Komponisto makes a strange assertion. The prior is not the reference that "someone would commit murder" - there is a body. A more appropriate prior is "someone who lives with someone who was murdered committed that murder" - I'm guessing that base probability is of the order of 0.1. Once we take into account that AK and MK aren't in a relationship, AK is female, and there is very strong evidence that someone else committed the murder then I'd agree that the probability drops, but these pieces of evidence don't cancel out leaving us with the original prior - the final probability may be higher or lower.
Also the "complexity penalty on the prosecution's theory of the crime is enormous" - that may mean the case was flawed, but it's not evidence she didn't kill MK unless you are willing to give some weight to the conviction (at <0.001, I assume you are not). Or to put it another way, even if the prosecution is completely wrong you cannot set the probability of guilt to 0. This is like assuming AK is guilty because her parents criticized the Italian legal system.
Overall I hope I am a bit more cautious about my abilities than you. In the first half you explain why you, as a human being, cannot be trusted to be rational. Then you set out your case. Why should I trust your rationality, but not others'?
"But come on," says a voice in your head. "Does this really sound like the behavior of an innocent person?"
Absolutely. I saw the amount of emphasis prosecutors (and 'guilty' advocates) were placing on this sort of crap and immediately updated in favour of innocent. Presenting lots of ridiculous nonsense is evidence that you haven't not anything better.
"But come on," says a voice in your head. "Does this really sound like the behavior of an innocent person?"
Absolutely. I saw the amount of emphasis prosecutors (and 'guilty' advocates) were placing on this sort of crap and immediately updated in favour of innocent. Presenting lots of ridiculous nonsense is evidence that you haven't not anything better.
What I found most interesting about this exercise is the number of people who made this deduction. It is an error. They are appealing to the public and the jury, whose rationality you impugn. The prosecutors and especially advocacy websites will present (a lot of) this crap regardless of whether they have better evidence. This is normal behavior for prosecutors, just as changing stories, implicating random people, and signing confessions is normal behavior for innocent people. Similarly, differences in tone and organization of the two advocacy sites is pretty much useless.
Measuring cellphone call times down to "3 seconds" is meaningless. Mobile-to-mobile call setup times over the cellular network can easily be 4-5 seconds or more. While the network is trying to find the phone you called guess what ... you hear ringing on your phone even though a connection hasn't been set up. So it wouldn't be unusual for the caller to hear 5-6 seconds of ringing before the called phone starts ringing. 3 seconds of ringing on the called phone could easily translate into 6-9 seconds of ringing on the calling phone.
In the US, I prefer to hang up before the voice mail prompt. It leaves a missed call message and makes it easier for the called party. But when in Italy, better let the phone ring until voice mail just in case the called party died ....
Here's a thought exercise, that for me clears the confusion in this case. Pretend that you don't already know who the suspects are in this case, and are looking at the evidence to try and find one for the first time. You have no preconceived notion as to who killed Kercher.
Your evidence comes in two weeks after the killing and you have a bloody hand print on a pillow, fingerprints elsewhere in the room, saliva DNA outside the victim and skin or saliva DNA inside the victim as well. All of this is of one person, Rudy Guede.
You look up Rudy Guede and you find that in the weeks prior to the murder he was involved in three separate break-ins involving a knife, but was not arrested. When you try to locate him, you find he has fled the country to Germany.
At this point, do Knox and Sollecito even come into this story as anything other than footnotes? There are no interrogations, no cartwheels, no rumors of bleach purchases, no "foxy knoxy", no stories of sex on a train, none of it. The knife in Sollecito's flat, with a minuscule amount of DNA on the blade that doesn't identify Kercher but can't exclude it never enters the scene. Neither does the bra clasp found 47 days later.
Blood drops of the victim found in a co-habituated bathroom with mixed DNA of roommates doesn't seem all that sinister.
For me, this clears up who the guilty party in this case quite nicely, and takes my "feelings" out of the equation.
I'm a bit curious about something:
If read your post correctly, you feel that you can discount as pretty much irrelevant the opinions of quite a lot of people (jurors, police, etc), on the simple basis that people can be spectacularly wrong on occasion. ( I'm really not sure about this.)
In fact, as far as I can tell, you start from “clean” priors and do all your updating based only on the “physical evidence”; no opinions entering your calculation.
This seems almost OK, but something's nagging at me: how can you obtain thirty bits of confidence in your estimate using only evidence received from other people, via the Internet?
I'm also not sure about this, but your post seems to imply that a “good Bayesian” would be expected to assign that amount of confidence to his answer after only a couple of hours of surfing the Internet. I'm not saying that's impossible, but it really sounds very unlikely to me.
I'd very much like to see a chain of numerical reasoning that reasonably puts a 1:1000 upper-bound on the likelihood that Guédé is innocent, without starting with implicit assumptions of 100% certainty about data read from the net.* If you think an hour on the Internet is enough to reach t...
Having review your evidence and some other evidence that I was pointed in the direction of I have to admit I may have been wrong. Knox and the other guy are probably innocent.
There were a few things that lead me to my original conclusion: -The DNA evidence -Amanda changing her story -My belief that it was ridiculous that the police would go to all this effort to frame them if they were innocent.
The DNA evidence has been refuted, I can't say I understand this but I'm willing to accept there is a lot of doubt there.
Amanda changing her story seems like evidence that she is a liar and seems a ridiculous thing to do if you are a murder suspect. (I still think it was really stupid of her and totally the wrong thing to do.) But at the the time she wasn't more of a witness than a suspect and she possibly believed that this would get her off the hook and out of interrogation.
The third point about the police conspiracy is the most interesting. I have a huge bias against conspiracy theories. As soon as anyone starts to go "Wake up sheeple, you're being controlled." I immediately switch off. The quote you use from me at the beginning of your article is partly a referenc...
Wasn't there a post here a while back that talked about how anyone positing a confidence of 0.999 on something non-trivial was most likely to be suffering from their own cognitive biases?
Good points, marred by what appears at first blush like double standards. Why are you willing to selectively discount some DNA evidence while you admit other ?
You say "the supposed Sollecito DNA on Meredith's bra clasp just plain does not count" - what is that "supposed" doing in here ? The FOA site admits that the clasp was shown to carry small amounts of Sollecito's DNA.
Why does it "not count" ? Admittedly, the handling of that evidence may not have been up to the standards normally demanded by the judicial system, but why should that matter to a Bayesian analysis ? All we're interested in as Bayesians is the ratio between P(DNA on clasp|Sollecito guilty) and P(DNA on clasp|Sollecito not guilty).
The defense may well have its own convenient narratives about how Sollecito's DNA "could have been transferred to the fastener in any number of ways" owing to carelessness on the part of the police. Those narratives are just as much noise as all the other noise you've pointed to. The details of US Department of Justice guidelines for forensics are also burdensome details for the defense.
