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The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom

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

Note: The quantitative elements of this post have now been revised significantly.

Followup to: You Be the Jury: Survey on a Current Event

All three of them clearly killed her. The jury clearly believed so as well which strengthens my argument. They spent months examining the case, so the idea that a few minutes of internet research makes [other commenters] certain they're wrong seems laughable

- 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 of 0.001 0.01 or 0.1 at most.  
2. Ditto.
3. About as high as the other two numbers are low. 0.999 0.99 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.

Comments (630)

Comment author: dilaudid 13 December 2009 05:23:15PM 22 points [-]

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'?

Comment author: brazil84 14 December 2009 03:48:16AM 3 points [-]

I think this is a good point, but I would go one step further. Because there was more than one crime committed. In addition to a murder, somebody tried to stage a burglary. Common sense says that whoever staged the burglary was also involved in the murder but it's still 2 separate crimes.

It seems to me that the prior probability that the person who staged the burglary is someone closely associated with Kercher, such as a roommate, is actually pretty high. A close associate would have a strong incentive to try to make the police think that a stranger committed the crime. Whereas a stranger or remote acquaintance would have little or no incentive to do so.

Comment author: bogdanb 13 December 2009 09:37:34PM *  13 points [-]

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 that kind of certainty, I don't see why writing the calculations (for an upper bound, not the precise value) would take much longer, assuming that one would be gathering data and doing the calculations in one's head during that hour.

(*: EDIT for clarification. By this I mean that, for instance, given claimed evidence E in support of theory T, you don't update on the probability of T given E, but update on the probability of T given “I've read on the Internet that E”. Of course, many claims of E on the Internet have some weight, but I doubt two hours of Internet reading can add lots of weight on non-trivial subjects.)

Comment author: Unknowns 13 December 2009 07:43:26AM 12 points [-]

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.

Comment author: brazil84 13 December 2009 02:11:14PM 2 points [-]

"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."

I agree. And also substantial evidence that someone was trying to make it look as though the crime was done by an outsider.

Comment author: magfrump 13 December 2009 08:57:56AM 2 points [-]

The Friends of Amanda site clearly stated that there was no evidence of cleanup and that "cleanup" had only been referenced in passing in the trial, and the prosecution did not pursue the point.

That is, there is not "substantial evidence" of the scene being rearranged, I'm not sure where you're getting that.

Comment author: Unknowns 13 December 2009 10:24:43AM 2 points [-]

Yes, it made that claim, but as far as I can see it was wrong. Among other things, the bloodstains on her bra and her body indicated that her bra was removed some time after her death. Even by itself, this implies someone rearranging things. Likewise, luminaled footprints, whether or not they were Amanda's and Sollecito's as claimed, proves that someone cleaned something.

Comment author: McJustice 02 January 2010 11:41:36PM 4 points [-]

Those who say Guede left quickly and therefore was not around to remove the bra, shift the body later and place the cover over her after the blood was dried... forget that she was killed resisting rape and he very likely stayed to complete what he started.

Rudy had plenty of time before he was seen at 2AM in the Disco to first clean up the mess that would have been in the way for what he did next (and by that I mean not only blood but the results of relaxed bowels and urethra) cut off her bra and lay her on her back adjusting where she lay so that he could enjoy what he set out to do originally. That is have sex with her... and he used condoms. And then still time to clean himself up, swab the obvious signs in the bathroom, throw the cover on her and lock the door.

The patrons at the disco who saw him dancing between 2 and 4 AM said he stank very badly....

Comment author: kodos96 14 December 2009 06:00:01PM 4 points [-]

"luminaled footprints, whether or not they were Amanda's and Sollecito's as claimed, proves that someone cleaned something"

No it doen't. Luminal doesn't reveal blood EXCLUSIVELY. I read somewhere, sorry, can't remember where, that it can also light up things like just sweaty/dirty footprints, no blood necessary.

Comment author: rmattbill 15 December 2009 07:27:15AM 7 points [-]

You're absolutely correct. Not only that, but the Luminol footprints specifically tested NEGATIVE for the presence of blood. Every single one of them.

Comment author: lordweiner27 14 December 2009 11:20:01AM 11 points [-]

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 reference to this. Of course you are right juries can be wrong. I just tend to think that the simplest answer is normally the best. That's it's more likely that she is guilty, than that the police dept in Italy have a massive desire to convict and innocent woman.

However on reading more about the case, I discovered that the police had a theory it was Knox, Sollecito and Knox's boss before the evidence about Guede turned up. They announced this to the world. When Guede turned up, which normally would have been the end of the case they stuck with their original theory substituting Guede for Knox's boss.
So their motive for wanting to convict Knox and Sollecito was not a conscious devious one but an unconscious subtle one. The didn't want to be embarrassed and shown to be wrong in the eyes of the world media.

Btw, this is the third time I've been proved to be wrong on the internet this week. Either I'm not a very good rationalist or I just spend to much time on the internet.

Comment author: JimS 20 June 2011 02:34:20AM 9 points [-]

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 ....

Comment author: MarkusRamikin 16 June 2011 12:38:54PM *  9 points [-]

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.

Comment author: komponisto 16 June 2011 02:46:48PM 1 point [-]

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!

Thank you! Though I would probably write it differently today, it remains my favorite post, in the sense that upvotes and positive feedback on it make me happier than on anything else I've written here.

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.

Perhaps, but remember that this isn't something like a political issue, where there are always advocacy websites on both sides. Very few defendants X even have "pro-X sources of information" to begin with -- even if they're privileged (which is not particularly the case of Knox, by American standards). And even when they do, it's often because the case has (or is perceived to have) political implications, and the support is politically-themed. In my view, availability bias resulting from hearing a lot about those types of cases results in an underestimation of the evidentiary value of advocacy on behalf of a defendant like Amanda Knox.

But, remember in any case that we have plenty of anti-Knox advocacy to contrast it with, in addition to the numerous media sources (now including several books) that attempt to be more "neutral" (though often fail). And there just isn't anything bad that anyone can actually find, despite many people trying really hard. The best the anti-Knox folks can do is to come up with their own highly sinister, distorted interpretations of Knox's and Sollecito's personalities, not shared by anyone who actually knows either of them. The absence of objectively negative anecdotes is conspicuous. Meanwhile there are all kinds of good things that have been said about both defendants by people who know them.

I'd also like to ask, how necessary to your argument was using that Jesus example?

Not necessary at all; it was indeed basically an applause light for this particular audience. Of course, there wasn't anything actually wrong about it. And the point I made with it was important: social consensus can't be trusted, or at any rate is very easily screened off.

