Let's say A="Knox killed Kercher", B="Kercher has been killed and Knoxed lived in Italy and is an intelligent 20-year-old female college student with no criminal history", C="evidence against Guede", D="Knox and Kercher were roommates", E="evidence of a staged burglary", F="bra and clasp", G="all other information about the case".
I'll redefine slightly:
A := "Knox killed Kercher, given background info about both, but not the fact of their acquaintance". P(A) = tiny.
B := "Kercher killed". P(A|B) = approximately P(A). (We are not yet given that they were roommates.)
C := "evidence against Guede". P(A|B&C) = approximately P(A). (No significant connection between Guede and Knox.)
D := "Knox and Kercher were roommates". P(A|B&C&D) = slightly higher than P(A), but still well below the threshold of consideration.
E := "Facts cited as evidence of staged burglary". P(A|B&C&D&E) = approximately P(A|B&C&D). (Likelihood ratios involved are close to unity; certainly small relative to P(~A)/P(A).)
F := "bra clasp and knife". P(A|B&C&D&E&F) = possibly as much as an order of magnitude higher than P(A|B&C&D). (Explaining results is a minor puzzle.)
G := "all other information". P(A|B&C&D&E&F&G) = approximately P(A|B&C&D&E&F). (Other evidence weak; slightly inculpatory facts canceled out by slightly exculpatory facts.)
Thanks, that's very helpful. Perhaps you could copy this to the main debate branch, so Rolf would see it and possibly respond in a similar fashion? Also, to seek a bit more clarification, what is your estimate of P(A|B&C&D) / P(A|B&C)?
Recently, on the main section of the site, Raw_Power posted an article suggesting that we find "worthy opponents" to help us avoid mistakes.
As you may recall, Rolf Nelson disagrees with me about Amanda Knox -- rather sharply. Of course, the same can be said of lots of other people (if not so much here on Less Wrong). But Rolf isn't your average "guilter". Indeed, considering that he speaks fluent Bayesian, is one of the Singularity Institute's largest donors, and is also (as I understand it) signed up for cryonics, it's hard to imagine an "opponent" more "worthy". The Amanda Knox case may not be in the same category of importance as many other issues where Rolf and I probably agree; but my opinion on it is very confident, and it's the opposite of his. If we're both aspiring rationalists, at least one of us is doing something wrong.
As it turns out, Rolf is interested in having a debate with me on the subject, to see if one of us can help to change the other's mind. I'm setting this post up as an experiment, to see if LW can serve as a suitable venue for such an exercise. I hope it can: Less Wrong is almost unique in the extent to which the social norms governing discussion reflect and coincide with the requirements of personal epistemic rationality. (For example: "Do not believe you do others a favor if you accept their arguments; the favor is to you.") But I don't think we've yet tried an organized one-on-one debate -- so we'll see how it goes. If it proves too unwieldy or inappropriate for some other reason, we can always move to another venue.
Although the primary purpose of this post is a one-on-one debate between Rolf Nelson and myself, this is a LW Discussion post like any other, and it goes without saying that others are welcome and encouraged to comment. Just be aware that we, the main protagonists, will try to keep our discussion focused on each other's arguments. (Also, since our subject is an issue where there is already a strong LW consensus, one would prefer to avoid a sort of "gangup effect" where lots of people "pounce" on the person taking the contrarian position.)
With that, here we go...