections in some detail before going on to what we believe the future holds in the way of probability at trial.

Today’s post will summarize the first part of Tribe’s article: a description of the kind of

mathematics at trial that he is aiming to discuss.

Tribe divides the use of mathematics in deciding what occurred on a particular occasion into three distinct possibilities:

(1) determining whether an event did or did not occur,

(2) determining the identity of the individual responsible for certain acts,

(3) determining the intention behind certain acts.

For each type, he gives a few examples of the kind of problem that may arise. For (1), one example is that of a man who is accused of leaving his car at a parking place for over one hour in defiance of the rules. The witness is the officer who testified that twice, at times separated by over an hour, he observed that car in that particular place, and that he noted the precise position of the front and back tires. The car owner’s defense is that he drove away during the hour and then came back later, and his wheel positions happened to be the same as they were the first time by chance. The probability of this happening is between about 1/12 and 1/144. But what role should this probability play in judging the car owner’s innocence or guilt?

A second example is that of a barrel falling out of someone’s window onto another person’s head: the question is whether some negligent act was the cause of the fall. Supposing that it is statistically known that over 60% of such incidents are caused by a negligent act, should this fact be allowed in court?

For (2), he gives the example of a plaintiff negligently run over by a blue bus, who accuses defendant of negligence on the grounds that defendant is a bus operator who operates 4/5 of the blue buses in town. How important should that figure be in judging whether the blue bus in question did or did not belong to plaintiff?

Another example is that of a man found shot to death in his mistress’ apartment, the question being whether she shot him. There is evidence to prove that in 95% of all known cases in which a man is killed in his mistress’ apartment, the mistress is the killer. Is this evidence of sufficient relevance to be introduced in trial? Does it have any role to play?

Finally, for (3), Tribe gives the example of a recently insured building burning down, with the owner insisting that the fire was an accident. If it is statistically known that less than one fire in 20 that occurs shortly after an insurance purchase occurs purely by chance, what role should such a statistic play in the investigation?

Tribe points out that courts faced with the emergence of this kind of evidence during trials have tended to deal with it in an entirely ad hoc manner, sometimes supporting the mathematical proof proffered by a lawyer, more frequently judging it to be improper. But, he points out, “as the number and variety of cases continues to mount, the difficulty of dealing intelligently with them in the absence of any coherent theory is becoming increasingly apparent.”

He is obviously right, even if the “coherent theory” that he develops in the rest of the article, which we’ll cover in the next posts, is far from satisfying everybody!