There's a mathematical law about this. If you split something into groups, there will always be a dividing line. Move it within epsilon, and it crosses the line.

Whether or not they're guilty may be beyond resonable doubt without whether or not its beyond resonable doubt being beyond reasonable doubt.

For example, if we define "reasonable doubt" to be < 99% chance of guilt, then if you think there's a 99% chance of them being guilty, you're pretty sure they're guilty, but there's about a 50% chance of them being convicted, based on whether the jury considers it slightly more likely or slightly less likely.

I love Dawkins' pop-sci works on biology and evolution, but like a lot of very smart and articulate people, he can be lazy when he goes outside the realm of his expertise. He uses "courtroom dramas" as evidence of what happens in real-life courtrooms. I wonder if he thinks Hollywood's portrayal of what scientists do is similarly accurate? Later, he relies on the O.J. Simpson criminal trial, which is famous partly because it was so incredibly weird and wildly outside the mainstream. He says the professionals in the courtroom are "on tenterhooks and hold their breath" when it's time for the verdict. Are they? My impression is that in the overwhelming majority of cases, experienced trial lawyers are not surprised by juries very often.

In any case, judges and juries see a trial from very, very different perspectives. Judges see defendants in chains and jail uniforms, juries see the defendant in a borrowed business suit. Judges know the when a defendant has tentatively agreed to a plea and then pulled out at the last minute. Moreover, it is the job of a trial judge to make sure that juries do not always see all the evidence. A defendant may have made a full confession and led the cops to the secret spot where the body was hidden, but if the police induced this confession by unconstitutional means, it can't go before the jury. The list of legal reasons to exclude evidence from a jury is very long. Many, many times, judges preside over criminal trials with the full knowledge that the defendant did in fact do what he (or she) was accused of. However, the trial goes forward, because one major purpose of the trial and the jury system is not just to determine the facts accurately, but to restrain the police and the government from becoming dangerous.

After each side in a criminal case rests, a judge will instruct a jury of laypeople (mostly not mathematicians and philosophers) that the defendant must be found not guilty unless the prosecution has proved its case beyond a reasonable doubt. Dawkins picks on the phrase "beyond a reasonable doubt." I would agree with him that this is a very vague and un-mathematical phrase. But he misses the point that the really important words are "unless the prosecution has proved its case."

The prosecution are only going to bring a case if they think they can get a conviction, i.e. prove it beyond the jury's reasonable doubt. In effect, the prosecution are another jury, but one subject to several biases compared with the real jury:

• self-serving assessment of how good their case is
• illusion of transparency
• priming by evidence they have which for one reason or another cannot be used in court
• regression to the mean.

So in general we should expect jurors to have a lower estimate of the prosecution's case than the prosecution themselves do.

In addition, cases only go to trial that are contestible -- where the prosecution thinks it can be proved beyond reasonable doubt but the defence does not. When the case is overwhelming and the accused is actually guilty, the accused is more likely to plead guilty without a trial. Jurors will never see those cases, only those that the accused finds worth contesting.

So it is not surprising that in a substantial proportion of cases, nobody can be sure of the jury's verdict until it is announced.

With regards to the comments here, a great deal of personal belief in morality of the world you live in, the fairness of the world, etc. relies on belief in good justice system, and those beliefs force you to believe justice system works better than it is and construct elaborate explanations of how it may be working well. It is not because the case is on dividing line between say 99% certainty, that you don't know what decision will court decide. The average people don't do probabilities that well as to estimate their uncertainty like that! We all know this.

Imagine you were dealing with a panel of chimpanzees or something else that's obviously dumber than you, deciding on the verdict while being demonstrably unable to comprehend much of the basic logic*, so that both sides HAVE to appeal to fallacies, and then sit nervous unknowing which fallacies latched onto the minds of jury better. The right side in principle could stick to logic alone but in any remotely complex case that is likely to fail.

*it suffices that average member of the jury has measured IQ of 100, with failure rate on the logic section of IQ test such that it implies inability to do much of even most basic reasoning. Nevermind probabilities. They can't do probabilities. Even for something as trivial as monty hall.

And you know what's worst? You can make a jury of PhDs, and the jury is still barely intelligent (even if more intelligent than average). Homo sapiens is barely intelligent, that's how things work - we evolved to be barely intelligent, at which point very rapid technological progress happened, and that was (in biological terms) very recently, and we are still barely intelligent.

Even worse still, there could be an utterly rational, effective agency at work as well. Selfish one. This agency determines that 1: thought-time expenditure on the process is not worth it (which leads to apparent stupidity well beyond one's stupidity on a test that might influence one's personal future), 2: if there is even 1% chance that the person is guilty of a major crime that can affect you, within even a large city, the personally rational, selfish action for you is to convict as the personal cost of convicting innocent is much smaller than personal cost of setting free the guilty (the social cost is however other way around). Even the perfect rational intelligence needs not arrive at a good judgement, nor to carefully listen and follow the argumentation, if that rational intelligence is selfish and optimizing it's use of computing time.

One should do scientific study on this. Do some experimental trials of the trial system, see if they can decide on correctness of proofs of theorems - two mathematicians represented by 2 barristers, one premise to a simple theorem, one mathematician trying to prove some fallacy, other trying to prove correct answer.

For me, lack of routine testing of the trial system in this fashion is evidence enough that it is probably not very effective - nobody tried to see what in practice does 'reasonable doubt' equate to (some juries may think its unreasonable to set free someone when there's doubts as to their innocence, some juries may get manipulated into setting free a certain murderer). It may be the best that we can do, but still be very bad.

I would prefer professional jurors now that transparency can be maintained via technological means. These would be people who give up their right to privacy and train in weighing evidence correctly in exchange for high social status and good pay.