The danger of coming across as arrogant - that is, more confide...
It seems to me that the prosecution's case against Sollecito relies quite heavily on the evidence they claim proves he was present at the crime scene since they have no other solid evidence against him.
The reasoning used by the prosecution is basically what Jaynes calls the 'policeman's syllogism' in Probability Theory: The Logic of Science. The reasoning is of the form:
Here A is (Sollecito was present at the crime scene) and B is (DNA tests on the bra clasp detected Sollecito's DNA). If we use C to stand for our background knowledge then by Bayes theorem:
p(A|BC) = p(A|C) * (p(B|AC) / p(B|C))
The premise of the policeman's syllogism "If A is true, then B becomes more plausible" takes the form
p(B|AC) > p(B|C)
And by Bayes theorem if this premise is true then:
p(A|BC) > p(A|C)
as stated in the syllogism. Now the significance of the evidence B depends on the magnitude of p(B|C) - the only way finding B to be true can greatly increase the plausibility of A is if p(B|C) is very small relative to p(B|AC). In other words, the prosecution's argument rests on the background ...
You're even more overconfident than Eliezer. Even he didn't say that the probability of guilt should be less than 10%.
Also, you ignored the evidence of the scene being rearranged. As far as I can tell, there was substantial evidence of this, and substantial evidence of it being by someone other than RG. This implies substantial evidence that someone else was involved. Even if this doesn't necessarily imply AK is guilty, it definitely implies a probability higher than the original prior (which itself would be much, much higher than the probability you assign of 1 in a 100,000, given the proximity of the persons).
Basically, you are overconfident if you assign less than 10% chance of guilt. And the fact that your opinion is much more extreme than anyone else's doesn't show that you are more rational, but is very strong Bayesian evidence of overconfidence bias on your part, since it is well known that humans are naturally overconfident, not underconfident.
I've wanted to reply here for a good while, so now that I've finally emerged from Lurkdom, I might as well do that. Great post!
Think about what you're doing here: you are invoking the hypothesis that Amanda Knox is guilty of murder in order to explain the fact that she hung up the phone after three seconds.
That was beautiful. Probably the single most important sentence in that whole article, at least in terms of convincing me to your reasoning.
I have to say though, at least one thing you say sounds not just overconfident but blatantly partisan:
known to have had utterly benign dispositions prior to these events".
I wonder how you could know this. If you picked it up from any pro-Knox source of information, it strikes me as a safe assumption that such a source would paint the defendants as angels regardless of the truth.
I'd also like to ask, how necessary to your argument was using that Jesus example? That's preaching to a very narrow choir, even considerably narrower than just "atheists". If that's what you wanted then no problem, but I'm thinking about the lost potential of this article to be persuasive to a more general public. This would be a great article to link friends to if it didn't rely on, not just the tools of rationality, but on specific conclusions shared by (I presume) most lesswrongians.
How much does the choice of words bias peoples' thinking?
"Lone wolf theory" - If you google this term, what comes up is, sadly, the Amanda Knox case, and then terrorist cases like the DC sniper and the holocaust museum shooting. Rudy was not a terrorist, so some people may unconsciously dismiss the likelihood that he was a "lone wolf." And although it's a "theory," the phrase "Lone Wolf theory" sounds like something nutty, whereas it's really the normal scenario in such murders. The onus should lay on disproving this scenario, not proving it.
"Cartwheels" - Amanda Knox is said to have done cartwheels during her interrogation. Cartwheels have a connotation of joy. To prove my point, if you google "cartwheels of joy", it gets 82,400 hits. If the police had chosen the term "gymnastics," then it might be easier to understand why a young girl cooped up for 30 hours might engage in such behavior. Even if she did cartwheels and only cartwheels, she wasn't joyful.
"Foxy Knoxy" - Amanda's character was assassinated by the press long before her trial, and this catchy phrase was responsible for much of it. Ironically, the phrase came from Amanda Knox herself on her Facebook page, according to one of her old friends who stood up for her character.
Words played a powerful role in bias in Amanda's case. I don't think I even need to qualify that as my opinion.
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.
Out of one thousand criminal trials in which the Less Wrong conventional wisdom gave the defendant a 35% chance of being guilty, you would expect to be able to correctly determine guilt nine hundred ninety nine times?
I'd like to suggest another type of rationality test for this site. The top contributors should randomly make posts that are flat-out wrong to see how they are received; and they should also randomly make legitimate posts under different names.
@OP: you have appealed to rationality in examining this case... then you come up with this:
"1. 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. "
The FACTS include 1) the police came to "her house" and discovered a murder victim in one bedroom and 2) she was tried and convicted. You seem to have given these zero weighting in your final c...
I know this is an old thread, but for any people just now reading it, I thought I'd pass along this bizarre development.
(Beginning thread for a debate with Rolf Nelson. Others also welcome to comment, of course.)
Okay, Rolf, so to get things started, I'd like to get your numbers out on the table. So, if you wouldn't mind, please tell me, first of all, your current posterior probability estimates for the guilt of:
(I expect we'll mainly focus on Knox and Sollecito, since that's obviously where our main disagreement is; I've included Guede for the sake of comparison.)
Next, I'd like to know your priors for Knox and Sollecito (and Gued...
*cackles evilly and cracks metaphorical knuckles*
The circle is defined as the locus of points an equal distance from a center on a plane. A square is defined as a regular quadrilateral - i.e. a shape with four sides of equal length separated by four angles of equal magnitude. If you allow that "distance" may be generalized) to be applicable to other geometries than Euclidean...
...what is the shape of a circle on a chessboard, where "distance" is measured by the number of king-moves?
I believe this is a useful object lesson in the difficulty of constructing properly impossible propositions.
Edited to make the square have four sides, not three. What was I thinking...?
Well, maybe she had superpowers. Or was killed by her time-traveling past self. When you get to probabilities this low, boy do you ever get to make shit up.
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.
I'm ashamed to say I failed this one, and badly.
I'm new to the Way of Bayes, and I've been reading the sequences regularly (that's why I'm on this post, actually) and thinking I've been doing pretty well, but this illustrates that I have a long, long way to go.
I did do a whole lot better than the jury in this case, such that I would never have convicted Knox and her boyfriend, but I still came away with about a 60% probability of their having been guilty, with Guede at >95%.
I started with the pro-guilty website, and thinking back I clearly privileged t...
A flurry of more recent comments, (concerning in particular the nature of evidence), plus some private message correspondence, provides me with an excuse to make what are probably somewhat-overdue comments succinctly summarizing the main points of this post, addressing the most important issues and objections raised by others, and tying up some loose Bayesian ends.
Objections raised to my arguments seem to fall mostly into the following categories:
(1) Bayesian pedantry: pointing out that weak evidence is distinct from zero evidence, that rational evidence ...
