Forensic Math

Applying Mathematical principles to improve our legal system.

Saturday, October 18, 2008

While waiting in line recently to enter the courtroom to participate in a jury selection process I struck up a conversation with the man next to me in line regarding the notion of "possible". I brought up the old conundrum as to whether a monkey sitting at a typewriter long enough could possibly, at random, type out the complete works of Shakespeare. In fact I told him that that someone in the magazine Scientific American had actually calculated this precise probability under certain constraints. Thus if the definition of "possible" is- that the probability of the event occurring is greater than zero- then we must conclude that even a monkey, given enough time, could possibly produce the complete works of Shakespeare.

Upon reaching the courtroom the potential jurists were instructed to write down any questions we had regarding the instructions we were being given by both prosecuting and defense attorneys as they gave a general overview of the case. I noted the following three, which the Judge and I subsequently discussed:

-The meaning of "reasonable doubt"
-Whether one could make a decision based on one side of the story
-The legitimacy of judging testimony based on body language

Regarding the notion of "reasonable doubt" I described the practice in the scientific community of relying on the standard of "95 percent level of certainty" as determined by standard tests of statistical significance. In other words, biologists for example, will accept the result of an experiment if statistical tests show that the results have less than a 5 percent chance of being due to random events. I inquired of the judge as to whether in the current circumstance, where a man's life was at stake, would not a higher level of certainty be warranted? Say, at least 99 percent, for example? The Judge recoiled and said that he "could not put a number on it". I responded that for me, without a number, the phrase carried no information and that I could not relate to it.

This starts to illustrate the most pernicious inherently mathematical tactic used in our legal system: The "isn't it possible" question. In terms of information theory which seeks to quantify information content, the answer to this question gives zero or a negligible amount of information. Unless, of course, you think a monkey could write a Bob Dylan song.

As to the second point, the prosecutor encouraged the jurists to be willing to make up their minds upon hearing one side of the testimony, assuming the account was adequately persuasive. I am reminded of radio host Paul Harvey who has made a living with his "other side of the story" shtick. I mentioned to the Judge that anyone with a modicum of real world experience had observed this phenomenon whereby hearing the other side of the story completely changes one's viewpoint- to which he readily agreed. He then asked me if it were not possible to hear evidence so overwhelmingly conclusive as to allow one to come to a conclusion. I responded that I did not know and would have to look at each case individually, but in any case that this certainly was not true in the general case, to which he agreed.

Mathematically speaking, hearing one side of the story establishes one set of parameters and their values upon which to judge the circumstances. Clearly, hearing the other side of the tale will give a better snapshot of the true values.

My final objection was to the prosecutors exhorting us to pay attention to the witnesses tone, and emotional expressions in judging the truth of the testimony. I argued that this was "body language" and that there were no scientific studies whose results could justify this practice.

Note that lie detector tests are not admissible in courts reflecting the fact that no known algebraic sum of biological signals is known to conclusively determine truth telling. Indeed "truth" is oft times difficult to define and may be a fuzzy (as in fuzzy logic) concept. Some people delude themselves, some drugs may obscure any kind of telltale signs of falsehood telling, and some people may be good actors.

In the end, the Judge asked me if despite these conflicts whether I thought could still be a good unbiased juror in the case. I responded that because of my background in math and logic that I would probably be an ideal juror with a superior set of "decision boundaries". I further added that I did not expect to be chosen as I had observed that the prosecutor had dismissed an earlier juror for being overly "analytic". (Evidently she preferred more emotional and less analytic jurors?)

A few seconds later the prosecutor called my number and I was dismissed.