I suspect as a start that it would result in a smaller percentage of defendants being found guilty at trial.
I disagree. The most obvious reason is that were our system that efficient, prosecutorial behaviour would change.
But more significantly, a Bayesian processing system would not need to exclude relevant evidence. The only evidence it would exclude would (presumably) be that obtained in violation of the defendant's rights. By incorporating and accurately weighting certain forms of character and hearsay evidence that are not available to a jury, I believe one could prove many cases beyond a reasonable doubt that currently impossible (drug lords and mafia bosses, for example, would be rather easier to convict of something).
Guilty people getting off is, in general, not big news, unless the defendant or crime is already very high profile. Moreover, since the criminal cannot be retried under double jeopardy, no one really goes about examining the wrongfully freed. One can be freed after being wrongfully convicted, so there is some incentive to examine the wrongly convicted. (If you count the people who could be proven guilty to a Bayesian intelligence, but not to a jury, this is a much more significant problem).
In other words, you may well be right, but I think you need a lot more evidence to get to that conclusion. And that still requires prosecutorial behaviour to be exogenous, which is an unreasonable assumption.
There are problems with an adversarial system-- attorneys are rewarded for using weak but plausible arguments for their clients, and as stated above, there are also inequities in the quality of attorneys that different people can afford. Further, attorneys are so expensive that poorer people get an attorney supplied by the court who may not bother to try, or be so ill-paid that they can't afford to put a good case together.
There are also problems with an inquisitorial system. Iterated prisoner's dilemma implies that the investigator may be on the side of t...
In 2004, The United States government executed Cameron Todd Willingham via lethal injection for the crime of murdering his young children by setting fire to his house.
In 2009, David Grann wrote an extended examination of the evidence in the Willingham case for The New Yorker, which has called into question Willingham's guilt. One of the prosecutors in the Willingham case, John Jackson, wrote a response summarizing the evidence from his current perspective. I am not summarizing the evidence here so as to not give the impression of selectively choosing the evidence.
A prior probability estimate for Willingham's guilt (certainly not a close to optimal prior probability) is the probability that a fire resulting in the fatalities of children was intentionally set. The US Fire Administration puts this probability at 13%. The prior probability could be made more accurate by breaking down that 13% of intentionally set fires into different demographic sets, or looking at correlations with other things such as life insurance data.
My question for Less Wrong: Just how innocent is Cameron Todd Willingham? Intuitively, it seems to me that the evidence for Willingham's innocence is of higher magnitude than the evidence for Amanda Knox's innocence. But the prior probability of Willingham being guilty given his children died in a fire in his home is higher than the probability that Amanda Knox committed murder given that a murder occurred in Knox's house.
Challenge question: What does an idealized form of Bayesian Justice look like? I suspect as a start that it would result in a smaller percentage of defendants being found guilty at trial. This article has some examples of the failures to apply Bayesian statistics in existing justice systems.