My ADHD brain lost interest in this after the huge discussion here covered pretty much everything having to do with the trial. And komponisto knows this stuff way better than I do so I'll let him respond. But nearly all of the regulars here looked at the exact same evidence you are bringing up now and nearly all of us eventually concluded that it was more likely than not that AK was innocent. Moreover, I specifically recall discussions of every single point you bring up and I believe every single one was resolved. So you might want to look back at the comments to the original post (the test of your rationality one) before you make komponisto go through all this again.
Since I was heavily involved in the discussion of the Lumumba 'accusation' I'll just add this: If AK and RS cleaned up their own involvement with the crime, but intentionally left the evidence implicating Guede wtf would AK not just accuse him to begin with? It seems likely bordering on obvious that AK was interviewed under duress, that the police had seen her text to Lumumba as implicating evidence and fed her his guilt. As a result, AK either made up or dreamed this bizarre pseudo-memory in which Lumumba was present....
komponisto, can I just say that you have very eloquently voiced my very thoughts on this case. In my blog article, "Logic Trumps Innuendo" I wrote the following:
"As I surf the net, reading a variety of comments in regards to this case there is much speculation about evidence in this case. Much of it was not used at trial, but somehow made it into the public consciousness through ongoing press leaks during the investigation, such as:
"Knox was seen with a mop and bucket the morning of the murder." What does that mean exactly? The inn...
Excellent post. I don't think I'm ready to wield those sharp implements with quite so much flourish yet; the chance of lopping off my own limbs is currently too high.
However, there are some specific parts of your post I disagree with.
...You have to shut that voice out. Ruthlessly. Because it has no way of knowing. That voice is designed to assess the motivations of members of an ancestral hunter-gather band. At best, it may have the ability to distinguish the correct murderer from between 2 and 100 possibilities -- 6 or 7 bits of inferential power on the ab
Can anyone find statistics that could tell us what is the probability the crime scene at any given murder contains physical evidence sufficient to indicate a suspect? I would expect it to be around .8-.9 but I don't really have any idea. I'm not convinced that that probability is high enough to completely outweigh the probability that AK and RS had something to do with the crime given that
they knew the victim
are sociable 21 and 24-year-olds (one of them studying abroad) without alibis on a Saturday night
the probability that Guede did not act alone (
How did Less Wrong do by comparison? The average estimated probability of Amanda Knox's guilt was 0.35 (thanks to Yvain for doing the calculation).
Yvain! How could you? What did the probabilities do to deserve that kind of abuse? (I strongly assert that averaging the probabilities is not a good way to combine such estimates.)
Am I really suggesting that the estimates of eight jurors -- among whom two professional judges -- who heard the case for a year, along with something like 60% of the Italian public and probably half the Internet (and a significantly larger fraction of the non-American Internet), could be off by a minimum of three orders of magnitude (probably significantly more)? That most other people (including most commenters on my last post) are off by no fewer than two?
Your assertion of such a high probability of guilt does not constitute a claim that most other c...
Serious nitpicking going on here.
Probability theories and the philosophies thereof are of interest to me and there are a lot of intuitive traps that are easy to fall into.
The whole point of my post is that from the information provided, one should arrive at probabilities close to what I said.
If that is what your point was then I actually disagree with it. I am not comfortable giving odds of 1:999 after looking briefly at two biassed webpages and a wikipedia page that you tell me is fluctuating at the whims of editorial bias. I know damn well I'd be wrong more than once if I did something like that 1,000 times.
Don't forget that "the order, manner, and quantity of browsing will be left up to [them]". It would be quite reasonable for someone to decide to read until a certain level of confidence has been reached. Once you are 99% confident that the poor girl is innocent what do you hope to achieve by marinating yourself in more and more evidence (or, for that matter, the lack of it)?
It would be great if I could go all Liam Neeson and say "if you let her go now, that'll be the end of it. I will not look for you, I will not pursue you. But if you don't, I will look...
these two things constituting so far as I know the entirety of the physical "evidence" against the couple
I'd like to know your reaction to this argument. There is some other evidence against the "lone wolf" theory and pointing more towards Amanda, specifically that Meredith's bra was removed and the scene rearranged after her death (and not by Rudy), the bloody footprints that match Amanda, and the witness placing all three of them together near the house around the time of Meredith's death.
(Edited to fix formatting)
I'm a little late to this game, but I spent over an hour, maybe two, comparing the information from the two websites. I had known nothing previously about the case.
My answers: 1: 0.05; 2: 0.05; 3: 0.95; 4: 0.65
So, I feel pretty vindicated. This was a great complement to Kaj Sotala's post on Bayesianism. With his post in mind, as I was considering this case, I assigned probabilities to the existence of an orgy gone wrong as against one rape and murder from one person. There is strong Bayesian evidence for Guédé's guilt, but it's exceedingly weak for...
On the "liar" issue, and the implication of Lumumba:
What numerous people (not here, for the most part, but with some exceptions) have been either forgetting or ignoring, almost to the point of obstinacy, is that Knox did not come up with Lumumba's name spontaneously. She and Lumumba had exchanged text messages on the night of the killing; in one of them, Amanda wrote "see you later". Her interrogators questioned her aggressively about this correspondence, clearly with the implication that Lumumba (as well as Amanda herself) might have b...
Rudy Guédé's won his appeal. His sentence has been reduced to 16 years -- ten less than Knox and nine less than Sollecito.
Funny world.
I have no opinion on the guilt or innocence of Knox or Sollecito. I've read the biased accounts of the evidence with amazement. I assumed Guédé's guilt was obvious. Kinda speechless over this new twist. While I can imagine someone thinking all parties were equally guilty, I am unable to find any rationale for deeming Guédé less guilty.
The error here is even asking a question about Amanda's motivations when you >haven't established an evidentiary (and that means physical) trail leading from >Meredith's body to Amanda's brain.
Indeed, that's counterintuitive. I believe it to be counterintuitive because it is incorrect. Amanda Knox was a roommate of Meredith Knox's; the initial likelihood of her being responsible is raised by that fact alone. It is normal for police to question motives of people close to the decedent, and it is good practice.
Suppose Hubby ends up shot a few dozen t...
http://www.casavaria.com/cafesentido/2009/12/05/5268/amanda-knox-sentenced-to-26-years-in-italy/
These are the concerns as delineated. From the above linked blog.
"The case for appeal is complex and rests on several very firm claims of prosecutorial misconduct:
1.The defense was denied the opportunity to present its own DNA experts;
2.A neurologist acting as witness for the defense testified that Knox could have been subjected to such intense stress, between the horror of the killing and police intimidation that she falsely remembered details that initia...
I haven't deeply read or studied the whole case itself — but by all means this is a beautiful, detailed, clearly written exposition of your train of thoughts. Thank you.