But yes, the post was definitely targeted specifically at Less Wrong readers, as opposed to the general public. Though I've been surprised at how little negative reaction there has been from outsiders on account of the swipes I took at religion -- virtually none, in fact. The main barrier is a general unfamiliarity with the LW culture of Bayesianism -- but since this post was designed to be a specific application of the LW perspective, I'm not sure how much that could have been helped.

Comment author: Yvain 13 December 2009 02:36:02PM 8 points [-]

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?

Comment author: Torben 13 December 2009 03:48:18PM 2 points [-]

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?

Maybe I'm missing something, but I think you read that wrong.

komponisto said the evidence should not cause anyone to change the prior probability much. Surely, for people in AK's reference class, the per-year probability of committing a 3-party sex killing is less than 0.001?

I think komponisto quite correctly described the effect of privileging the hypothesis, which might be what caused the LW community to be so much off from his estimate. Everybody seemed to be going backward from assuming AK's guilt at 50-50, whereas komponisto went forward from the background probability.

Comment author: gelisam 13 December 2009 05:56:35PM 1 point [-]

Everybody seemed to be going backward from assuming AK's guilt at 50-50, whereas komponisto went forward from the background probability.

I think I can see why. komponisto pretended to be a juror following the "innocent unless proven otherwise" mantra and updating on the evidence presented in the court. We, on the other hand, did what komponisto challenged us to do: figure out the answer to his riddle using the two websites he gave us. This being a riddle, not a court, we had no reason to favour one hypothesis over the other, hence the 50-50.

That being said, I did favour one hypothesis over the other (my stated priors were 75/75/25) because at the moment I paused to write down an approximation of my current beliefs, I had already updated on the evidence presented by komponisto himself in his post, namely, that there was a trial against AK and RS.

Maybe the reason why many of us gave so much importance to the fact that those particular individuals were on trial for murder was because it was our very first piece of information; and I don't think it's right for rationalists to do that.

Comment author: luzhin 13 December 2009 09:26:49PM *  0 points [-]

komponisto should not be going forward from the background probabilities because he isn't an experienced investigator with access to the crime scene. he's just a guy reading about evidence on the internet. a more reasonable prior for him to start with is, ''how often are people convicted of murder when they did not in fact commit a murder?'' (there are actual #s for this, too)

when juries sit around thinking, ''is this person guilty or not?'' they assume the investigators working on the case are competent. they assume, quite rightly, that there must be a damn good reason why reasonable investigators couldnt quickly dismiss a hypothesis with such an insanely low prior probability. lesswrong.com readers should do likewise.

Comment author: Sebastian_Hagen 13 December 2009 06:41:46PM *  6 points [-]

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 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.)

Agree completely. Now apply it both ways. Specifically:

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.

This is extremely weak evidence. If you think that psychology doesn't really matter (and I agree with that), then it notmatters in both directions. There's no obvious motive, but that's very weak evidence that no motive existed. We just don't have enough evidence for what these people really think like, relative to the population at large. Re. motive, I'd definitely stick with the prior for murderous intentions among associates.

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 [count]

I was surprised at you dismissing the knife DNA evidence. The linked FOA page claims:

Low Copy Number (LCN) tests, like the one performed on the knife blade, are regarded by many experts as inherently unreliable, because it is not possible to prevent biological contamination at the level of picograms. Even in well-run labs, control samples regularly show up with DNA that theoretically should not be there.

The actual experts doing DNA-testing in the case evidently thought that it was significant evidence. Wikipedia has an article on LCN, though a lot of the citations are broken. According to the article, the method went through an extensive review, and was finally cleared for use in the UK justice system (and with a fairly definite statement at that: "The CPS has not seen anything to suggest that any current problems exist with LCN"). The situation in some other western countries appears to be rather different, though. I still think this is fairly strong evidence, though much less so than I did before doing some research on the general acceptance of this test method.

While not particularly flattering to the defendants (how would you like to be told that there's a 35% chance you're a murderer?)

Keep in mind this verdict uses (among other pieces of information) the existing jury verdict as empirical evidence (and of course in our epistemological position, that's the right thing to do); if our judgements had been based on just the primary evidence - i.e. without an existing guilty verdict by a jury - these probabilities would have been lower.

Comment author: Questor 16 December 2009 02:07:44AM 4 points [-]

Low copy number Test... you left out that there are very few labs certified as being acceptable to do that test which is still regarded as experimental and in the UK there is a stringent set of minimum standards for equipment, procedures for the lab itself not to mention the person doing the test. Would you be surprised to hear that the lab that did the test did not meet these requirements in the slightest? It may also be true that though equipped for standard DNA tests was not technically certified at the time even for that? An expert who is convinced the results are reliable when she had never done this type of test before using equipment not designed or set up for such extreme amplification plus leaving out the other calibration tests and tests on a control and not releasing a lot of other details of what she did. She is an employee of the Italian Government just like the prosecutor who unlike many other systems also runs or in this case directs the investigation. The results on the Bra clip and the knife blade are not scientifically usable and should never have been accepted as reliable evidence. This is in the realm of pseudo science. these links have all the details http://freeaman.001webs.com/pdfs/LCN_DNA_I.pdf http://freeaman.001webs.com/pdfs/Methods_of_the_Polizia_PseudoScientifica.pdf The same with pictures and video http://www.sciencespheres.com/2009_10_01_archive.html And New Scientist Magazine has an article about concerns that world experts in DNA testing have. http://www.sciencespheres.com/2009_10_01_archive.html http://freeaman.001webs.com/pdfs/LCN_DNA_II.pdf All of this leaves 2 key bits of evidence, the only 2 alleged to link AK or RS to the crime scene... revealed to not be credible evidence at all no matter what the prosecution expert(s) said about it

This blog is great... the lead post does a good job of showing that the theory came first before any evidence and all the efforts since then have been aimed at proving the originally baseless theory which was based on pop psychology disguised as some sort of science...Dietrologia combined with a casual hunch driven version of BIA Behavioral Interview analysis. http://deception.crimepsychblog.com/?p=78 And just this short clip of Giobbi, the lead investigator at the start... is just about the best encapsulation of the mindset that originated and drove the entire wrongheaded prosecution. THEORY First , evidence after... http://www.youtube.com/watch?v=sWkZPWRS3N0&feature=PlayList&p=A24DFCC06CD8360D&index=0

Comment author: Sebastian_Hagen 16 December 2009 02:23:03PM 1 point [-]

Very interesting reports about the LCN analysis performed in this investigation; I hadn't come across those before (FOA doesn't seem to link to them). This diminishes my confidence in those results meaning much of anything significantly. Thanks!

