Laurence Tribe: Maths on Trial (2)

Tribe’s reaction to the Kaplan-Cullison model

Tribe’s most important article on the subject of maths on trial is divided into two parts. One of them discusses the use of Bayes’ theorem at trial, and the other discusses the merits and lack thereof of the Kaplan-Cullison model for jury decisions, that we explained in an earlier post.

Today we’ll look at Tribe’s reaction to the Kaplan-Cullison model. (Reference: pp. 1381-1389 of Trial by Mathematics, Harv. L. Rev. 1970-1971).

In the first sentence of this part of his article, Tribe puts his finger on the obvious problem in the Kaplan-Cullison: assigning numerical answers to such vague questions as “How much would you regret the erroneous conviction of this defendant for armed robbery?” Indeed, as he points out, the answer to this question can depend largely on the consequences of such a conviction; consequences to the defendant’s children, for example, if he is a single father, yet these consequences may have absolutely nothing to do with judging the case at hand, and therefore the “quantity of regret” (if quantifiable, already doubtful) may not be relevant in coming to a decision. For these reasons, Tribe says, “any equation designed to compute the threshold probability above which conviction would be preferable to acquittal would have to be far more complex than Kaplan and Cullison have supposed”.

Indeed, Tribe points out that the Kaplan-Cullison model contains some properties which are in inherent contradiction with the law itself. For example, in order to properly numerically assess their own preference for acquitting the defendant if he is guilty over convicting him if innocent, the trier would naturally need to consider as much information as possible about the consequences of conviction, for example to the defendant’s family, to his reputation etc., or the proposed length of his sentence, and also the consequences of his acquittal if he is guilty, for example if it is known that he holds many prior convictions for the same type of crime or has been engaging in behavior that can appear relevant. But these facts are generally kept from the jury in a trial, given that their duty is restricted to the sole determination of whether or not the defendant is guilty of the crime charged.

For example, in the very recent conviction of Vincent Tabak for the strangling murder of Joanna Yeates in England, the jury (and the public) learned only after his conviction that he had spent an enormous amount of time during the days and weeks preceding the crime in searching out pornography sites showing images of women being choked, with a particular concentration on blonde women some of whom bore a resemblance to Joanna. It was considered that this information could not provide the jury with any factual knowledge about whether Tabak was guilty, and it was therefore withheld.

Tribe concludes his analysis by explaining that in any case, no such model can be considered in the absence of an absolute numerical decision about what kind of precision is aimed at in the trial process. If it is known, for instance, that convicting 60% of the guilty correlates to the unfortunate conviction of 1% of innocent people, and convicting 80% of the guilty correlates to the conviction of 1.2% of innocents (correlations which are obviously very difficult to establish at all), then the trial process must be designed with a specific fixed goal in general corresponding to one such level of precision.

But this specific goal then flies in the face of some of the basic tenets of justice: the “presumption of innocence” and “acquittal in all cases of doubt” since as Tribe says, “After deciding in a deliberate and calculating way that it is willing to convict twelve innocent defendants out of 1000 in order to convict 800 who are guilty – because that is thought to be preferable to convicting just 6 who are innocent but only 500 who are guilty – a community would be hard pressed to insist in its culture and rhetoric that the rights of innocent persons must not be deliberately sacrificed.

In conclusion, Tribe rejects the use of a mathematical model for these reasons: because the rights which are threatened by the use of specific desired proportions of success versus failure in trial go deeper than simply a question of desirable outcomes.

“The presumption of innocence, the rights to counsel and confrontation, the privilege against self-incrimination, and a variety of other trial rights, matter not only as devices for achieving or avoiding certain kinds of trial outcomes, but also as affirmations of respect for the accused as a human being – affirmations that remind him and the public about the sort of society we want to become and, indeed, about the sort of society we are.