And yes, the mental suffering of spending two decades in jail + being despised by everyone around when you're actually innocent shouldn't be easy to face even with the highest possible dose of stoicism one could inject herself.
Hi Nick, While I appreciate that you don't seem to be one of the irrational Knox haters, your comments about the evidence contain a couple of errors, and the one that don't leave out some important facts which cast doubt on almost every single claim.
-Yes, Knox's DNA was founded mingled with Kercher's, but almost all of it was in the bathroom they shared. It would've been almost impossible NOT to find a few instances of their DNA mixed in such a small place, and a place where humans shed copious amounts of hair and skin cells, and even blood (shaving cuts, etc.).
-Not one shred of Knox's DNA was found in Kercher's room. The idea that she somehow managed to remove every microscopic shred of her DNA, while leaving Rudy Guede's behind, is completely implausible. This alone casts enormous doubt on the prosecution's theory. DNA in the bathroom simply proves Knox and Kercher lived together. A total lack of DNA in Kercher's room is compelling evidence she was not at the scene of the crime.
-No traces of bleach were found at the crime scene. Numerous rumors about bleach are clogging message boards all over the internet, including false stories about receipts which showed Knox buying bleach ...
For those interested, Netflix has a new documentary out about the case: https://youtu.be/9r8LG_lCbac
Dear fellow-poster Desrtopa --
Something called a "karma problem" has prevented me from replying directly to your comment at 03 February 2014 08:52:06AM. In the hope you will spot it, my reply will be posted here. I'm afraid it's the last comment I'll have time for; your reply to it, should you choose to post one, will be the last word in our exchange.
...Suppose that you were living in a rather more paranoid country, where the government suspected you of subversive activities. So, they took a current captive suspect, tortured them, and told them
Reply to myself:
I hereby withdraw every negative thing I have said about Amanda Knox at this website. In the period since I posted the comment immediately above, I could not drive from my mind a remark my fellow-poster Desrtopa made in a post at 03 February 2014 07:39:06AM. In effect, Desrtopa asked whether I would fault a person for giving changed-stories because of torture; if I wouldn't, why would I fault the person for giving changed-stories under interrogation so harsh that its effect on the person being questioned would be tantamount to that of torture? At the time, I avoided answering Desrtopa's question.
Just a few minutes ago, I read commentary by a "veteran FBI agent" named Steve Moore. The commentary was posted at http://www.injusticeinperugia.org/FBI7.html , which is a page of a website called Injustice in Perugia. Having known really nothing about interrogation before I read Moore's remarks--and having had no sense how a law-enforcement professional would evaluate various types of interrogation--I had no right to remark on Amanda Knox's performance under interrogation in this case. Moore's remarks have persuaded me of what Desrtopa was, in effect, asking...
Enter a comment here
Komponisto I have read your account and interpretations of the evidence, and am refreshed and somewhat relieved to finally find some sense of perspective regarding the events. I was troubled by the outcome of the trial, in my mind the events as they were presented simply did not correlate together. When events are correctly modelled, all additional evidence reinforces the hypothesis. Your Bayesian analysis brought a perspective to the likelihood of the various evidence aspects. The prosecutors presentation of the facts was full of i...
A fascinating look at Roman law versus Germanic:
"Italian Law and You - Welcome to the Jungle!" by Amanda Sorensen
http://www.bestofsicily.com/mag/art315.htm
By far the most important evidence in a murder investigation will therefore be the evidence that is the closest to the crime itself -- evidence on and around the victim, as well as details stored in the brains of people who were present during the act.
the evidence against Guédé is such that the hypothesis of her guilt is superfluous -- not needed -- in explaining the death of Meredith Kercher
I think you’re begging the question here. Those who are convinced that K&S are guilty seem to believe that the evidence from the crime scene itself suggests tha...
And by the way, if one takes your approach of starting from the crime scene and working backwards you must immediately confront the apparent staging of a break-in at the victim's residence. Which, if I recall correctly, was what initially made the Italian authorities suspicious of Amanda Knox.
Your point about privileging the hypothesis, and the fact that we feel a need to explain away weird facts in order to believe Knox's innocence, is excellent, though it gets rather buried in a very long post.
As far as the probability estimates go, I expect that many people (like me) did two things: erred on the side of underconfidence, and used numbers as conveying a general feeling. Particularly since it's a criminal case, it doesn't take much to disagree with a conviction. If I'd put the odds of Knox's guilt at .95, I'd say she'd been wrongly convicted, a...
there's really no reason those numbers should too much higher than they are for a random inhabitant of the city
Actually simply being in the local social network of the victim should increase the probability of involvement by a significant amount. This would of course be based on population, murder rates, and so on. And likely would also depend on estimates of criminology models for the crime in question.
I have heard that the acquittal of Amanda Knox has been overturned. The sources I have found have mentioned the possibility that Knox could be extradited from the US back to Italy and don't rule that out as a possibility. I am hoping someone with an interest in the Knox case (Komponisto) or someone familiar with US laws could tell me whether that is a possibility.
This is relevant to me since simply labeling Italy as a corrupt state that I wouldn't ever visit costs very little (I have no particular reason to visit Italy). However if Knox is (or even could b...
This post is a year and a half old now, but I think this is still worth saying:
..."But come on," says a voice in your head. "Does this really sound like the behavior of an innocent person?"
You have to shut that voice out. Ruthlessly. Because it has no way of knowing. That voice is designed to assess the motivations of members of an ancestral hunter-gather band. At best, it may have the ability to distinguish the correct murderer from between 2 and 100 possibilities -- 6 or 7 bits of inferential power on the absolute best of days. That ma
This type of thing has no place on Less Wrong. You're telling us to ignore an intuition—not just to be skeptical of it, but to ignore it—because of what is, at best, an educated guess about how we evolved.
This is not correct. I'm not telling you to ignore it; I'm telling you that it's worth no more than a few bits of evidence -- few enough to be swamped into unnoticeability by the other data in this context. And, as far as I know, the idea that we evolved in small bands has more than enough scientific support to be taken as a given.
"This type of thing has no place on Less Wrong" is far too harsh, even if you disagree. (It reminds me of "entirely wrong".) Do you have any important disagreement with me about the relative strengths of the evidence under discussion here?
I have a strong preference for the pragmatism of Occam's razor. If William of Occam had been the Knox case prosecutor it would have never come to trial. When supporting negative cultural stereotypes (i.e. promiscuity of American college girls) becomes more important than a rational outcome results like the Knox verdict arise as the judge overlooks evidence to punish the stereotype instead of the defendant.
Ok- many people have already pointed out that the prior should be probability of having committed murder if you live in the same house as someone murdered. Now, I would like to add that the psychological evidence shouldn't be completely and utterly discounted.
