Decisions

 

Cocaine Blues

Into the courtroom my trial began
Where I was judged by twelve honest men
Yes as the jury started walkin' out
I saw that little judge commence to look about

Why twelve honest men on the jury?

A jury is charged with making a finding of the truth. But we live in a random universe. So how certain can we be certain that the jury’s finding is indeed the truth? The scientific standard is 3 Sigma, 3σ. If the odds are 50%, True and False, then if the jury consisted of only 1 person, then a finding of Truth would only have a 50% chance of being certain, which is no better than the odds. If the jury consists of two persons, then the chances that both persons made a finding of truth is one out of four outcomes, which means that two people have a 75% percent certainty of being correct. To reach a scientific standard of certainty, it requires that 12 members make a finding. If all twelve members make a finding that the evidence is true, then there is a 99.976% certainty, while 3 Sigma is 99.97% certainty, that they are correct.

Might the jury still be certain but wrong? Remember the wisdom of Abraham Lincoln that “you can fool all of the people some of the time, and some of the people all of the time.” The evidence might have fooled the jurors such that at least one of their findings of truth should have been false. In statistics this would be called a false positive. It is also possible that any juror could have a bias such that a finding NOT in evidence affected their decision. For that reason even a 99.976% certainty does not mean that the jury might still be wrong. That is why findings of trial by jury should always be reversible.

Similarly, the scientific standard can be used to determine when a decision might have passed a lower standard, such a 1 Sigma, or the mean plus one Standard Deviation.  Decisions by a group are no more certain than the odds if no Standard Deviation is used. Most decisions do NOT require a decision by the whole group and thus a decision that is greater than the mean will be more timely. The group decision passes the 1 Sigma test for certainty only if it is by 68% percent of the group. It takes a group of at least three  to approximate such certainty. If the group has, for example, 435 members, but that group has only two parties, and decisions are on a party line, the certainty is only 50%, which is no better than the odds. Which is why the most important decisions affecting the group, such as declarations of war, require 2/3, approximately a certainty of 1 Sigma. It also means that decisions of say a Supreme Court of nine members should not be considered certain unless they are 6-3 decisions. Judges are bound by the same rules of math as are juries. What is good for the goose, is good for the gander.