Comment author: pataz1 16 December 2009 11:46:32PM 0 points [-]

The problem for the trial was the Defense's argument against the DNA on the knife was undermined by Sollecito admitting there may be the victim's blood/dna on the knife because of a dinner at his house that never happened. Although it tested negative for blood, at that point, the critique against the LCN DNA on the knife is almost superfluous. Sollecito made up a reason to excuse evidence that the defense was challenging the proof of.

Comment author: McJustice 02 January 2010 11:20:05PM 2 points [-]

About LCN DNA... only the UK currently approves that kind of evidence in a trial BUT they have an extremely strict set of standards on how to run those kinds of tests AND require a very expensive specially built and equipped lab. There are very few DNA labs in the entire world that comply. And there are not many properly trained "experts" who are certified to carry it out. I should mention that none of those labs happen to be in Italy and the Italian technician was not trained or certified to do it. Also her boss in the lab worked as a paid consultant for Mignini at times and there is the implication that she was under the gun to come up with results.

All her original DNA tests showed no DNA on the knife at all. Only when she circumvented the built-in limits in the equipment and without doing any of the recommended calibration for false positives and running a lot more amplification runs did she finally come up with partial matches in a very statistically noisy result. And even then great care must be taken in interpreting the results which are much more liable to contamination than standard DNA tests. And even at this point the results with her "interpretation" of the results only yields suggestion of Meredith's DNA... not blood. And this is important: If the knife was cleaned with bleach there would be no DNA but blood would still be detectable. And blood was not detected. The test for blood is very sensitive and it is very hard to eliminate all blood traces and yet there was no blood. That implies strongly that whatever DNA was detected was contamination and a weak result open to interpretation. Her DNA test reports as presented to the court are not complete so the entire process she used for all of these key tests is not available for review. Additionally the court did not allow defense DNA experts to testify about the faults in the prosecution's DNA evidence.

Italian judges have poor understanding of forensics and tend to accept unquestioningly the results of government forensic labs.

http://www.foreignpolicy.com/articles/2009/12/10/can_anyone_get_a_fair_trial_in_italy "For one, they say that coerced confessions and the use of dubious forensic evidence, as might have happened in the Knox case, are way too common. "Inquiries are conducted without any reliable methods," says Roberto Malini, president of EveryOne, a nongovernmental organization that defends ethnic minorities in jail. "Tests take place solely in the laboratories of the state police. There's no independent lab, and independent observers do not have access to the police's work."

"Legal experts also share concerns about Italy's bar for admissibility. Il Giornale, a conservative newspaper, for instance, recently published an interview with Marco Morin, a Venice-based firearms expert who declared he no longer wanted to work in Italian courts. "In the United States, federal judges must study a 637-page manual in order to be able to evaluate [forensic] evidence," he told the newspaper. "Here, they accept everything without questioning, as long as it comes from the institutional laboratory."

Comment author: Jack 13 December 2009 01:05:17PM *  6 points [-]

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 (which is high or low depending on how well his presence explains all the evidence at the crime scene with a prior involving the chances any given murder involves more than one perpetrator) Obviously the absence of other physical evidence is evidence that he acted alone, so this value is the probability dictated by the other evidence, rearranged crime scene, broken windows etc.

  • the facts about the morning of November 2, the non-negligible probability RS called the police after the police had arrived, the short phone calls, even the weird behavior that can be explained, which once conjoined, looks like it is at least slightly indicative of being involved in Kercher's murder.

I don't think this is actually sufficient evidence to bring the probability AK and RS are guilty over .5. But it also isn't obvious to me that this evidence is "swamped" by the lack of physical evidence implicating them.

Comment author: komponisto 19 February 2010 02:17:02AM 5 points [-]

(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:

  1. Amanda Knox
  2. Raffaele Sollecito
  3. Rudy Guede

(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 Guede as well, if you wish), by which I mean your estimate of the probability that each suspect would commit a crime of this sort, as of (let's say) a month before Kercher's death.

Then, if you could, please list, in descending order of evidentiary strength, the pieces of information most responsible for moving your estimates away from the above priors -- along with, if you wouldn't mind, a rough order-of-magnitude estimate of the strength of each piece of evidence, in terms of likelihood ratios, bits, or bels, whatever you prefer. (Again, I'm most interested in Knox and Sollecito; Guede is optional, at least for now.)

This should allow us to quickly pinpoint our disagreement(s).

Comment author: FAWS 22 February 2010 12:28:48AM *  2 points [-]

Oh, let me play!

(When you made your first post on this issue I found trying to look for unbiased information a terribly frustrating experience so I didn't look for more than 20 minutes, and haven't done any reading on it since, except for a cursory look the the wikipedia page just now. A list of all points that are agreed on by both sides (with sub-points arguing about the relevance of the point from both perspectives, perhaps) would have been very welcome)

Current posterior: not really sure, let's see what I end up with below, but as a starting point:

0.01<P(S) < P(K) <0.2 < 0.8< P (G) < 0.99

Priors for commiting a homicide in a specific month:

P(K)= 4.7 *10^-6 (US homicide rate, assuming being female and a young adult roughly cancel out)

P(S)= 4 *10^-6 (Italian homicide rate assuming young adult males are 4 times as likely to commit murder as average)

P(G)=1*10^-5 (had been implicated in a break-in)

An inhabitant of the top floor of that apartment being murdered in her room in this same specific month (R):

P(R|K)=0.1, P(R|~K)=4.5*10^-6

P(R|S)=0.04, P(R|~S)=4.95*10^-6

P(R|G)=0.0005, P(R|~G)=5*10^-6

Guede's DNA being found all over and inside the victim of a homicide in this same specific month (D_G):

P(DG|K)=1*10^-4, P(DG|~K)=6*10^-7

P(DG|S)=5*10^-5, P(DG|~S)=6*10^-7

P(DG|G)=0.6, P(DG|~G)=1*10^-7

I can't think of any other pieces of evidence that I can treat as effectively independent. Given R and treating the probability of any murders except R as effectively 0: Knox' DNA not being found on the victim (D_K):

P(DK|K)=0.5 P(DK|~K)=0.8

P(DK|S)==0.85 P(DK|~S)=0.81

P(DK|G)=0.82 P(DK|~G)=0.82

Sollecito's DNA being found on bra clasp of the the victim, but nowhere else (D_S):

P(DS|K)=0.0002 P(DS|~K)=0.00006

P(DS|S)==0.001 P(DS|~S)=0.00005

P(DS|G)=0.00007 P(DS|~G)=0.00007

Minimal trances of R's DNA found on the blade of one of the knifes in Sollecito's kitchen possibly matching one of three wounds, along with Knox' DNA on the handle (D_R):

P(DR|K)=5*10^-6 P(DR|~K)=1*10^-6

P(DR|S)=1*10^-5 P(DR|~S)=1*10^-6

P(DR|G)=1*10^-6 P(DR|~G)=1*10^-6

Trying to calculate the probabilities based on those estimates I find that I shouldn't have treated DG and R as independent either, I get a stupidly high result of 0.9999983 for P(G), and the indirect association with Guede shouldn't make the other two much more likely given that they are already more directly associated with the victim, if anything DG should make them less likely. The background probability for R should be higher because I forgot to properly account for the fact that there was more than 1 possible victim. Since Guede's DNA and being a room mate alone would already be enough to make Knox almost certainly guilty based on the numbers above and this makes no sense whatsoever I think we can safely say I thoroughly failed this test. I guess the lesson is that making up plausible numbers for various conditional probabilities well outside your intuitive range and then applying them in a basian update doesn't improve your calibration if you have no experience at it at all.