1) Knox knew Guede and Kercher, the murderer and the murdered, and is thus not random. This alone is reason for suspicion (though certainly not indictment).
2) Knox wrote a story about the drugging and rape of a young woman. Anyone have statistics on how many murderers have written such rape- fant...
komponisto - you are a genius. For months I have felt that Amanda and Rafaelle were clearly innocent, but I could not properly rationalize or verbalize my feelings. How could the entire internet be wrong? How could the jury be unanimously wrong? Now I understand. Thank you and I love your blog. As others have noted, this site is the only place I have found cordial and intelligent debate among the opposing viewpoints.
I find the evidence of the conspicuousness of the prosecution's investigation and case for Amanda and Raffaele's guilt much more suspicious and compelling than the evidence left by Amanda and Raffaele. What would the probability/certainty numbers be on that?
I think it's important to establish that it is likely that Knox and Sollecito could be lying about large portions of the night's events. Certainly they have told some lies. They were even legally allowed to lie as witnesses in Italian court. They may very well have been at the apartment before or even during the murder. It still does not make them guilty of murder.
This was a brilliant post. You deserve buckets of karma.
I didn't read the first part of the series until later - I wish I could have participated.
There something like a TV bias. In TV shows there often physical evidence at a crime scene that's needed for the narrative of the story. In real life there often isn't a lot of physical evidence.
That bias is strong enough to let some prospectors ask jurors about how much they watched shows like CSI to select jurors that don't believe that there has to be physical evidence.
To me it seems you are a victim of the bias that real life crime scenes look like TV crime scenes.
For what it's worth, I would have been much more inclined to agree with you before I became a practicing attorney. Having practiced law for many years, I've had many opportunities to assess a case based on hearing one (sometimes 2) sides of the story and then to learn a lot more about the case through the discovery process and then the trial process.
In short, I have a lot of practice in assessing peoples' guilt or innocence and I'm pretty confident that Amanda Knox was involved in the murder of her roommate.
The most important of which is: if you only do what feels epistemically "natural" all the time, you're going to be, well, wrong.
Then why do I see the term "intuitive" used around here so much?
I say this by way of preamble: be very wary of trusting in the rationality of your fellow humans, when you have serious reasons to doubt their conclusions.
Hmm, I was told here by another lw user that the best thing humans have to truth is consensus.
Somewhere there is a disconnect between your post and much of the consensus, at least in practice, of LW users.
Related: Netflix has a new show about the Knox case. https://www.facebook.com/netflixus/videos/10153892712508870/
I am sorry to ask since it looks like a great post, but could you kindly point me to the bit you actually do the math/reasoning about the estimatives?
Whoops, looks like Amanda Knox is guilty again. Of course, the lack of double jeapordy protection in Italy might be an impediment to their extradition request.
This might not be seen by many, but it might make your day to hear that Amanda Knox has just been acquitted.
Your first paragraph was enough for me to halt. Consider the source. If what the internet is saying is more correct than what the Italians were told and innocently believe, as did I, then it's no waste of time at all. Some of the people on the internet are whack, some have studies hours and hours and hours with an open mind.
I'm a little late to this game, but I spent over an hour, maybe two, comparing the information from the two websites. I had known nothing previously about the case.
My answers:
So, I feel pretty vindicated. This was a great complement to Kaj Sotala's post on Bayesianism. With his post, as I was considering this case, I assigned probabilities to the existence of an orgy gone wrong as against one rapist-murderer. There is strong Bayesian evidence for Guédé's guilt, but it's exceedingly weak for Sollecito and Knox. This has really he...
I'm a little late to this game, but I spent over an hour, maybe two, comparing the information from the two websites. I had known nothing previously about the case.
My answers:
So, I feel pretty vindicated. This was a great complement to Kaj Sotala's post on Bayesianism. With his post, as I was considering this case, I assigned probabilities to the existence of an orgy gone wrong as against one rapist-murderer. There is strong Bayesian evidence for Guédé's guilt, but it's exceedingly weak for Sollecito and Knox. This has really he...
I'm a little late to this game, but I spent over an hour, maybe two, comparing the information from the two websites. I had known nothing previously about the case.
My answers:
So, I feel pretty vindicated. This was a great complement to Kaj Sotala's post on Bayesianism. With his post, as I was considering this case, I assigned probabilities to the existence of an orgy gone wrong as against one rapist-murderer. There is strong Bayesian evidence for Guédé's guilt, but it's exceedingly weak for Sollecito and Knox. This has really he...
Made a claim that verdict used Bayesian inference and then failed to support it . It also overlooked elements of the verdict were composed of complete supposition that had no supporting evidence
Your argument is entirely flawed.
A flurry of more recent comments, (concerning in particular the nature of evidence), plus some private message correspondence, provides me with an excuse to make what are probably somewhat-overdue comments succinctly summarizing the main points of the post, addressing the most important issues and objections raised by others, and tying up some loose Bayesian ends.
Objections raised to my arguments seem to fall mostly into the following categories:
(1) Bayesian pedantry: pointing out that weak evidence is distinct from zero evidence, that rational evidence i...
I had heard about the case casually on the news a few months ago. It was obvious to me that Amanda Knox was innocent. My probability estimate of guilt was around 1%. This makes me one of the few people in reasonably good agreement with Eli's conclusion.
I know almost nothing of the facts of the case.
I only saw a photo of Amanda Knox's face. Girls with cute smiles like that don't brutally murder people. I was horrified to see that among 300 posts on Less Wrong, only two mentioned this, and it was to urge people to ignore the photos. Are they all too PC or so...
It's clearly absurd to say that pretty girls never murder people. But allowing for the normal hyperbole and inexactitude of conversational English, I don't think that's what SforSingularity means, rather, 'pretty girls are one of the demographic least likely to be responsible for a brutal murder'.
This isn't too unreasonable.
komponisto - you are a genius. For months I have felt that Amanda and Rafaelle were clearly innocent, but I could not properly rationalize or verbalize my feelings. How could the entire internet be wrong? How could the jury be unanimously wrong? Now I understand. Thank you and I love your blog. As others have noted, this site is the only place I have found cordial and intelligent debate among the opposing viewpoints.
Something new I saw this morning. Quite incriminating of the investigation.
"Amanda Knox - Police Deceit - "Assassins" of Character" http://www.youtube.com/watch?v=AHleYhBJy8k
Can you show your math for your apparent belief that any murder occurred at all, and that Guédé is guilty? I'd think you'd start with similar priors (the VAST majority of people are not murdered, and the VAST majority of people do not murder others. It seems like you're giving a LOT of weight to at least some of the reported evidence or agreement about this portion of the belief.
Which evidence is this, and what is your estimate of false-positives for it?
There is another Occam's Razor at work here. With the blaringly obviousness of the truth of this case, how can it not be that it has been actively and intentionally ignored at best and fabricated at worst?
