Indeed, a prior conviction raises the Bayesian probability of a given suspect having committed a similar crime. In probability terms, the prior probability of suspect S having committed crime Cn, given that they committed crime C0, C1, etc., is certainly higher than without that information.

But how much higher? Given 8 billion people in the world, the priors are quite low for any given person P having committed any particular crime Cn. On the other hand, humans (including jurors) are liable to bias, and without other alternatives they can very easily be fooled. By the time someone has been dragged in front of you, and you're told that they committed C0, C1, etc., then you're asked if they committed crime C and to you it looks very plausible because it's hard to take into account the (still) very low prior, especially if you lack other alternative hypotheses.

So while you're right that it is a valid inference, we choose not to allow that inference in order to counter the much higher magnitude of bias caused by the representativeness heuristic and the like.

> playing the devil's advocate

Ok. IANAL :)

> The fact that someone robbed 10 banks is a fact.

The legal world is, officially, very humble. It isn't a fact that someone robbed 10 banks. It is a fact that they were /convicted of/ robbing 10 banks. The legal system isn't perfect, lots of basically guiltless people get chewed up by the machine. An acceptance of that reality permeates a lot of legal practice (embedded in the system, although I expect a lot of lawyers get it too).

> How is a person's history not a fact?

The key word you are missing is relevant fact. Some very great minds have put a lot of effort into making the legal system robust against the unreliability of all the evidence that passes through it. The rules regarding evidence in the Common Law tradition are quite well thought out. A case starts by gathering evidence of what transpired, proceeds by assessing it against some standard and finishes taking a (more or less) predictable action.

If someone has 10 convictions, they have received an appropriate treatment for what they have done. Imagine that a bank robbery has occurred and someone has a history of 10 bank robberies is the suspect. If the case is borderline, and the 10 prior convictions is what pushes it over the edge, then this is effectively the same as further punishment for past misdeeds.

If the 10 past misdeeds are acceptable evidence, then it is equivalent to punishing someone further for past crimes. That isn't acceptable - the sentence at the prior conviction is meant to be the end of the matter and to allow otherwise violates principles of fairness. For reason of fairness, they can't be accepted and the current case must be tried on the merits of only evidence about that instance of crime.

Keeping in mind you are playing Devils Advocate.

I can see how from a risk and prevention perspective, prior convictions are highly relevant. The ML example factors into this. Banks would not be unwise to lock the doors when a person with 9 bank robbery convictions walks past.

In fact, I would suspect that even if the jurors should base it just on the facts, the person is more likely to end up in front of the court because the police would run through the list of convicted bank robbers in the area.

The risk of an incorrect conviction for this person must go up.

The facts standing on their own is important because it's not just about risk prevention, ML learning is a (potentially highly accurate) guess, but still a guess. Admitting prior convictions is basically the same for humans, it fires up the predictive nature of our brains.

Because its prejudicial nature outweighs its evidence. If someone robbed a bank, their character shouldn't be necessary to figure out if they did or didn't. If the prosecutor wants to put him on trial for all the banks at once, then he can do that.

The problem with all of this is that we aren't trying to predict whether the guy will ever rob a bank again or assess the odds of him doing this one, which is where your logic works best-- we are trying to determine beyond a reasonable doubt that he did, in fact, rob this one.

That he robbed banks before is a fact, yes, but not one that puts him at the scene of this crime. Statistical likelihood is not a relevant fact in a criminal trial (but might be acceptable in a civil matter, where the standards are lower).

Does anyone really put much faith in character witnesses though? One possible point: someone who can’t produce anyone to say something positive about them is clearly guilty.