Okay, so we seem to be in complete agreement about how the math works out. If so, then I’m confused as to why you object so strongly to the prosecution’s argument on purely mathematical grounds; I haven’t read their argument myself, so it’s entirely possible that the argument itself is weak in some way, but I think that right now we’re just talking about the math.
If we ignore their specific language, the plan of coming up with ~20 pieces of moderate evidence is a perfectly reasonable strategy for correctly establishing guilt, assuming that there is absolutely no mitigating evidence. Your complaint seems to be that they use different language/notation than you and I do to talk about evidence, which seems hardly fair.
Although I would also note that since humans are bad at intuitively distinguishing between moderate evidence for and moderate evidence against a hypothesis, trying to find many pieces of weak evidence is probably not a good strategy if the goal is to get humans to correctly decide the accuracy of an assertion.
ETA: By the way, I’ve been working under the assumption, based on the tone of the original post, that you think there are serious mathematical flaws in the prosecutions argument. If that’s not the case, and you just wanted to use this case as a point of illustration, then I apologize for the confusion.
What I gather is that the prosecution concludes, after the first twenty pages of the brief that discuss the break-in exclusively that the break in was almost certainly staged by Knox and Sallecito. But if they really thought that they would have already more or less made the case the Knox and Sallecito are guilty and the remaining 380 pages would be unnecessary. So the prosecution can’t be weighing the evidence correctly.
Okay, so we seem to be in complete agreement about how the math works out. If so, then I’m confused as to why you object so strongly to the prosecution’s argument on purely mathematical grounds; I haven’t read their argument myself, so it’s entirely possible that the argument itself is weak in some way, but I think that right now we’re just talking about the math.
If I may presume to diagnose your confusion, it seems that you’re compartmentalizing between “mathematical” aspects of an argument and “other” aspects. But I’m not. I’m taking it for granted that “the math” is the argument. Probability theory is a mathematical formalization of the process of argument and inference. It isn’t just a cool gadget that one throws in on special occasions.
So, I don’t object to Massei and Cristiani’s argument on “purely mathematical grounds”. I simply object to it, period—and in this post I have used mathematical language to describe, in precise terms, what my objection is.
(And I expected readers to assume, given my previous writing on the case, that this particular point was far from my only objection to Massei and Cristiani’s 427-page argument that Knox and Sollecito killed Kercher; hence I was not expecting replies of the form “well, but they might have other good evidence that Knox and Sollecito are guilty”. They don’t; we’ve already covered that.)
If we ignore their specific language, the plan of coming up with ~20 pieces of moderate evidence is a perfectly reasonable strategy for correctly establishing guilt, assuming that there is absolutely no mitigating evidence. Your complaint seems to be that they use different language/notation than you and I do to talk about evidence, which seems hardly fair.
I honestly have no idea where you’re getting this from. I don’t know of any passage in the post where I complained about Massei and Cristiani’s choice of language; and nor did I attempt to argue (as several people seem to have thought I did) against a strategy of proving one’s case by adducing a large amount of weak evidence in one’s favor (although as a matter of fact I do believe that is the wrong type of argument to expect for a proposition of this sort, and that people have probably been misled by detective stories and the like into thinking it a reasonable strategy, when it would actually be very difficult to make work in practice—that however would be the topic of a separate post, and isn’t addressed in this one).
My criticism of Massei and Cristiani in this post is really quite simple, or so I thought: the type of evidence that they cite to prove that the burglary was faked suggests that they did not realize how high the burden of proof for this proposition was—that, just to prove the burglary was faked, they needed evidence of the same level of strength as would be required to directly prove Knox and Sollecito guilty of murder.
Quite frankly, I’m baffled at how this point seems to have gotten lost, because I thought I was emphatic and indeed repetitious about it in the post.
If we ignore their specific language, the plan of coming up with ~20 pieces of moderate evidence is a perfectly reasonable strategy for correctly establishing guilt, assuming that there is absolutely no mitigating evidence. Your complaint seems to be that they use different language/notation than you and I do to talk about evidence, which seems hardly fair.
I think the assertion is that they appear to be coming up with ~20 pieces of evidence and then trying to say that each piece is very strong—or at least, they have done so for the burglary hypothesis, so they might be doing so for the other pieces of evidence too. Naturally, their methods of making each piece look very strong are flawed.