Comment author: komponisto 22 February 2010 02:15:28AM 3 points [-]

When you made your first post on this issue I found trying to look for unbiased information a terribly frustrating experience

One of the lessons of this exercise, that may be worth stating explicitly, is that there's no "outside referee" you can look to to make sure your beliefs are correct. In real life, you have to make judgments under uncertainty, using whatever evidence you have.

It's not as hard as you (and others) think. Yes, of course, the sources are "biased" in the sense that they have an incentive to mislead if they can get away with it. But what they say is not literally all the information you have. You also have background knowledge about how the world works. Priors matter. If A says X and B says ~X, and there's no a priori reason to trust one over the other, that doesn't mean you're stuck! It depends on how plausible X is in the first place.

I guess the lesson is that making up plausible numbers for various conditional probabilities well outside your intuitive range and then applying them in a basian update doesn't improve your calibration if you have no experience at it at all.

Here's the real lesson: Bayesian calculations are not some mysterious black-magic technique that you "apply" to a problem. They are supposed to represent the calculations your brain has already made. Probability theory is the mathematics of inference. If you have an opinion on this case, then, ipso facto, your brain has already performed a Bayesian update.

The mistake you made was not making up numbers; it was making up numbers that, as you point out in the end, didn't reflect your actual beliefs.

Comment author: FAWS 22 February 2010 03:11:44AM *  2 points [-]

One of the lessons of this exercise, that may be worth stating explicitly, is that there's no "outside referee" you can look to to make sure your beliefs are correct. In real life, you have to make judgments under uncertainty, using whatever evidence you have.

I meant that questions that should have an easily determinable answer, like "Did someone clean the blood outside her room up before the police was called" were unreasonably difficult to settle. Every site was mixing arguments and conclusions with facts. Sure, it's possible to find the answers if you look long enough, but it's much more work than it should be, and more work than I was willing to invest for a qestion that didn't interest me all that much in the first place.

Here's the real lesson: Bayesian calculations are not some mysterious black-magic technique that you "apply" to a problem. They are supposed to represent the calculations your brain has already made. Probability theory is the mathematics of inference. If you have an opinion on this case, then, ipso facto, your brain has already performed a Bayesian update.

The brain doesn't operate with very small or very big numbers, though. And I doubt it operates with conditional probabilities of the sort used above, as far as it operates Bayesian at all I would guess it's more similar to using venn diagrams.

The mistake you made was not making up numbers; it was making up numbers that, as you point out in the end, didn't reflect your actual beliefs.

The point is that I didn't spot that until after I did the calculation, and while I don't usually do much in the way of statistics I intuitively got the simple Bayesian problems like the usual example with false positives in a medical test right before hearing about Bayes theorem for the first time, so I don't think it's because I'm particularly bad at this. If you need to tweak afterwards anyway doing the Bayesian update explicitly isn't very useful as self-control.

Comment author: Blueberry 13 December 2009 07:16:33AM *  5 points [-]

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)

Comment author: McJustice 03 January 2010 12:06:06AM 4 points [-]

Why not by Guede? There is no evidence of him leaving right away only supposition. He was next seen at 2AM in a Disco. He is a known burglar and his bloody fingerprints are on Meredith's purse and also he had expressed interest in Meredith to other people prior to that night. He was there for money and also for sex if he could get it. It is perfectly consistent with what is know that he could have stayed and carried out his probable 2nd intention... having sex with her... something he could only accomplish after she died. After a clean up of the mess left when a recently deceased person relaxes certain muscles and voids waste which took long enough for blood to dry and certain marks to become fixed on the body. He may have gone to the other toilet during this time. After a while he returned to her the bra strap was cut and her body rearranged to facilitate sex. He wore condoms and left internal DNA traces either from his fingers or from the outer surface of the condom from when he handled it... After that he did a quick clean of himself and the bathroom.... it is interesting that the people who saw him at the disco later stated that he STANK.

There are no bloody footprints that match Amanda's. None. No blood found on alleged footprints in the hall therefore not linked to the murder. The shoeprint in the bedroom originally thought to match her shoe size were on cloth that had a crease that made the print appear shorter and it later was found to be consistent with the distinctive shoes that Guede wore. The bloody print on the bathmat has toe and arch characteristics that are again consistent with Guede's and not the others.

Besides the original coroner's conclusion was that there was only one attacker. He was fired from the case and replaced by a new coroner who had a new finding more in agreement with Mignini's theory of a group attack.

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: wedrifid 13 December 2009 05:34:27AM 13 points [-]

"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.

Comment author: Douglas_Knight 13 December 2009 04:22:53PM 8 points [-]

"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.

Comment author: AnnaGilmour 15 December 2009 11:42:01PM 2 points [-]

Douglas, you mention that crap evidence is "normal" even if they have better evidence, but is it normal to not also present the claimed better evidence?

Comment author: wedrifid 13 December 2009 09:32:42PM 2 points [-]

What I found most interesting about this exercise is the number of people who made this deduction. It is an error.

I am not convinced. The ratio of speaking nonsense to providing relevant evidence is a valid signal even with our less than entirely rational species.

Comment author: Morendil 13 December 2009 10:47:25AM *  12 points [-]

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 confident than your own entanglement with the evidence justifies, not the jurors' or someone else's - is that it provides others with an excuse to abandon the hard work of thinking rationally about the case, and letting themselves be swayed by the affective components: pretty pictures of Meredith or Amanda.

What I liked about your previous post was that, without any rah-rah propaganda about rationality, you outlined a procedure for laying out our current state of (un)certainty while minimizing some of the predictable biases. There was something delightful about the implausibly level-headed discussion thread it generated. We started with an open, almost playful invitation to rationality, in a spirit of inquiry.

