In this post, I intend to prove to you beyond a reasonable doubt that the concept of "proof beyond a reasonable doubt" is nothing more than a legal fiction. This shouldn't take too long.





I begin by asking you to consider the burden of proof in a civil case. That burden is usually described as the "preponderance of the evidence." It's a 50-50 type decision. If the evidence favors the plaintiff even by a teensy weensy bit, the jury is to find in favor of the plaintiff. If, on the other hand, the evidence favors the defense even by a smidgeon, then the jury is to find in favor of the defense. It's so simple.





I present the idealized concept of preponderance of the evidence in the figure below. Click to enlarge.

Matters are a little more confusing for jurors in a criminal case. They are asked to decide if the evidence proves the State's case beyond a reasonable doubt. The jurors must figure out how heavily the evidence favors the prosecution AND they must figure out what the hell the term reasonable doubt means AND they must decide whether the weight of the evidence provided by the prosecution exceeds the reasonable doubt threshold.





Courts are of almost no help in determining the meaning of reasonable doubt. One thing they absolutely will not do is apply any numeric value to reasonable doubt. They never suggest anything such as "you must be 90% certain."



Never. Ever.



Not now. Not ever.



Instead, they give you a reasonable doubt instruction something along the line of:

The question naturally is what is a reasonable doubt. The words almost define themselves. It is a doubt based upon reason and common sense. It is a doubt that a reasonable person has after carefully weighing all of the evidence. It is a doubt which would cause a reasonable person to hesitate to act in a matter of importance in his or her personal life. Proof beyond a reasonable doubt must be proof of such a convincing character that a reasonable person would not hesitate to rely and act upon it in the most important of his own affairs.

There you go. I'm sure that clarified things.





Legal scholars, and I've been reading a lot of their scholarly work on this issue recently, recognized that if you are to quantify the number, it should be greater than 50%. That after all is the standard for civil cases, and the burden of proof in criminal cases is supposed to be substantially greater. Legal scholars tend to throw out a value of 90% as a starting point. This corresponds roughly to William Blackstone's 250 year old claim that it is "better that ten guilty persons escape than that one innocent suffer."





That traditional view is portrayed in the figure below.

Those legal scholars who believe that figure portrays reality are full of scholarly beans





beans, at least with respect to this concept. When Rita Simon and Linda Mahon asked 106 judges to put a non-legally-binding number to proof beyond a reasonable doubt, those judges gave a number (presumably on average) of 89%. Since that's almost identical to the number the full-of-beans legal scholars provided, I declare that judges too are full of judicial, at least with respect to this concept.





Simon and Mahon also asked 25 jurors to put a number to the concept. Those jurors put the number at 79%. That number is not far from a couple other studies I've seen where jurors put the number around 75%, assuming they are asked before they deliberate in a mock trial. If they are asked after they deliberate, the put the number closer to 55%. The suggestion is that they wanted to convict, the evidence didn't support conviction at even a 75% standard, so they reduced the standard.





beans, at least with respect to this issue. Even though the students eventually put the standard just barely above a civil suit "preponderance of the evidence" standard, I declare my fellow jurors to be full of deliberative, at least with respect to this issue.





I'll allow the judges and jurors to make my point for me. During the NCSC judge-jury agreement study used by Bruce Spencer to establish a wrongful conviction rate around 10%, the judges and jurors were asked to provide their estimate of the strength of the evidence used to convict (or acquit) a defendant. I'll simply provide a summary plot of the results below, and move away from the keyboard a bit as you study the plot and say "What the hell?" Click to enlarge.

Okay. I'm back. The first thing the Skeptical Spouse said when I showed her this plot was "That's not right!!?" She was pointing to the portion where the jurors voted more frequently to convict when the strength of evidence was 1 than when it was 2. I replied with something equally as scholarly, something along the lines of "Screw that. They're voting to convict a third of the time when by their own admission the evidence strongly favors the defense."





beans. Even when the evidence favors neither the prosecution nor the defense, both judge and jury are voting two out of three times to convict. Anyone who studies the chart for more than a minute and still believes that we presume defendants to be innocent, or that we burden the prosecution with proof beyond a reasonable doubt, is full of blog-reading





This one simple plot, based directly on data provided by judges and juries, demolishes dozens of scholarly works I've read regarding quantifying reasonable doubt. This plot causes me to propose an alternative hypothesis of jury behavior. It may not be scholarly, but it better explains the data. Here goes.









Besides destroying much scholarly work and putting the lie to some of the most fundamental principles of our judicial system, the plot also tells you that those who guess and those who divide are pretty much wrong when they arrive at wrongful conviction rates of 1 or 2 or 3%. There is no way that the behavior portrayed in the chart would result in such low error rates.





I'll add one final chart, then I'll step away from the keyboard. In the chart below, I simply overlay the idealized and realized worlds of proof beyond a reasonable doubt. I'll allow the chart to speak for itself.

Originally posted on 21 November 2010.