Discussion on Hacker News points to http://www.zimbio.com/Amanda+Knox/articles/58/Understanding+Micheli+2+Judge+Micheli+Rejected which is a better prosecution summary than anything else I've seen, though you've got to read Wikipedia first to know who the actors are.
It looks like I have to do some updating too... based on the original version I had concluded that komponisto wasn't capable of updating, but it seems I was mistaken.
if you don't ever -- or indeed often -- find yourself needing to zig when, not only other people, but all kinds of internal "voices" in your mind are loudly shouting for you to zag, then you're either a native rationalist...
Shouldn't this start with "if you frequently..." ?
. . . then you're either a native rationalist -- a born Bayesian, who should perhaps be deducing general relativity from the fall of an apple any minute now -- or else you're simply not trying hard enough.
Hey, now, don't confuse rationality with intelligence. Imagine the world as consisting of spiked pits and gold coins. Rationality is about not walking into spiked pits, and following any pit-free path you find that leads to a gold coin. Intelligence is about actually finding a path leading to a gold coin. Naturally, in order to safely arrive at a gold ...
Within the last twenty-four hours, I think, I posted here a comment that has been removed--unless my browser is not displaying the page properly. The comment was a reply--an addendum--to my own comment of 31 January 2014 09:33:17PM. Going by memory, I'll say it read as follows:
...Having pursued, over the past twenty-four hours or so, some information about the case, I would say that, whether she was involved in the murder, Knox is a catastrophic failure of personality formation, one who, at the least, increased the agony of Kercher's family by making an u
How about this:
What are the odds that, given a murder in a shared accomodation, one of the occupants is involved if someone known to one of the occupants is known to be involved, more than one person is known to be involved, and that occupant is found to have a false alibi?
"If Amanda Knox and Raffaele Sollecito were to be in investigators' thoughts at all, they had to get there via Guédé -- because otherwise the hypothesis (a priori unlikely) of their having had homicidal intent toward Kercher would be entirely superfluous in explaining the chain of events that led to her death." They have fake alibi's, a crime scene they believed had been tampered with to conceal evidence, the whole Lumumba story from Knox and evidence from the body suggesting multiple people were involved in the murder. I'm not sure that these ar...
"If Amanda Knox and Raffaele Sollecito were to be in investigators' thoughts at all, they had to get there via Guédé -- because otherwise the hypothesis (a priori unlikely) of their having had homicidal intent toward Kercher would be entirely superfluous in explaining the chain of events that led to her death." They have fake alibi's, a crime scene they believed had been tampered with to conceal evidence, the whole Lumumba story from Knox and evidence from the body suggesting multiple people were involved in the murder. I'm not sure that these ar...
this is an extract from Wendy Murphy's article (http://www.milforddailynews.com/opinion/x327822063/Murphy-Foxy-Knoxy-Innocent-coed-or-manipulative-murderer)
"while Knox's defenders have no trouble complaining that jurors judged her unfairly based on her behavior in the days after the murder (purchasing sexy lingerie, frolicking around town and making out with her boyfriend), they don't mind pointing out her gentle appearance - or arguing that she has a reputation for being "sweet and generous and kind" etc. In other words - they're fine with ...
I find a number of logical errors in what you've presented.
The first is a difference in the the interpretation of the term 'guilty'. For the mass of the internet, guilty is understood to mean definitively "So-and-so did the action." However, a verdict of guilty is quite a different thing; being related to a human enterprise, a verdict of guilty is necessarily bounded by time, technology, and common agreement, to list a few. For example, we frequently argue the technology part- the LCN DNA test on the knife. The ability to prove "guilty"...
Note: The quantitative elements of this post have now been revised significantly.
Followup to: You Be the Jury: Survey on a Current Event
- lordweiner27, commenting on my previous post
The short answer: it's very much like how a few minutes of philosophical reflection trump a few millennia of human cultural tradition.
Wielding the Sword of Bayes -- or for that matter the Razor of Occam -- requires courage and a certain kind of ruthlessness. You have to be willing to cut your way through vast quantities of noise and focus in like a laser on the signal.
But the tools of rationality are extremely powerful if you know how to use them.
Rationality is not easy for humans. Our brains were optimized to arrive at correct conclusions about the world only insofar as that was a necessary byproduct of being optimized to pass the genetic material that made them on to the next generation. If you've been reading Less Wrong for any significant length of time, you probably know this by now. In fact, around here this is almost a banality -- a cached thought. "We get it," you may be tempted to say. "So stop signaling your tribal allegiance to this website and move on to some new, nontrivial meta-insight."
But this is one of those things that truly do bear repeating, over and over again, almost at every opportunity. You really can't hear it enough. It has consequences, you see. The most important of which is: if you only do what feels epistemically "natural" all the time, you're going to be, well, wrong. And probably not just "sooner or later", either. Chances are, you're going to be wrong quite a lot.
To borrow a Yudkowskian turn of phrase: if you don't ever -- or indeed often -- find yourself needing to zig when, not only other people, but all kinds of internal "voices" in your mind are loudly shouting for you to zag, then you're either a native rationalist -- a born Bayesian, who should perhaps be deducing general relativity from the fall of an apple any minute now -- or else you're simply not trying hard enough.
Oh, and another one of those consequences of humans' not being instinctively rational?
Two intelligent young people with previously bright futures, named Amanda and Raffaele, are now seven days into spending the next quarter-century of their lives behind bars for a crime they almost certainly did not commit.
"Almost certainly" really doesn't quite capture it. In my previous post I asked readers to assign probabilities to the following propositions:1. Amanda Knox is guilty (of killing Meredith Kercher)
2. Raffaele Sollecito is guilty (of killing Meredith Kercher)
3. Rudy Guédé is guilty (of killing Meredith Kercher)
I also asked them to guess at how closely they thought their estimates would match mine.
Well, for comparison, here are mine (revised):
1.
Negligible. Small.Hardly 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 of0.0010.01 or 0.1 at most.2. Ditto.
3. About as high as the other two numbers are low.
0.9990.99 as a (probably weak) lower bound.Yes, you read that correctly. In my opinion, there is for all intents and purposes zero Bayesian evidence that Amanda and Raffaele are guilty.Needless to say, this differs markedly from the consensus of the jury in Perugia, Italy.How could this be?
Am I really suggesting that the estimates of eight jurors -- among whom two professional judges -- who heard the case for a year, along with something like 60% of the Italian public and probably half the Internet (and a significantly larger fraction of the non-American Internet), could be off by
a minimum of three orders of magnitude (probably significantly more)such a large amount?That most other people (including most commenters on my last post) are off by no fewer than two?Well, dear reader, before getting too incredulous, consider this. How about averaging the probabilities all those folks would assign to the proposition that Jesus of Nazareth rose from the dead, and calling that number x. Meanwhile, let y be the correct rational probability that Jesus rose from the dead, given the information available to us.
