A long trial, intended to establish a truth about the natural world “beyond a reasonable doubt” may be a complex problem.

By “complex problem” I mean some kind of puzzle where you need to be quite organised to keep a large number of details under control, where the solution is not obvious, where a problem needs to be broken down into smaller components, and each component needs to be carefully examined and considered separately. We have to do this with large problems, because the human brain simply cannot think about very many bits of information at one time.

Most people, in most jobs, will never or hardly ever encounter complex problems they are required to solve. I am not sure what you should call the required skill, perhaps analytical skill, although I am not sure that captures it.

This skill is needed in mathematics, where the proof of a non-trivial mathematical theorem has to be constructed from “lemmas” (which are minor theorems used during the proof construction ).

Mathematics is similar to justice in that proof is the central concept, although of course mathematical proof has a different kind of certainty to it – mathematical certainty rather than legal certainty, which is usually built around the somewhat fuzzy concept of “reasonable doubt”, which is more akin to probability theory* than mathematical certainty.

But although mathematical proof is different to legal proof, there are still similar errors that can be made. False assumptions, clerical errors and errors that arise from our imperfect understanding of the extremely complex natural world, including human behaviour.

Analytical skill is also needed in engineering and computer programming. For example, software to control a large aircraft needs to be broken down into small components, there may be many thousands of such components in a large project.

People with very good “analytical skills” (for want of a better word) may be quite rare, and rarer still in jury pools where employers of people with very good analytical skills may be reluctant to release employees for long periods of time.

So there is a strong chance of serious error when a group of unskilled people are asked to analyse a complex problem.

There is no way to independently test if the jury solution to a criminal problem is correct. While aircraft can be carefully tested, to see if the solution works, there is no way to test the verdict of a jury. If it is wrong, the error may take decades to discover, or the error may never be discovered ( at least in a court of law ).

This could perhaps help explain why there are many wrongful convictions.

* It is reasonable to view the job of a juror as calculating a probability of innocence ( while incorporating uncertainties about the calculation itself into their reasoning in a conservative way ). A typical jury instruction would state “If you are firmly convinced that the defendant is guilty of the crime charged, you must find him/her guilty”. If a juror concludes the probability of innocence is very small, say less than 1% then it would be reasonable and rational to be “firmly convinced” of guilt, even though the required level of certainty is never made explicit in jury instructions, it is left to the personal interpretation of each juror.