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.

In both instances, the prosecution case amounts to roughly zero bits of evidence. However, demographics give Willingham a higher prior of guilt than Knox, perhaps by something like an order of magnitude (1 to 4 bits). I am therefore about an order of magnitude more confident in Knox's innocence than Willingham's.

Challenge question: What does an idealized form of Bayesian Justice look like?

Bayesian jurors (preferably along with Bayesian prosecutors and judges); that's really all it comes down to.

In particular, discussions about the structure of the judicial system are pretty much beside the point, in my view. (The Knox case is not about the Italian justice system, pace just about everyone.) Such systematic rules exist mostly as an attempt at correcting for predictable Bayesian failures on the part of the people involved. In fact, most legal rules of evidence are nothing but crude analogues of a corresponding Bayesian principle. For example, the "presumption of innocence" is a direct counterpart of the Bayesian prohibition against privileging the hypothesis.

There is this notion that Bayesian and legal reasoning are in some kind of constant conflict or tension, and oh-whatever-are-we-to-do as rationalists when judging a criminal case. (See here for a classic example of this kind of hand-wringing.) I would like to dispel this notion. It's really quite simple: "beyond a reasonable doubt" just means P(guilty|evidence) has to be above some threshold, like 99%, or something. In which case, if it's 85%, you don't convict. That's all there is to it. (In particular, away with this nonsense about how P(guilty|evidence) is not the quantity jurors should be interested in; of course it is!)

From our perspective as rationality-advocates, the best means of improving justice is not some systematic reform of legal systems, but rather is simply to raise the sanity waterline of the population in general.