How big do you suppose the ratio x/y is?
Anyone want to take a stab at guessing the logarithm of that number?
Compared to the probability that Jesus rose from the dead, my estimate of Amanda Knox's culpability makes it look like I think she's as guilty as sin itself.
And that, of course, is just the central one of many sub-claims of the hugely complex yet widely believed proposition that Christianity is true. There are any number of other equally unlikely assertions that Amanda would have heard at mass on the day after being found guilty of killing her new friend Meredith (source in Italian) -- assertions that are assigned non-negligible probability by no fewer than a couple billion of the Earth's human inhabitants.
I say this by way of preamble: be very wary of trusting in the rationality of your fellow humans, when you have serious reasons to doubt their conclusions.
The Lawfulness of Murder: Inference Proceeds Backward, from Crime to Suspect
We live in a lawful universe. Every event that happens in this world -- including human actions and thoughts -- is ultimately governed by the laws of physics, which are exceptionless.
Murder may be highly illegal, but from the standpoint of physics, it's as lawful as everything else. Every physical interaction, including a homicide, leaves traces -- changes in the environment that constitute information about what took place.
Such information, however, is -- crucially -- local. The further away in space and time you move from the event, the less entanglement there is between your environment and that of the event, and thus the more difficult it is to make legitimate inferences about the event. The signal-to-noise ratio decreases dramatically as you move away in causal distance from the event. After all, the hypothesis space of possible causal chains of length n leading to the event increases exponentially in n.
By far the most important evidence in a murder investigation will therefore be the evidence that is the closest to the crime itself -- evidence on and around the victim, as well as details stored in the brains of people who were present during the act. Less important will be evidence obtained from persons and objects a short distance away from the crime scene; and the importance decays rapidly from there as you move further out.
It follows that you cannot possibly expect to reliably arrive at the correct answer by starting a few steps removed in the causal chain, say with a person you find "suspicious" for some reason, and working forward to come up with a plausible scenario for how the crime was committed. That would be privileging the hypothesis. Instead, you have to start from the actual crime scene, or as close to it as you can get, and work backward, letting yourself be blown by the winds of evidence toward one or more possible suspects.
In the Meredith Kercher case, the winds of evidence blow with something like hurricane force in the direction of Rudy Guédé. After the murder, Kercher's bedroom was filled with evidence of Guédé's presence; his DNA was found not only on top of but actually inside her body. That's about as close to the crime as it gets. At the same time, no remotely similarly incriminating genetic material was found from anyone else -- in particular, there were no traces of the presence of either Amanda Knox or Raffaele Sollecito in the room (and no, the supposed Sollecito DNA on Meredith's bra clasp just plain does not count -- nor, while we're at it, do the 100 picograms [about one human cell's worth] of DNA from Meredith allegedly on the tip of a knife handled by Knox, found at Sollecito's apartment after the two were already suspects; these two things constituting pretty much the entirety of the physical "evidence" against the couple).
If, up to this point, the police had reasons to be suspicious of Knox, Sollecito, and Guédé, they should have cleared Knox and Sollecito at once upon the discovery that Guédé -- who, by the way, was the only one to have fled the country after the crime -- was the one whom the DNA matched. Unless, that is, Knox and Sollecito were specifically implicated by Guédé; after all, maybe Knox and Sollecito didn't actually kill the victim, but instead maybe they paid Guédé to do so, or were otherwise involved in a conspiracy with him. But the prior probabilities of such scenarios are low, even in general -- to say nothing of the case of Knox and Sollecito specifically, who, tabloid press to the contrary, are known to have had utterly benign dispositions prior to these events, and no reason to want Meredith Kercher dead.
If Amanda Knox and Raffaele Sollecito were to be in investigators' thoughts at all, they had to get there via Guédé -- because otherwise the hypothesis (a priori unlikely) of their having had homicidal intent toward Kercher would be entirely superfluous in explaining the chain of events that led to her death. The trail of evidence had led to Guédé, and therefore necessarily had to proceed from him; to follow any other path would be to fatally sidetrack the investigation, and virtually to guarantee serious -- very serious -- error. Which is exactly what happened.
There was in fact no inferential path from Guédé to Knox or Sollecito. He never implicated either of the two until long after the event; around the time of his apprehension, he specifically denied that Knox had been in the room. Meanwhile, it remains entirely unclear that he and Sollecito had ever even met.
The hypotheses of Knox's and Sollecito's guilt are thus seen to be completely unnecessary, doing no explanatory work with respect to Kercher's death. They are nothing but extremely burdensome details.
Epistemic Ruthlessness: Following the Strong Signal
All of the "evidence" you've heard against Knox and Sollecito -- the changing stories, suspicious behavior, short phone calls, washing machine rumors, etc. -- is, quite literally, just noise.
But it sounds so suspicious, you say. Who places a three-second phone call?
As humans, we are programmed to think that the most important kinds of facts about the world are mental and social -- facts about what humans are thinking and planning, particularly as regards to other humans. This explains why some people are capable of wondering whether the presence of (only) Rudy Guédé's DNA in and on Meredith's body should be balanced against the possibilty that Meredith may have been annoyed at Amanda for bringing home boyfriends and occasionally forgetting to flush the toilet -- that might have led to resentment on Amanda's part, you see.
That's an extreme example, of course -- certainly no one here fell into that kind of trap. But at least one of the most thoughtful commenters was severely bothered by the length of Amanda's phone calls to Meredith. As -- I'll confess -- was I, for a minute or two.
I don't know why Amanda wouldn't have waited longer for Meredith to pick up. (For what it's worth, I myself have sometimes, in a state of nervousness, dialed someone's number, quickly changed my mind, then dialed again a short time later.) But -- as counterintuitive as it may seem -- it doesn't matter. The error here is even asking a question about Amanda's motivations when you haven't established an evidentiary (and that means physical) trail leading from Meredith's body to Amanda's brain. (Or even more to the point, when you have established a trail that led decisively elsewhere.)
Maybe it's "unlikely" that Amanda would have behaved this way if she were innocent. But is the degree of improbabilty here anything like the improbability of her having participated in a sex-orgy-killing without leaving a single piece of physical evidence behind? While someone else left all kinds of traces? When you had no reason to suspect her at all without looking a good distance outside Meredith's room, far away from the important evidence?
It's not even remotely comparable.
Think about what you're doing here: you are invoking the hypothesis that Amanda Knox is guilty of murder in order to explain the fact that she hung up the phone after three seconds. (Remember, the evidence against Guédé is such that the hypothesis of her guilt is superfluous -- not needed -- in explaining the death of Meredith Kercher!)