You almost pinpointed the reason why this happening here:
trying to find many pieces of weak evidence is probably not a good strategy if the goal is to get humans to correctly decide the accuracy of an assertion.
Humans are bad at intuitively handling evidence in general. There is a possibility that this case suffers from a serious malady: presiding judge Massei has decided the correct, accurate decision in this matter is that Knox and Sollecito are guilty, and has strategically prepared the judge’s report to get people to decide this way. This hypothesis explains why the judge has produced such a weighty document when 20 pages of it would have sufficed.
Okay, so we seem to be in complete agreement about how the math works out. If so, then I’m confused as to why you object so strongly to the prosecution’s argument on purely mathematical grounds; I haven’t read their argument myself, so it’s entirely possible that the argument itself is weak in some way, but I think that right now we’re just talking about the math.
If we ignore their specific language, the plan of coming up with ~20 pieces of moderate evidence is a perfectly reasonable strategy for correctly establishing guilt, assuming that there is absolutely no mitigating evidence. Your complaint seems to be that they use different language/notation than you and I do to talk about evidence, which seems hardly fair.
Although I would also note that since humans are bad at intuitively distinguishing between moderate evidence for and moderate evidence against a hypothesis, trying to find many pieces of weak evidence is probably not a good strategy if the goal is to get humans to correctly decide the accuracy of an assertion.
ETA: By the way, I’ve been working under the assumption, based on the tone of the original post, that you think there are serious mathematical flaws in the prosecutions argument. If that’s not the case, and you just wanted to use this case as a point of illustration, then I apologize for the confusion.
What I gather is that the prosecution concludes, after the first twenty pages of the brief that discuss the break-in exclusively that the break in was almost certainly staged by Knox and Sallecito. But if they really thought that they would have already more or less made the case the Knox and Sallecito are guilty and the remaining 380 pages would be unnecessary. So the prosecution can’t be weighing the evidence correctly.
If I may presume to diagnose your confusion, it seems that you’re compartmentalizing between “mathematical” aspects of an argument and “other” aspects. But I’m not. I’m taking it for granted that “the math” is the argument. Probability theory is a mathematical formalization of the process of argument and inference. It isn’t just a cool gadget that one throws in on special occasions.
So, I don’t object to Massei and Cristiani’s argument on “purely mathematical grounds”. I simply object to it, period—and in this post I have used mathematical language to describe, in precise terms, what my objection is.
(And I expected readers to assume, given my previous writing on the case, that this particular point was far from my only objection to Massei and Cristiani’s 427-page argument that Knox and Sollecito killed Kercher; hence I was not expecting replies of the form “well, but they might have other good evidence that Knox and Sollecito are guilty”. They don’t; we’ve already covered that.)
I honestly have no idea where you’re getting this from. I don’t know of any passage in the post where I complained about Massei and Cristiani’s choice of language; and nor did I attempt to argue (as several people seem to have thought I did) against a strategy of proving one’s case by adducing a large amount of weak evidence in one’s favor (although as a matter of fact I do believe that is the wrong type of argument to expect for a proposition of this sort, and that people have probably been misled by detective stories and the like into thinking it a reasonable strategy, when it would actually be very difficult to make work in practice—that however would be the topic of a separate post, and isn’t addressed in this one).
My criticism of Massei and Cristiani in this post is really quite simple, or so I thought: the type of evidence that they cite to prove that the burglary was faked suggests that they did not realize how high the burden of proof for this proposition was—that, just to prove the burglary was faked, they needed evidence of the same level of strength as would be required to directly prove Knox and Sollecito guilty of murder.
Quite frankly, I’m baffled at how this point seems to have gotten lost, because I thought I was emphatic and indeed repetitious about it in the post.
I think the assertion is that they appear to be coming up with ~20 pieces of evidence and then trying to say that each piece is very strong—or at least, they have done so for the burglary hypothesis, so they might be doing so for the other pieces of evidence too. Naturally, their methods of making each piece look very strong are flawed.
You almost pinpointed the reason why this happening here:
Humans are bad at intuitively handling evidence in general. There is a possibility that this case suffers from a serious malady: presiding judge Massei has decided the correct, accurate decision in this matter is that Knox and Sollecito are guilty, and has strategically prepared the judge’s report to get people to decide this way. This hypothesis explains why the judge has produced such a weighty document when 20 pages of it would have sufficed.