Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Psychohistorian comments on The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom - Less Wrong

42 Post author: komponisto 13 December 2009 04:16AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (632)

You are viewing a single comment's thread.

Comment author: Psychohistorian 13 December 2009 06:21:11AM 5 points [-]

Negligible. No different from the prior, which is dominated by the probability that someone in whatever reference class you would have put Amanda into on January 1, 2007 would commit murder within twelve months. Something on the order of 0.001 at most.

Suppose it were somehow revealed to you that three people had in fact committed the murder. Would you still maintain that K and S are no more likely to have been involved than anyone else in the relevant reference class? If not, doesn't this suggest that this quoted bit is an overstatement?

That's a genuine question; I haven't fully thought that concept through.

Comment author: komponisto 13 December 2009 06:46:48AM 0 points [-]

Suppose it were somehow revealed to you that three people had in fact committed >the murder. Would you still maintain that K and S are no more likely to have been >involved than anyone else in the relevant reference class?

There is a proximity effect, just as in the actual situation K's probability is slightly raised by the fact that a killing occurred in her house (and S's is in turn raised by his intimacy with K). But the evidence against G utterly destroys her explanatory value, and brings her probability back down to the prior.

If not, doesn't this suggest that this quoted bit is an overstatement?

No, because this is my posterior probability after taking into account the evidence against G.

Comment author: Psychohistorian 13 December 2009 06:58:35AM *  4 points [-]

But the evidence against G utterly destroys her explanatory value, and brings her probability back down to the prior.

This is true in reality, not in my hypothetical. If it were a fact that three people had been involved, as posited, the evidence against G would not explain anyone else away on its own. I'm using a counterfactual to attempt to show that your claim that there's no special evidence of her guilt is false.

You've stated: [A] P(Knox is guilty) = P(Random person from relevant social circle is guilty). It seems to me that [B] P(Knox is guilty; given multiple killers) > P(Random person from relevant social circle is guilty; given multiple killers). Assume [B] is true. The additional specification does not point to K, it only says that people other than G are guilty. Therefore, [A] should be false. So, I'm assuming you would take issue with the truth of [B], or else with my reasoning, and I'd be curious as to how and why either way.

Comment author: komponisto 13 December 2009 07:17:57AM 0 points [-]

[A] is only true given the evidence against G. Not knowing that evidence, we would have P(Knox) > P(random peer) by proximity.

Comment author: michaelsullivan 16 December 2009 02:59:57PM -2 points [-]

This is entirely wrong. The evidence against G should modify both P(Knox) and P(random peer that is not G) downward.

Proximity should keep P(Knox) > P(random peer) unless there is evidence specific to Knox which lowers her P (i.e. a good alibi).

Your statement about proceeding from the physical evidence and ignoring other things is a heuristic. The fact is that some random suspicious behavior by K is evidence against K, it is just extremely weak evidence. Let R = random suspicious behavior by K. I contend that P(K|R) > P(K|^R). Your arguments that many people do R all the time and are not murderers address the strength of the evidence, but do not address the sign, unless you wish to contend that people who engage in R are less likely or equally likely to be murderers than people who do not. You have made no such argument.

It's clear that the evidence against K should be overwhelmed by the evidence against G, given that no solid connection was established between G and K. But it isn't zero evidence, it is merely very weak evidence.

You have established a safety heuristic to keep yourself from overvaluing weak evidence, but your safety heuristic has it's own shortcomings, because it has caused you to give it zero weight, which is obviously wrong.

Comment author: komponisto 02 March 2010 03:37:48PM 0 points [-]

This is entirely wrong. The evidence against G should modify both P(Knox) and P(random peer that is not G) downward.

No, it is most certainly not "entirely wrong", if it is even wrong at all.

Explanatory value is the only attractor of probability: there is nothing that can possibly raise P(Knox) except improbable facts that require explanation (where the amount of probability flow as a function of the improbability of the explanandum is governed by Bayes' Theorem).

In this case, virtually all of the improbability of the data is contained in the mere fact of Kercher's death. But that fact is entirely and adequately explained by the actions of Rudy Guede; the evidence against Guede completely obstructs -- screens off -- the probability flow toward Knox.

That is the argument made in the post. Nowhere did I say that evidence of Guede's guilt is evidence of Knox's innocence, in the sense of lowering P(Knox) to below the prior. But the evidence against Guede absolutely is evidence against the hypothesis that Knox killed Kercher without Guede -- which is most of the Knox hypothesis-space (and thus where most of the probability flow toward Knox arising from Kercher's death was concentrated)!

(This point is especially important in view of all those comments from people saying that "the prior" should (already) take into account the fact that Kercher was killed. Well, if that's your prior, then it most definitely is lowered by the evidence against Guede!)

When you make a statistical argument of the form "well, a homicide was committed, so there's some probability of multiple attackers", you're starting from a position of ignorance of the details of the case, and computing an expected probability over all the various scenarios where there exists evidence of multiple attackers. But here, we know the details of the case, and we know that there is scant evidence of anybody but Rudy Guede being guilty (at least, we do if we're capable of telling strong evidence from weak).

Finally, these comments of yours

It's clear that the evidence against K should be overwhelmed by the evidence against G, given that no solid connection was established between G and K. But it isn't zero evidence, it is merely very weak evidence.