Here we seem to be back to a spirit of established truth and advocacy, a spirit of "getting at the teacher's answer" - we even get averaging of the students' grades. I'm expecting the discussion to be more run-of-the mill, too. (Your Postscript is also mildly insulting; if someone is smart enough to arrive at the appropriate level of uncertainty in Knox's guilt, then surely they are smart enough to figure out what to do about it.)

Here, I believe, is the bottom line. Make rationality fun, and people will play along without for a second realizing it's hard work. Make rationality sound like something people ought to have, to be as smart and righteous as you - that's a turn-off.

Comment author: mattnewport 13 December 2009 07:30:13PM 2 points [-]

The Friends of Amanda site claims:

Tests also revealed the DNA of at least three other unidentified people on the bra fastener.

If that is true then it suggests to me that finding Sollecito's DNA as well is not very strong evidence for anything.

Comment author: Morendil 13 December 2009 09:12:53PM 3 points [-]

Can you explain your reasoning here, in terms of P(other folks' DNA on clasp|Sollecito guilty) vs P(other folks' DNA on clasp|Sollecito not guilty) ?

I can understand how this fact might be "suggestive" of something, but "suggestive" is the same kind of thinking as "suspicious": it's narrative rather than analytical.

Comment author: mattnewport 13 December 2009 11:47:45PM *  10 points [-]

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:

  • If A is true, then B becomes more plausible
  • B is true
  • Therefore, A becomes more plausible

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 probability of finding Sollectio's DNA on the bra clasp being very low relative to the probability of finding it if he were present at the crime scene.

Now it seems to me that the fact that the DNA of several other unidentified individuals (who it is not suggested were present at the crime scene) was also found on the bra clasp indicates that p(B|C) is not so much smaller than p(B|AC). B is only strong evidence for A if DNA on the clasp is much more likely if the person was present at the crime scene but we have several counter examples of DNA on the clasp from individuals who were not at the crime scene so we have reason to doubt that p(B|AC) is much greater than p(B|C) and therefore reason to doubt the significance of the evidence.

Comment author: Morendil 14 December 2009 07:24:38AM 1 point [-]

Now that is analytical.

And by and large I agree with the analysis - that is, I agree that how much weight to give to that particular evidence is determined by your estimates of P(B|AC) and p(B|C).

We may yet disagree on these, but if we do it should be on the basis of models that further evidence can in principle confirm or rule out, for instance whose DNA exactly was found on the clasp - does it match the investigators' ? They were at the crime scene. Contamination of that sort would help (in a Bayesian sense) the prosecution, not the defense.

What I take issue with is to say that something "does not count" when we have a previous commitment to take into account every bit of evidence available to us. Either we use Bayesian standards of inquiry, or judicial standards of inquiry, but we do not cherry-pick which is convenient to a given point we want to make.

Comment author: Cyan 14 December 2009 03:26:08AM 1 point [-]

Very well said.

Comment author: AnnaGilmour 15 December 2009 01:45:36AM 2 points [-]

Check out the blog ScienceSpheres by Mark Waterbury. He discusses at length the issues of negative controls, field controls, and pinpoints the problems with the LCN DNA analysis. One of his key points is that the mistakes in the evidence gathering and testing aren't hit or miss - they are consistent - which reveals a pattern of intention.

Comment author: Questor 16 December 2009 02:52:39AM 1 point [-]

Why are you willing to selectively discount some DNA evidence while you admit other ?

Because the 2 key pieces of evidence should be discounted because they were not arrived at by using the same type of test and were collected differently. All the other DNA testing was done using standard DNA testing in a lab that was nominally set up to do it but which did not always follow all guidelines and procedures and who did not release all data for defense experts to evaluate.

NO DNA that helped the prosecutions case was found initially on the 2 items... the bra clasp and the knife. Regular testing on the rest of the bra had strong findings for Meredith and Rudy. Amanda's DNA was on the knife handle and the bra clasp did have Meredith's as well.

Now the problem comes... the DNA specialist then attempted doing what amounts to Low Count Number (LCN) DNA test which is still experimental in most places and while now accepted in the UK it requires a very specialized expensive lab that must meet many stringent minimum requirements. The tester in this situation had never done this before, the lab was fundamentally lacking in every way to do this test and come up with verifiable, trustworthy data. And yet they did allege that they found MKs DNA or something like it... on the knife... not blood.... no blood on the knife. The DNA would have been in picogram amounts originally and easily contaminated in that lab or elsewhere by the smallest flecks of skin or dust. And there are the same problems with the bra clasp except that along with RS's alleged DNA there are 5 other peoples... unidentified. There can be little doubt that all the DNA and "all" is a very very tiny amount, much smaller than regular standard DNA can reliable even detect as being there...

Add to that no control tests were done and the "evidence" involving these 2 items evaporates. They are rightly to be judged differently from all the other DNA evidence. This looks like a DNA fishing expedition done after no DNA evidence for RS & AK turned up in MK'S bedroom. check these for details http://www.sciencespheres.com/2009/10/methods-of-polizia-pseudoscientificaa.html http://freeaman.001webs.com/pdfs/LCN_DNA_I.pdf http://freeaman.001webs.com/pdfs/LCN_DNA_II.pdf

Comment author: pataz1 16 December 2009 11:48:20PM 0 points [-]

the LCN dna test was only done on the knife; the bra clasp was a regular DNA test, i believe.

Comment author: Dreaded_Anomaly 03 October 2011 08:13:22PM 17 points [-]

Amanda Knox acquitted.

Justice is finally served.

Comment author: MarkusRamikin 05 October 2011 07:15:20AM *  4 points [-]

That took a while.

BTW, it just struck me, why do we tend to talk about Amanda Knox and fail to mention Rafaelle Sollecito?

Comment author: Desrtopa 05 October 2011 10:57:42PM 7 points [-]

Amanda Knox is American, so she gets more attention from American news media.

Comment author: JoshuaZ 05 October 2011 11:37:23PM 1 point [-]

And a white female. Don't forget that part.

Comment author: MarkusRamikin 06 October 2011 05:56:40AM 4 points [-]

And easier to type out.

Comment author: wedrifid 05 October 2011 08:15:16AM 3 points [-]

Mostly because she is more attractive.

Comment author: APMason 03 October 2011 08:20:05PM 9 points [-]

Or at least injustice has stopped being served.

Comment author: private_messaging 31 January 2014 09:58:40AM *  3 points [-]

Overturned, though.

With regards to "bayesian" analysis in question, as dilaudid said, the fact that a body was found makes for a fairly high probability that one out of a fairly small number of people connected to the victim has committed or participated in the murder. Even more so for a staged break-in.

