But notice that these are examples of restrictions on evidence of guilt.
No, they're not. The first one I listed can go either way.
"Since my client is a woman, you should reduce the odds you assign to her having committed a murder by a factor of 4."
The second one can go either way too; it just as much excludes e.g. hearsay evidence that implicates someone else.
The assumption (very reasonable, it seems to me) is that human irrationality tends in the direction of false positives, i.e. wrongful convictions.
Sure, but that needs to be accounted for via the guilt probability threshold, not by reducing the accuracy of the evidence. Favoring acquittal through a high burden and biasing evidence in favor of the defendant is "double-dipping".
If juries are capable of convicting on the sort of evidence presented at the Knox/Sollecito trial (and they are, whether in Italy, the U.S., or anywhere else)...well, can you imagine all the false convictions we would have if such rules as you listed were relaxed?
I only listed a few examples off the top of my head. The appropriate comparison is to the general policy of, per Bayesianism, incorporating all informative evidence. This would probably lead to more accurate assessments of guilt. In particularly egregious cases like K/S, it would have been a tremendous boon to them to allow them to have an explicit guilt threshold and count up the (log) likelihood ratio of all the evidence.
In any case, remember that there's a cost to false negatives as well. Although that's heavily muddled by the fundamental injustice of so many laws for which such a cost is non-existent.
Let me take a step back here, because despite the fact that it sounds like we're arguing, I find myself in total agreement with other comments of yours in this thread, in particular your description of how trials should work; I could scarcely have said it better myself.
Here's what I claim: the rules of evidence constitute crude attempts to impose some degree of rationality on jurors and prosecutors who are otherwise not particularly inclined to be rational. These hacks are not always successful, and occasionally even backfire; and they would not be necessa...
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.