You have established a safety heuristic to keep yourself from overvaluing weak evidence, but your safety heuristic has it's own shortcomings, because it has caused you to give it zero weight, which is obviously wrong.

represent nothing but uncharitable pedantry -- the Bayesian analogue of my pointing out to you that "its" in the above sentence should be spelled without an apostrophe. It's not, and has never been, a question of whether P(Knox) is literally greater than P(random peer); the question is whether it's noticeably greater. If it makes you happy, I'm willing to concede that the evidence in this case raises P(Knox) from 0.001 to something like 0.0034. But that scarcely makes my argument "wrong", let alone "entirely wrong".

So that's why I have downvoted your comment: because, while it sounds all learned and serious, like you have an important probability-theoretic lesson to teach, it reduces to nothing more than a snark. (In fact, it may have been the exact comment I was thinking of when I wrote this.)

Seriously: "entirely wrong"? WTF?

Comment author: michaelsullivan 25 March 2010 06:06:04PM 0 points [-]

since you appear to still be watching this thread, it seems worth a reply even 3 months later.

Clearly "entirely wrong" is too strong and unnecessary verbiage in any case. I admit it did not even occur to me that you were using "=" to mean only "essentially equal in absolute terms".

Note, my comment was referring only to your response to Psychohistorian, not your general argument about why P(Knox) is very small given the information presented at trial, with which I agree wholeheartedly.

I apologize for my confusion. Here and in a few other comments, you seemed to be asserting not merely that the strong evidence against G put so much probability mass into P(G) that the differences between P(Knox) and P(random peer) became much too small to care about in absolute terms, but that it somehow changed the relative dynamic between P(K) and P(rp). The fact that neither probability was worth worrying about in legal terms doesn't change the '>' vs. '=' question, and that's the only thing I was responding to there. I also suspect the distinction matters in practice in rare cases, so I saw it as important enough to be worth picking the nit.

Comment author: komponisto 16 December 2009 07:05:18PM 0 points [-]

Your statement about proceeding from the physical evidence and ignoring other things is a heuristic.

It's clear that the evidence against K should be overwhelmed by the evidence against G, given that no solid connection was established between G and K. But it isn't zero evidence, it is merely very weak evidence.

Yes, I agree. Did you read this discussion before making this comment?

Comment author: magfrump 13 December 2009 08:54:24AM 0 points [-]

the issue at stake is P(multiple killers) being very small, and P(knox guilty) - P(random person guilty) is less than zero due to the P(G guilty).

Or at least that is how I would weight them.

Comment author: Unknowns 13 December 2009 10:30:12AM 1 point [-]

Given that someone was killed, the probability of multiple killers is not "very small", according to statistics. Definitely not more than 50% but definitely substantial (as I stated in another comment.)

Comment author: Unknowns 13 December 2009 08:06:09AM 1 point [-]

The percentage of murder cases that involve multiple murderers is relevant to the idea that the evidence against G "brings her probability back down to the prior," and this percentage is much higher than you think it is (i.e. it is higher than 1% of cases, and this is enough that AK's probability will definitely not go back to the prior. In fact it seems to be in 10-20% of cases),

Comment author: rmattbill 15 December 2009 12:39:39AM 3 points [-]

That may be true, but many cases of wrongful conviction involve multiple innocent defendants. The Norfolk Four is a perfect example. At one point the police suspected SEVEN men of the attack, even though the coroner said there was only evidence of an attack by one person. In the end, it turned out one person, a known rapist, had committed the crime, but not before four of the innocent served over a decade in prison.

For those who criticize Knox pointing the finger at Lumumba, again, look at the Norfolk Four case where the first suspect, innocent, wrongfully accused a friend, who then wrongfully accused several friends, who then wrongfully accused several of their friends! It might be impossible to understand the mindset that leads to something as wrong as falsely accusing someone else, but it's happened to a lot of people, and normally they are treated with far less scorn than has been poured on Knox by her critics.

Comment author: komponisto 14 December 2009 07:37:34AM 1 point [-]

This is accounted for in my updated estimates.

Comment author: Unknowns 14 December 2009 07:59:15AM 0 points [-]

Ok, but given your updated estimates, it is consequently unreasonable to just dismiss psychological and interpreted physical evidence (i.e. bloody footprints, crime scene rearrangement and so on). Whether this is actually so or not, it is very possible that these things could add together to give enough evidence to say that someone is probably guilty; going from a 1% to a 99% chance does not take an extremely large amount of evidence.

And this seems to imply that an hour on the internet does NOT beat a year in the courtroom. To know whether this is true or not you would actually have to know the evidence in more detail. For example it does seem that even in Judge Micheli's report there is a good deal of detail that has been generally unreported in English.

Comment author: komponisto 14 December 2009 08:07:26AM 1 point [-]

Ok, but given your updated estimates, it is consequently unreasonable to just dismiss psychological and interpreted physical evidence

I don't see why this kind of stuff is any more powerful than its counterparts on the other side: K & S's benign personalities, lack of criminal history, lack of motive, etc.

Comment author: Unknowns 14 December 2009 08:15:07AM 0 points [-]

That may be true. I read (I didn't pay attention to the source, it could be just a rumor for all I know) that AK sent an email to a friend, shortly after coming to Italy, saying that she had convinced a stranger to have sex with her on a train. If true that would show a dangerous kind of behavior, even though not criminal. Assuming she might be guilty (for the sake of argument) the most likely explanation would be that they were "playing around" and things got out of hand, not that anyone ever was planning to murder someone.

In any case it seems my last point stands: the evidence as it has been presented to us may be unpersuasive but that doesn't mean that the same kinds of evidence couldn't become persuasive in principle, and this may be exactly what happened in the trial.