The reason why we shouldn't imprison people based on things such as apparently weird behaviour has little to do with it's impact on probability, and everything to do with the potential for the abuses that a subjective criterion would create, as well as discrimination against "weird people" such as borderline autistic. We have to think what is going to happen on the bigger scale if we start using "weirdness" as evidence in the court.

The issue in this case is that the narrative presented by the police seems incredibly improbable even given all the facts, and there are far more probable narratives where she committed a lesser crime (such as being an accessory after the act). People who would commit murder are much rarer than people who may act as an accessory.

Comment author: gwern 03 October 2011 09:48:23PM *  2 points [-]

Thanks for the link; I've updated both predictions on PB.com.

Comment author: beoShaffer 29 June 2011 07:18:48PM 4 points [-]
Comment author: Seth_Goldin 11 June 2010 03:03:19AM 4 points [-]

I know this is an old thread, but for any people just now reading it, I thought I'd pass along this bizarre development.

Comment author: komponisto 11 June 2010 04:29:54AM 2 points [-]

See discussion here.

Comment author: ABranco 14 December 2009 07:52:44PM 4 points [-]

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.

Comment author: komponisto 14 December 2009 06:00:07AM 4 points [-]

Post now revised in light of comments.

Comment author: [deleted] 14 December 2009 07:34:16AM 4 points [-]

I posted this in response to the Hacker News thread but i wanted to cross-post it here. I appologise for not having read all the comments here first before responding. It seems your post is largely misrepresenting the facts of the case.

Have you read the judge's summary?

http://www.zimbio.com/Amanda+Knox/articles/58/Understanding+Micheli+2+Judge+Micheli+Rejected

A few key points in the prosecutions case:

  • 4 mixed DNA samples of the Knox and Kercher. Bloody footprints that match. Blood on the tap put Knox at the crime scene that evening or in the early morning.
  • A bloody bra in the washing machine
  • Attempts to frame an innocent man for the crime.
  • Repeated lying to authorities regarding her whereabouts. Still no fixed alibi.
  • Knox and Kercher's house was cleaned with bleach.
  • Sollecito's trainers were cleaned with bleach. A defect in the sole match a blood print on the scene. The decision went through going through 19 expert judges and 6 lay judges. Conviction was unanimous.
  • Eye witness putting all 3 suspects together outside the cottage that night, and the night previous.
  • Knox and Sollecito standing outside the crime scene when the police arrived with mop and bucket.

Certainly, we can ignore some of the strange behaviour of the convicted (the phone calls, the lies, her past). But the case is much stronger than what this article makes out. It's also worth pointing out that various aspects reported in the media aren't correct - such as the 14-hour interrogation and police violence.

Rational thought takes anyone first to the conclusion that there was more than one killer. Guede left the scene soon after the murder (eye witness reports; evidence of cleaning, Guede's own statement). It is clear the crime scene was later returned to, and altered to cover evidence (faked break-in; footprints; removal of bra from the body). With all the additional evidence against Knox and Sollecito, physical and circumstantial, clear motive, and consitantly irrational behaviour, gives a very strong prosecution case.

Whether they are guilty or not isn't for me to say, nor would i think i'm qualified enough to give such probabilities. But the case appears to be largely misrepresented in your blog post.

Comment author: rmattbill 14 December 2009 06:21:07PM 11 points [-]

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 twice the morning after the murder, but those stories did not pan out and were not presented at trial. One witness emerged, seven months AFTER the murder, to say he saw Knox buy bleach in his store, but his co-worker said he was lying. This testimony must be treated skeptically, since no traces of bleach were found at the crime scene. The crime scene was extensively examined using Luminol, and in addition to revealing blood, Luminol illuminates trace amounts of bleach.

-The Albanian witness who says he says Knox and Sollecito with Guede is the only person to allege that the three knew each other, and his testimony at the trial was contradictory and underwhelming, to say the least. Throughout his interrogation and trial, Guede denied knowing Knox or Sollecito, and denied they were at the house. He knew what Amanda looked like, as he had twice visited the downstairs neighbors to play basketball, but didn't even know what Sollecito looked like.

-Knox and Sollecito had taken the mop to Sollecito's house to mop up water that had come from a broken pipe under the sink. Was any blood or DNA found on the mop?

-Whether or not the bloody footprint on the bath mat matches Sollecito or Guede is highly debatable. Another bloody footprint, found in Kercher's room, was a definitive match for Guede. Although people have posted claims about bloody footprints revealed using Luminol, those prints were left by sweat and oil, and tested negative for any trace of blood.

Briefly, on a few other points, the prosecution's fingerprint expert said it was not unusual that he didn't find usable prints for Knox in her own bedroom. There were lots of smeared prints (fingerprints, made by a tiny amount of oil on our skin, are easily disturbed), just no USABLE prints. Lots of smeared and partial prints is evidence the room was NOT wiped down, and he testified he saw no evidence of a wipe down.

Last, the so-called "fake" break-in is highly contentious issue and neither conclusion can be viewed as beyond doubt. The prosecution tried to say it's impossible to climb the wall (ignoring photos of a 40-year old Italian detective in dress slacks and dress shoes easily scaling the bars on the window below), but Judge Micheli dismissed them, noting that anyone in reasonable shape could've easily climbed into the window. Rudy Guede, who had committed at least three burglaries in the previous week, was 20 years old, and a former semi-pro athlete.

But again, I appreciate your rational approach to the evidence, and respect your opinion. It's nice to see someone on the internet talking about the evidence, and not just Knox's immature behavior.

Cheers, Matt

Comment author: Jack 14 December 2009 08:05:23PM *  4 points [-]

Rudy Guede, who had committed at least three burglaries in the previous week

Jeeze, how did I miss that. Do you have a link?

Edit: Also. New people! Welcome.

Comment author: rmattbill 14 December 2009 11:37:57PM 5 points [-]

Sorry, my post contained an error. It was three burglaries in five weeks, not one week.

This is from an article at the Daily Mail entitled "Amanda Knox: The Troubling Doubts Over Foxy Knoxy's Role in Meredith Kercher's Murder."

Here's the link: http://www.dailymail.co.uk/news/article-1234298/Amanda-Knox-The-troubling-doubts-Foxy-Knoxys-role-Meredith-Kerchers-murder.html

And the pertinent text from the article:

On September 27, 2007 - five weeks before the killing - Perugia bar tender Cristian Tramantano heard a noise downstairs in his home and found Guede wandering around with a large knife. Tramantano recognised Guede from his work in a nightclub.

There was a confrontation between the two, which ended when Guede ran away. On four occasions, Tramantano went to Perugia's central police station to report the break-in, identify Guede as the culprit and to detail how the intruder was armed and threatened him.

On each occasion, he says he was ignored and the police refused to log his complaint.

