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handoflixue comments on Inherited Improbabilities: Transferring the Burden of Proof - Less Wrong
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The sentence in particular that I objected to was
My impression was that you were claiming that, since the fake burglary hypothesis would imply murder, evidence must be extremely strong to be counted in favor of fake burglary. But I may have misunderstood you. At any rate, you elsewhere state that
If you agree with my point, then I don't see how you can find it odd that they would feel obliged to include more in their report than just the claim that the burglary was faked. Like you said, even if the evidence is fairly strong in favor of this assertion, far more evidence would be needed to convict those two of murder, which is presumably the point of the remaining 400 pages.
My claim is that to reach a desired level of certainty about the burglary being faked, you would need evidence of approximately the same strength required to reach the same level of certainty about murder. (In other words, that the prior probability of fake burglary is roughly the prior probability of murder.)
This is the very opposite of what I said! What I said was that if you knew with high confidence that the burglary was fake, then you would need almost no additional evidence to convict of murder.
"my claim is that to reach a desired level of certainty about the burglary being faked, you would need evidence of approximately the same strength required to reach the same level of certainty about murder."
This assumes that the burglary being faked is the only piece of evidence. If we have three sets of evidence, and each one suggests a 90% chance of guilt, and each is independent of the other, then we have probability (10:1) x (10:1) x (10:1) = (1000:1). No one set of evidence needs to have a (1000:1) probability of guilty in order to reach a final conclusion that the odds are (1000:1). Arguing via modus tollens about a single piece of evidence tells us only that that evidence, in and of itself, is insufficient proof. It tells us nothing about how that evidence may act cumulatively with other pieces of evidence.
No; I fully grant that other evidence that Knox and Sollecito are guilty, if it exists, would be evidence of the burglary being fake, which would lower the burden of proof on that hypothesis.
However, that isn't how Massei and Cristiani reason. They don't say, in the section on the burglary (which is at the beginning of the report), "and since we know from all the other evidence that Knox and Sollecito are guilty, we can therefore easily use these arguments about glass patterns to confirm that they did in fact stage the burglary, in case you were wondering about that". And it's easy to see why they don't say that: there wouldn't be much point, because if they've already shown that Knox and Sollecito are guilty, their work is done! (*)
Instead, what they say is "these arguments about glass patterns etc. prove that the burglary was staged. Now, having established that piece of evidence against them (i,e. the staging of the burglary), let us now consider the other evidence, which, in combination with the burglary, will show how really guilty they are."
(* ) Technically, staging a burglary is itself an offense, so there may actually have been reason for them to proceed this way. But in that case the burglary issue would have come at the end of the report, not the beginning.
"these arguments about glass patterns etc. prove that the burglary was staged. Now, having established that piece of evidence against them (i,e. the staging of the burglary), let us now consider the other evidence, which, in combination with the burglary, will give us an accurate probability on whether they are guilty"
I've bolded a single change to your quote. With that change made, do you feel this is a reasonable assertion?
No. The error is in the first sentence
They only (conceivably) prove the burglary was staged if you're already taking into account the rest of the evidence of murder.
That's only true if you assume p(A=>B) is 1
...or approximately 1.
(And by P(A=>B), I think you meant P(B|A), didn't you?)
P(Someone faked the burglary) != P(Amanda Knox faked the burglary). The report asserts the first, not the second, from my reading.
Given that "someone faked" is true, I think assigning an approximately 100% chance that Amanda Knox is guilty is rather seriously unfounded. What am I missing?
That "burglary was faked" is shorthand for "burglary was faked by Knox and Sollecito" throughout this post and discussion. The latter is what Massei and Cristiani argue, and is what would most strongly imply that Knox and Sollecito are guilty of murder.