Maybe that's not quite as bad as invoking a superintelligent deity in order to explain life on Earth; but it's the same kind of mistake: explaining a strange thing by postulating a far, far stranger thing.
"But come on," says a voice in your head. "Does this really sound like the behavior of an innocent person?"
You have to shut that voice out. Ruthlessly. Because it has no way of knowing. That voice is designed to assess the motivations of members of an ancestral hunter-gather band. At best, it may have the ability to distinguish the correct murderer from between 2 and 100 possibilities -- 6 or 7 bits of inferential power on the absolute best of days. That may have worked in hunter-gatherer times, before more-closely-causally-linked physical evidence could hope to be evaluated. (Or maybe not -- but at least it got the genes passed on.)
DNA analysis, in contrast, has in principle the ability to uniquely identify a single individual from among the entire human species (depending on how much of the genome is looked at; also ignoring identical twins, etc.) -- that's more like 30-odd bits of inferential power. In terms of epistemic technology, we're talking about something like the difference in locomotive efficacy between a horsedrawn carriage and the Starship Enterprise. Our ancestral environment just plain did not equip our knowledge-gathering intuitions with the ability to handle weapons this powerful.
We're talking about the kind of power that allows us to reduce what was formerly a question of human social psychology -- who made the decision to kill Meredith? -- to one of physics. (Or chemistry, at any rate.)
But our minds don't naturally think in terms of physics and chemistry. From an intuitive point of view, the equations of those subjects are foreign; whereas "X did Y because he/she wanted Z" is familiar. This is why it's so difficult for people to intuitively appreciate that all of the chatter about Amanda's "suspicious behavior" with various convincing-sounding narratives put forth by the prosecution is totally and utterly drowned out to oblivion by the sheer strength of the DNA signal pointing to Guédé alone.
This rationalist skill of following the strong signal -- mercilessly blocking out noise -- might be considered an epistemic analog of the instrumental "shut up and multiply": when much is at stake, you have to be willing to jettison your intuitive feelings in favor of cold, hard, abstract calculation.
In this case, that means, among other things, thinking in terms of how much explanatory work is done by the various hypotheses, rather than how suspicious Amanda and Raffaele seem.
Conclusion: The Amanda Knox Test
I chose the title of this post because the parallel structure made it sound nice. But actually, I think an hour is a pretty weak upper bound on the amount of time a skilled rationalist should need to arrive at the correct judgment in this case.
The fact is that what this comes down to is an utterly straightforward application of Occam's Razor. The complexity penalty on the prosecution's theory of the crime is enormous; the evidence in its favor had better be overwhelming. But instead, what we find is that the evidence from the scene -- the most important sort of evidence by a huge margin -- points with literally superhuman strength toward a mundane, even typical, homicide scenario. To even consider theories not directly suggested by this evidence is to engage in hypothesis privileging to the extreme.
So let me say it now, in case there was any doubt: the prosecution of Amanda Knox and Raffaele Sollecito, culminating in last week's jury verdict -- which apparently was unanimous, though it didn't need to be under Italian rules -- represents nothing but one more gigantic, disastrous rationality failure on the part of our species.
How did Less Wrong do by comparison? The average estimated probability of Amanda Knox's guilt was 0.35 (thanks to Yvain for doing the calculation). It's pretty reasonable to assume the figure for Raffaele Sollecito would be similar. While not particularly flattering to the defendants (how would you like to be told that there's a 35% chance you're a murderer?), that number makes it obvious we would have voted to acquit. (If a 65% chance that they didn't do it doesn't constitute "reasonable doubt" that they did...)
The commenters whose estimates were closest to mine -- and, therefore, to the correct answer, in my view -- were Daniel Burfoot and jenmarie. Congratulations to them. (
But even they were off by a factor of at least ten!)In general, most folks went in the right direction, but, as Eliezer noted, were far too underconfident -- evidently the result of an exorbitant level of trust in juries, at least in part. But people here were also widely making the same object-level mistake as (presumably) the jury: vastly overestimating the importance of "psychological" evidence, such as Knox's inconsistencies at the police station, as compared to "physical" evidence (only Guédé's DNA in the room).
One thing that was interesting and rather encouraging, however, is the amount of updating people did after reading others' comments -- most of it in the right direction (toward innocence).
[EDIT: After reading comments on this post, I have done some updating of my own. I now think I failed to adequately consider the possibility of my own overconfidence. This was pretty stupid of me, since it meant that the focus was taken away from the actual arguments in this post, and basically toward the issue of whether 0.001 can possibly be a rational estimate for anything you read about on the Internet. The qualitative reasoning of this post, of course, stands. Also, the focus of my accusations of irrationality was not primarily the LW community as reflected in my previous post; I actually think we did a pretty good job of coming to the right conclusion given the information provided -- and as others have noted, the levelheadedness with which we did so was impressive.]
For most frequenters of this forum, where many of us regularly speak in terms of trying to save the human species from various global catastrophic risks, a case like this may not seem to have very many grand implications, beyond serving as yet another example of how basic principles of rationality such as Occam's Razor are incredibly difficult for people to grasp on an intuitive level. But it does catch the attention of someone like me, who takes an interest in less-commonly-thought-about forms of human suffering.
The next time I find myself discussing the "hard problem of consciousness", thinking in vivid detail about the spectrum of human experience and wondering what it's like to be a bat, I am going to remember -- whether I say so or not -- that there is most definitely something it's like to be Amanda Knox in the moments following the announcement of that verdict: when you've just learned that, instead of heading back home to celebrate Christmas with your family as you had hoped, you will be spending the next decade or two -- your twenties and thirties -- in a prison cell in a foreign country. When your deceased friend's relatives are watching with satisfaction as you are led, sobbing and wailing with desperation, to a van which will transport you back to that cell. (Ever thought about what that ride must be like?)
While we're busy eliminating hunger, disease, and death itself, I hope we can also find the time, somewhere along the way, to get rid of that, too.
(The Associated Press reported that, apparently, Amanda had some trouble going to sleep after the midnight verdict.)
I'll conclude with this: the noted mathematician Serge Lang was in the habit of giving his students "Huntington tests" -- named in reference to his controversy with political scientist Samuel Huntington, whose entrance into the U.S. National Academy of Sciences Lang waged a successful campaign to block on the grounds of Huntington's insufficient scientific rigor.
The purpose of the Huntington test, in Lang's words, was to see if the students could "tell a fact from a hole in the ground".
I'm thinking of adopting a similar practice, and calling my version the Amanda Knox Test.
Postscript: If you agree with me, and are also the sort of person who enjoys purchasing warm fuzzies separately from your utilons, you might consider donating to Amanda's defense fund, to help out her financially devastated family. Of course, if you browse the site, you may feel your (prior) estimate of her guilt taking some hits; personally, that's okay with me.