The following weekend, there was a break-in at an English-speaking nursery school in Milan in which 2,000 euros and a digital camera were stolen. The school owner, Maria Antoinette Salvadori del Prato, reported it to her local police station.

Three weeks later, on Saturday, October 27 - one week before the murder - Mrs Prato arrived at the school early in the morning with a locksmith to replace the front door, only to be confronted by Guede standing in the main entrance.

Police were called and Guede questioned. A stolen laptop, digital camera and ten-inch kitchen knife were found in his backpack.

But instead of being arrested and charged, Guede was merely escorted to Milan central railway station and placed on a train back to Perugia.

In the interim, on the weekend of October 13, there had been a break-in at the office of lawyers Paolo Brocchi and Luigi Palazzoli, in which a firstfloor window was smashed - similar to the break-in at Meredith's house. A computer and other items were stolen.

They were later found in Guede's possession, but he was not arrested or charged.

Comment author: zero_call 14 December 2009 11:46:00PM 2 points [-]

The Daily Mail is a British tabloid... frequently posting completely fraudulent information about football players, for example... check your sources friend...

Comment author: AnnaGilmour 15 December 2009 05:14:17PM 3 points [-]

For the most horrible information about Guede, read his journal. Not fun to read, as it is very dark, but reveals a telling psychological profile as well as shows his time line the night of the murder. His Skype conversation as well gives a lot of information.

On the other hand, if you read Raffaele's writing, it shows his innocence.

Comment author: snarles 13 December 2009 07:04:39PM 10 points [-]

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.

Comment author: wedrifid 13 December 2009 11:12:56PM 4 points [-]

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.

When moving from my real name to this more anonymous persona the responses to my comments were noticeably different. This effect diminished over time. I've actually considered creating mechanisms by which I could make a self-blinded test of the effect of names on reception, but this was more with OkCupid in mind. Perhaps because investigating human psychology is even more fun than the dating itself.

Comment author: Douglas_Knight 14 December 2009 02:08:53AM 4 points [-]

When moving from my real name to this more anonymous persona the responses to my comments were noticeably different.

Could you elaborate?

Comment author: wedrifid 14 December 2009 05:15:59AM 7 points [-]

Could you elaborate?

Sure. I'll compare what I perceive to be the differences between wedrifid now and, say, < 100 karma wedrifid. The difference in reception was more apparent given that wedrifid didn't have the steep learning curve associated with learning a new micro-culture. * Comprehension. Comments by young wedrifid were less likely comprehended than comments of approximately equal quality now. Not understanding people is a signal of high status. It obliges the lower status people to spend effort to second guess your way of thinking and adapt towards your preferred set of concepts in order to communicate with you. This signalling appears to run deeper than an outward display. Higher status people at times seem actually unable to comprehend things that would otherwise be in their grasp, often to their own detriment. * Rebuttal. People were more likely to reply with retorts to upstart-wedrifid and, more significantly, provided less or lower quality reasons when doing so. This is to be expected less from high status people and more from people with more moderate status who would like to raise it. (There isn't much point going one up if you have to reach 3 down in order to do so.) I get less replies now that I consider to be absolutely idiotic. Again, I don't think that is just because people generate inane nonsense then decide whether or not to post it by whether they recipient is a newbie or for some reason other reason an easy target (eg. out-of-group or currently being scapegoated). I think the calibration of carefulness is built in to the rebuttal generation system.

Of course, I don't know how much of my perception is just me seeing what I expect to see: normal social behaviour. I also don't think this effect would be sufficient to overshadow a top level post by a renamed Yvain or Eliezer. I would probably just wonder who this amazing new poster was. I still remember Yvain catching me by surprise with that burst of brilliant posting in LessWrong's early weeks. Those seem to be received no worse than Eliezer's would have been if he were still posting regularly. Although come to think of it I may have rejected WeiDai's probability posts if I hadn't seen the quality of his other contributions. They are confusing enough topics that I needed to take a while to absorb them before they made sense. Of course, maybe I would have been convinced anyway while trying to write a rebuttal to RenamedWei_Dai and realising that he was absolutely right.

I am intrigued somewhat by snarles' other suggestion, the posts by top contributors that are flat out wrong. My dark side wants to suggest that maybe that is the explanation that those anthropic reasoning posts are examples of this! (Of course, a somewhat wiser side of myself reminds me that it is conceivable that I am confused, not Eliezer.)

Comment author: ciphergoth 14 December 2009 08:55:52PM 1 point [-]

Eliezer has made it explicit on several occasions that he never does this. I'm not saying it's necessarily a bad idea, but he doesn't do it.

Comment author: Eliezer_Yudkowsky 14 December 2009 08:58:07PM 2 points [-]

Aye, and I'll say it again just to be sure. If I want to say something that's not true, I write a story and put it in the mouth of a fictional character.

Comment author: Shalmanese 13 December 2009 02:32:57PM 12 points [-]

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?

Comment author: Feh 17 December 2009 10:57:32AM 8 points [-]

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.

Comment author: bigjeff5 02 March 2011 06:33:25PM 3 points [-]

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 their hypothesis. In fact I had only assigned about an 80% probability that they were guilty after reading their evidence, which would not have been enough to convict. They made scant mention of how little DNA evidence was actually used to convict them (even calling the braw-clasp significant, damning evidence), and they certainly didn't compare this to the massive amounts of DNA evidence found for Guede. In fact they made it sound as though the evidence was equivalent.

I then updated based on the pro-defense website, down to 60%, a clear case of anchoring. Had I considered the defense's evidence from a fresh perspective there is no way I could have come away with the estimate I did. The overwhelming DNA evidence against Guide should have relegated all other evidence to almost negligible importance. Everything else was unreliable, and I did not treat it as such even though in my mind I even thought that it was unreliable.

A good analogy for the DNA evidence compared to everything else would be like trying to star-gaze at high noon - the light from the sun overwhelms the starlight because the starlight is far, far too weak. Likewise the circumstantial evidence was far too weak to be of any importance when compared to the DNA evidence.

Comment author: komponisto 04 March 2011 03:57:58AM 1 point [-]

I'm ashamed to say I failed this one, and badly...this illustrates that I have a long, long way to go.

On the other hand, you'd be surprised at how difficult it is for people to understand this even after seeing the explanation. While of course it's always preferable to get things right on the first try, the fact that you saw it so clearly after reading this post places you in a high percentile for learning speed.

(I know whereof I speak here, because I've spent some time arguing about this in other parts of the internet, only to be dismayed by the true extent of people's ability to clack. Heck, even here in the comments section of this post there are some pretty confused comments with depressingly high scores.)

