Tribe’s reaction to the use of Bayes’ theorem at trial
In this last post of the series, we continue to summarize Tribe’s objections to the use of Bayes’ theorem at trial, with our responses. Last time we discussed his first objection:
1….The Distortion of Outcomes
Today, we continue with the other three objections.
2….The End of Innocence: A Presumption of Guilt?
“At least in criminal cases, and perhaps also in civil cases resting on allegations of moral fault, further difficulties lurk in the very fact that the trier is forced by the Finkelstein-Fairley technique to arrive at an explicit quantitative estimate of the likely truth at or near the trial’s start, or at least before some of the most significant evidence has been put before him.” Tribe’s argument in this section is that the idea of forcing a juror to arrive at some kind of mathematical figure for the prior probability of guilt, before applying Bayes’ theorem to update that prior according to some new piece of numerical evidence, is fundamentally against the presumption of guilt, and that this injustice is not rectified even by setting the prior probability to an unreasonably low value.
Tribe stresses the importance of the juror listening to all of the evidence before “reaching any judgment, even a tentative one, as to his probable guilt”; he terms this one of the “intangible aspects” of our commitment to the proposition that “a man who stands accused of crime is no less entitled than his accuser to freedom and respect as an innocent member o the community”. Tribe admits that in reality, a juror listening to a trial may not actually be considering the accused as certainly innocent until a complete proof has been laid out before him; he may, in fact, swing backwards and forwards in his estimate of guilt as the trial proceeds, thus holding some vague idea of “prior probability of guilt” at all times. However, according to Tribe, these impulses must not be spoken or expressed, let alone called to the fore, out of respect for the presumption of innocence. “Society ought to speak of accused men as innocent, and treat them as innocent, until they have been properly convicted after all they have to offer in their defense has been carefully weighed,” and “Jurors cannot at the same time estimate probable guilt and suspend judgment until they have heard all the defendant has to say.”
We feel that the proper method to counter Tribe’s worries and to allow jurors to keep all their thoughts about possible guilt, and their personal, intimate estimates of probability of guilt, silent and unspoken throughout the trial, is the presentation of a table such as the one given by Finkelstein and Fairley, in which many different values for the prior probability of guilt are entered, and the update according to the new evidence is calculated for each of them. In this way, the jury members are never required to explicitly formulate a probability of guilt at any stage; it is enough for them to place themselves loosely within the table, without being asked to specify where, or even to consider the entire set of output results and the meaning they indicate before coming to any final decision. This would certainly respect the duty of silence that Tribe describes.
We note as an aside that Tribe himself appears disturbed by the fact that the duty of silence is at the same time a call for lack of candor. In a few well-chosen words he expresses his obviously deeply held feeling that while a lack of candor should not be something that is required lightly, there are cases in which it serves a higher moral purpose. Lies or refusals to consider the full weight of the evidence are not required, merely a silence on the subject in respect for the presumption of innocence: “One need not say everything all at once in order to be truthful, and saying some things in certain ways and at certain times in the trial process may interfere with other more important messages that the process should seek to convey and with attitudes that it should seek to preserve.”
We respect and agree with this approach, but as explained above, Bayes’ theorem can be correctly presented and used at trial without undermining it.
3…The Quantification of Sacrifice
One extremely disturbing factor about the use of any mathematical method to determine guilt is that since the final probability, when all the evidence has been taken into account, is rarely likely to be equal to 1.0, it will, in cases of conviction, tend to be some concrete and convincing figure such as, for example, 0.98. Unfortunately, accepting such a figure as the probability of guilt can also be expressed as saying that one accepts that 2 people out of every 100 convicted are expected to be innocent. While there is no doubt that many innocent people are convicted each year, it is indeed disturbing to have an actual figure of the number of such people that one expects. “There is something intrinsically immoral about condemning a man as a criminal while telling oneself, “I believe that there is a chance of one in twenty that this defendant is innocent, but a 1/20 risk of sacrificing him erroneously is one I am willing to run in the interest of the public’s – and my own – safety.” Tribe wishes for any justice system to be structured in such a way as to avoid ever having to make such a proclamation with a specifically published figure. He considers that it is morally superior for a juror to express himself as being “very sure” or “as sure as possible” of guilt than to give an actual figure, which would prove his readiness to accept such or such a percentage of innocent sacrificial victims.
Naturally, there are miscarriages of justice in any justice system, but Tribe points out the vast moral difference between society’s recognizing the necessity of tolerating them, and the fact of its actually embracing a policy that juries “ought to convict in the face of this acknowledged and quantified uncertainty”. He prefers sticking to the notion of “guilt beyond a reasonable doubt”, which represents “a subtle compromise between the knowledge, on the one hand, that we cannot realistically insist on acquittal whenever guilt is less than absolutely certain, and the realization, on the other hand, that the cost of spelling that out explicitly and with calculated precision in the trial itself would be too high.”
Our response to this argument is that Bayes’ theorem should not, probably ever, be used to compute the probability of guilt. It should be brought in to establish certain factual subsidiary questions, such as the probability of its being the defendant or another person who left a certain print, was seen in a certain place, was present at a certain time, transported a certain object, and so forth. The actual final decision of innocence or guilt should and must be made by jurors without recourse to any numerical calculation.
4…The Dehumanization of Justice
Tribe’s final argument against the use of mathematical methods at trial is simply that they “threaten to make the legal system seem even more alien and inhuman than it already does to distressingly many…The need now is to enhance the community comprehension of the trial process, not to exacerbate an already serious problem by shrouding the process in mathematical obscurity.” Tribe worries that “guided and perhaps intimidated by the seeming inexorability of numbers, induced by the persuasive force of formulas and the precision of the decimal points to perceive themselves as performing a largely mechanical and automatic role, few jurors could be relied upon to recall, let alone to perform, this humanizing function, to employ their intuition and their sense of community values to shape their ultimate conclusions.”
Our response to this is that with the advent of DNA analysis, mathematics at trial is here to stay. It is perhaps not yet fully understood that the statistical analyses used on DNA are no different than many other cases and situations where Bayes’ theorem can be applied. The public has grown used to seeing DNA analyses presented at trial over the decades since Tribe wrote his article, and juries deal with the situation competently enough in the main, having expert witnesses explain the issues to them in layman’s terms, and not, generally, forgetting to employ their common sense.
It seems to us that what is needed is a general education aimed at the public, so that little by little, the notions used there, which are not more difficult than much of the mathematics seen at school, become familiar and trustworthy to the public at large, from which juries are drawn. We believe that this is the only way in which Tribe’s profound moral and social concerns can be reconciled with the fact that mathematics at trial is here to stay. We also believe that such a general public education is a legitimate and reasonable aim to work towards, which is the whole purpose of this blog.
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