Friday, October 21, 2011

A Lesson in Probability by the Massachusetts Supreme Judicial Court

A slight shudder goes over me when I realize that I am about to encounter another judicial disquisition on probability and factual inference.

I will give you the citation first, and I will discuss the opinion in a later post or posts: Commonwealth v. Ferreira, No. SJC-10902, 2011 Mass. LEXIS 977 (Oct. 21, 2011).

But I feel compelled to make very brief comment on two points now:

1. The case involved a pretrial identification. The prosecutor made an off-the-cuff argument about the improbability that the victim would have picked, out of two photo arrays containing a total of 14 people, two suspects who happened to know each other. Whether or not the court got the final result right, the court failed to understand the point of the prosecutor's argument about random selection.

2. Whether or not the court got the final result right, the court -- like practically every other court before it -- parroted vacuous and misleading cliches about the non-mathematical character of the reasonable doubt standard:
The prosecutor also erred in equating proof beyond a reasonable doubt with a numerical percentage of the probability of guilt, in this case, ninety-eight per cent. "[T]o attempt to quantify proof beyond a reasonable doubt changes the nature of the legal concept of 'beyond a reasonable doubt,' which seeks 'abiding conviction' or 'moral certainty' rather than statistical probability." Commonwealth v. Rosa, 422 Mass. 18, 28 (1996). "The idea of reasonable doubt is not susceptible to quantification; it is inherently qualitative." Commonwealth v. Sullivan, 20 Mass. App. Ct. 802, 806 (1985). See Commonwealth v. Mack, 423 Mass. 288, 291 (1996) ("the concept of reasonable doubt is not a mathematical one").
Compare P.Tillers & J. Gottfried, United States v. Copeland: A Collateral Attack on the Legal Maxim that Proof Beyond a Reasonable Doubt Is Unquantifiable?, 5 Law, Probability and Risk 135 (Oxford University Press, 2006).


Unknown said...

The Supreme Judicial Court said, "Defense counsel's closing argument noted that the victim was 'only eighty per cent sure' of his identification of the defendant in the photographic array." The court did not comment on the propriety of defense's "mathematical" (my word) argument. (Apparently the prosecutor did not object to defense counsel's argument.) Question: After _Ferreira_ if a Massachusetts prosecutor _does_ object to a similar "mathematical" argument by defense counsel, must a Massachusetts trial judge sustain the prosecutor's objection to such argument? (Would the Massachusetts Supreme Judicial Court -- in all if its wisdom -- say that the prosecutor "invited" such error -- if error it be -- by offering a witness who testified in numerical terms? [If so, isn't it fair to ask if the Massachusetts Supreme Judicial Court would have upheld a trial court ruling barring the prosecution witness from saying that he was only "eighty per cent sure"?])

Unknown said...

It is interesting to note that if the testimony of the prosecution witness's "I-am-80-per-cent-sure" identification of the defendant was the only evidence of the defendant's guilt, the Massachusetts Supreme Judicial Court perhaps went through a considerable number of contortions to avoid saying that an 80% chance of guilt does not satisfy the requirement of proof beyond a reasonable doubt. (But perhaps the Court sensed the point I intend to make in my next comment.)

Unknown said...

Numbers aside, the eyewitness identification evidence in _Ferreira_ is perhaps a nifty illustration of the general point that the probative force of testimonial evidence may be greater than the probability or certitude that the witness ascribes to the accuracy of his or testimony: The making of an eyewitness identification, when combined with other evidence, may establish a fact in issue to a greater probability than the probability that the witness ascribes to the matter he or she asserts. (The law of evidence would say that in such circumstances the testimony of the witness has circumstantial value, that it can be taken circumstantially, it can amount to circumstantial evidence.) Numbers aside, was the identification in _Ferreira_ an example of such a situation?

Unknown said...

The prosecutor effectively argued that the chances that the victim would have picked by sheer chance two men who knew each other out of the array of 49 photographs shown to him -- and who thus could have been the two men who committed the crime for which defendant was on trial -- were very low. The Massachusetts Supreme Judicial Court was correct in saying (in a rather otiose way) that the fact finder's ruminations about the possibility that this could happen by chance should take into account the possibility that yet other persons in the 49-person array knew each other. But can or should we trust defense counsel and the jury's common sense to recognize such variables? Is it really true -- as the court asserts by quoting Laurence Tribe -- that the prosecutor's argument about the probability of selection by chance of two people who knew each other is an example of a mathematical argument that is "surround[ed]" by "mystery," that it is an example of "mathematical arguments [whose] relative obscurity ... makes them at once impenetrable by the layman." Is it really true that jurors are so befuddled by numbers that they cannot sense or pinpoint the possible weaknesses in the prosecutor's argument that the chances of a lucky hit out of a 49-person array on two people who knew each other were 1/7 x 1/7 = 1/49? Do you suppose the some of the jurors play numbers or poker and -- perhaps more to the point -- do you suppose that some or many jurors have the ability to understand the sorts of hedges sometimes made by weather forecasters? Or are only judges and lawyers likely to be befuddled by such numbers, calculations, and ruminations? My observations about the possible gross innumeracy of the judiciary are, I acknowledge, acerbic; they verge on being disrespectful. But it is worth reconsidering the question of whether jurors are really as innumerate and as mindless as is (condescendingly?) usually supposed in judicial disquisitions about the evils of "trials by mathematics." (Some jurors have college degrees. Some jurors have studied mathematics. Some have even studied calculus and probability theory. Some jurors are scientists and engineers. Some jurors know something about computer science. Some jurors are knowledgeable about quality control. Etc. Of course, reliance by other jurors raises other issues. My only point here is that it may not be safe to say that jurors are "mystified" by numbers, mathematics, the product rule, the product rule for dependent conditional probabilities, or what have you.)

Unknown said...

But the prosecutor did apparently commit the "prosecutor's fallacy": He effectively argued that probability of guilt was the inverse of the probability that the victim picked out two men who happened to know each other. This was exactly the same mistake that was made in _People v. Collins_.