David Spiegelhalter's blog, Understanding Uncertainty, informs us of a recent insane ruling from the England and Wales Court of Appeal, concerning the usability of probabilities as evidence in court cases. Lord Justice Toulson's ruling contains the following wisdom:
The chances of something happening in the future may be expressed in terms of percentage... But you cannot properly say that there is a 25 per cent chance that something has happened... Either it has or it has not.
This is wrong. Shockingly, scarily wrong. The judge is saying that probabilities only apply to future events, and not to past events, and is effectively decreeing that such evidence in inadmissible in a court of law. This ruling is based, it seems, on an earlier case, in which a judge ruled:
It is not, in my opinion, correct to say that on arrival at the hospital he had a 25 per cent. chance of recovery. If insufficient blood vessels were left intact by the fall he had no prospect of avoiding complete avascular necrosis, whereas if sufficient blood vessels were left intact on the judge's findings no further damage to the blood supply would have resulted if he had been given immediate treatment, and he would not have suffered the avascular necrosis.
It seems that Justice Toulson is not alone among judges for his profound ignorance of probability, logic and the basic principles of how knowledge is acquired. In fact, for almost 30 years, the legal profession has had its own special probabilistic fallacy, the prosecutor's fallacy, named after it. You might think that by now they should have made an effort to get to grips with basic methodology, but instead, they just keep on making stupid judgements.
I have pointed out that a judge who can claim that probabilities in general can't be assigned to past events is incompetent and not fit to perform their duties. Though it might seem harsh, I stand by this analysis. You might think that this is some obscure point of epistemology with little or no practical importance, but it is much more than that.
There are three main reasons blunders like this, made by a high court judge, should scare the crap out of society at large. Firstly, as pointed out, it demonstrates a serious ignorance of what probabilities are. Probability theory is completely symmetric with regard to time, and probabilities are simply a systematic way of quantifying our current knowledge. Just an obscure mathematical point? Not at all. Such ignorance shows off a complete disregard for what knowledge is, what it means to be rational, and what is actually involved when evidence is evaluated. What has been asserted is that calculations of the kind when I worked out the probability that somebody has contracted a certain disease are completely meaningless. Maybe the judge won't find it meaningless next time he is in his doctor's office trying to plan his future. Call me overly strict, but I expect somebody in such a position of power, whose job consists to such a high degree of evaluating evidence, to be able to wield a modest understanding of what evidence actually is. How can any reasonable standard of statistical evidence be enforced, when judges are so ignorant about probability?
But its not just ignorance thats on display here - also a shocking disrespect for logic. In the same paragraph as his pronouncement on the meaninglessness of probabilities, when applied to past events, the judge manages to immediately contradict himself rather blatantly:
In deciding a question of past fact the court will, of course, give the answer which it believes is more likely to be (more probably) the right answer than the wrong answer
How can anybody capable of holding such obviously incompatible positions at the same time, on any topic, be capable of presiding over a court? What is clear, is that every single judgement of fact, in every single sphere of life relies on some kind of probability assessment. The question that remains, then, is whether we want to make that assessment as systematic and rigorous as we can, or are we happy relying on unexamined instinct and faulty logic? For high-ranked judges to favour the latter is a nightmare scenario.
Secondly, this ruling, if implemented, would make an enormous variety of important types of evidence impossible to use in legal cases, and would severely hinder the capacity of courts to efficiently determine what is the likely truth. Genetic evidence, for example, is based on Bayesian calculations, as it must be, in order to attain validity.
To present probabilities is to make the highest quality of inference available. Why is this judge against high-quality inference? Indeed, why is he so overtly opposed to scientific method? In Toulson's ruling, we also have this:
When judging whether a case for believing that an event was caused in a particular way is stronger that the case for not so believing, the process is not scientific...
Why not scientific? Why not demand the highest standards of logic and inference? Why is he not complaining that the process is not scientific enough, instead of insisting that we rely on some inefficient and non-systematic procedure? The mind boggles. There is only one correct way to assess the implications of evidence, and to quantitatively combine multiple pieces of evidence, and that is Bayes' theorem (techniques that successfully replicate its outcomes can occasionally be used also). Judge Toulson's ruling constitutes a rejection of Bayesian reasoning, and thereby demands that the legal profession turn its back on the rational evaluation of empirical facts.
Thirdly, the judges on this case have made a serious blunder with a technical issue, while obviously being unaware of their incompetence to reason about the topic. Certainly, a judge doesn't need to be an expert in all the technical subjects that may be relevant to any given case. But then they must be able to appreciate that the technical issues are beyond them. They can not perform technical analyses that they are unqualified to perform. If they want to base their decisions on philosophy, probability, mathematical theorems, or whatever, they damn well get it right, or ask somebody else, who knows what they are doing. In what other technical forensic issues are these judges hopelessly unaware of their complete lack of understanding? A society that aspires to be a free and enlightened society must not tolerate such oblivious overconfidence among people with such an important job.