I think your analysis is excellent, and is an admirable example of "cognitive debugging". This part in particular is worth dwelling on:

Everything else was unreliable, and I did not treat it as such even though in my mind I even thought that it was unreliable.

It is really difficult for people to discount information, and to actually update on evidence of the form "that information may not be reliable", rather than treating it as an "opposing argument" to be rationalized away, or simply forgetting it altogether. Something like the bra clasp provides an example of this: people hear about it, and decide that Sollecito is guilty. Then, when they hear the defense argue that it's unreliable, they mentally dismiss it as "the defense trying to poke holes in the prosecution's case". They may respect the social obligation to provide some sort of answer to the defense's arguments, but they don't consider that the defense arguments should actually impact their belief about whether Sollecito is guilty; the belief-formation process was over and done with at the first stage!

It's not that they explicitly, consciously think like this, of course; rather, they have just failed to fully incorporate the "rules" into their unconscious belief-generating system. The third and fourth virtues are hard.

I like the star-gazing-at-noon analogy, and may use it myself in the future.

Comment author: bigjeff5 04 March 2011 05:07:27AM 2 points [-]

I think your analysis is excellent, and is an admirable example of "cognitive debugging". This part in particular is worth dwelling on:

Everything else was unreliable, and I did not treat it as such even though in my mind I even thought that it was unreliable.

That's what upset me the most. I made a special note of it, in order to give it a very low weighting, yet it was still a major factor in my assessment. It had to be, because the prosecution's case hinged on it.

I think next time I notice something like that I will have to assign it a specific weight as soon as I decide that it should be given a low weight. Instead I just labeled it as "weak" in my head and moved on.

So when I think "that's likely true" I should stop and consider what the actual number is that I would assign to it. This would help considering in spotting cases where I assign more than 100% total probability to an outcome. If I am thinking it is 70% likely that they are guilty and 60% likely that they aren't, there is an obvious problem. If I don't assign any numbers until I'm finished looking at the problem then I'll never spot this error, as I'll simply calculate not-guilty likelihood from the guilty likelihood.

Much to think about and much to learn still.

Comment author: Seth_Goldin 24 March 2010 03:23:41AM *  3 points [-]

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 Sollecito and Knox. This has really helped the idea of Bayesianism "click" for me.

komponisto, your reasoning is wonderfully thorough and sound. I can corroborate that I deliberately found myself "shutting the voice out" concerning the activity with the mop. You have a great explanation, overall. These two posts of yours are in the running for my all-time favorites.

Comment author: komponisto 25 March 2010 05:53:30AM *  7 points [-]

Thanks for the kind words!

Actually, looking back, I now think I could have done better. In particular, I wish I had been more explicit about the central probability-theoretic point: the fact that the evidence against Guede screens off Kercher's death as evidence against Knox and Sollecito. This point was missed by a number of commenters; if you read the discussion you'll find various people saying that the prior probability "should" take into account the fact that a murder occurred in Knox's house. In actuality, of course, it doesn't matter where you start, so long as you eventually incorporate all of the relevant information; but what must be understood is that if you start with probability mass assigned to Knox and Sollecito because of Kercher's death, then you have to take (most of) that probability mass away upon learning of the evidence against Guede. In other words, under this setup, evidence of Guede's guilt becomes evidence of Knox's and Sollecito's innocence -- something which is counterintuitive and very easy to forget (with tragic consequences).

This issue of "choosing the prior" and other Bayesian subtleties encountered in these discussions may be worth revisiting at some point.

Comment author: redlizard 17 August 2013 12:32:40AM *  1 point [-]

In particular, I wish I had been more explicit about the central probability-theoretic point: the fact that the evidence against Guede screens off Kercher's death as evidence against Knox and Sollecito.

I think this insight warrants a great amount of emphasis. The fact that Kercher's death is screened off by some factor unrelated to Knox and Sollecito means that the question of whether the given evidence against Knox and Sollecito is sufficient to judge them co-conspirators is equivalent to the question of whether the given evidence against them would have been sufficient to judge them murder-conspirators in the absence of a body. And I don't think anyone believes THAT is the case.

Comment author: komponisto 20 January 2010 02:09:28PM *  3 points [-]

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 been involved in the murder. The idea of Lumumba's guilt was planted in her head by the police. Knox's "accusation" of Lumumba amounted to no more than saying "Well, all right, I guess maybe he could have done it."

To "lie" is to make an assertion that one knows to be false. Amanda Knox was unambiguously clear about the fact that her "story" about Lumumba being the killer was a dreamlike vision, not an actual claimed memory. It does not constitute a positive assertion about the state of the world, and thus cannot be a "lie". Now, definitions don't matter, of course; but the point is that the lack of correspondence between this particular account and the actual reality of the situation is not Bayesian evidence of her having wished to deceive police about her state of knowledge (which would in turn be Bayesian evidence of her guilt).

Comment author: pete22 14 December 2009 08:52:49PM *  3 points [-]

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 that Guede could not have been the only participant – i.e. his involvement does NOT completely explain the death of Meredith Kercher. They seem to believe this for two reasons:

  1. The various evidence at the crime scene itself of a clean up and/or staged break-in, things like the bra being cut off or the body being moved – hard to attribute to Guede because a. he wouldn’t have had time (is this true?), and b. little effort was taken to remove evidence against Guede himself, even very obvious things like flushing the toilet.

  2. I haven’t seen any commenters mention it here, but one of the anti-Amanda sites, in quoting the Micheli report, seemed to imply that Kercher’s injuries were inconsistent with a single attacker.

Your post appears to take for granted that these are not credible arguments, but they seem like a very significant part of the prosecution’s case – and the part that I found hardest to assess without English versions of the Micheli report and other source documents. Can you explain how you reached this level of confidence?

FWIW, I'm not an Amanda-hater …my prior probability of her guilt was 30%, and I'm ready to revise it down. I’m just not sure I fully understand your argument on this point.

Comment author: rmattbill 15 December 2009 02:55:55AM 7 points [-]

"little effort was taken to remove evidence against Guede himself, even very obvious things like flushing the toilet."

The assumption here is that Knox and Sollecito carefully removed their DNA, but did not remove Guede's. Isn't the more rational explanation for all of the evidence against Guede, and the lack of evidence against K&S, that Guede did it and K&S weren't even there, as they have always claimed, and as Guede claimed no less than 5 times?

Further, there's a lot of supposition about a "clean-up" floating around on the web, but no evidence of one. There's lot of talk about bleach, bleach receipts, bleach on the knife, etc., but no evidence was introduced to support any of these claims.

Another claim is no prints were found for Knox, therefore she must've wiped them down. This presumes, incorrectly as it turns out, that no unusable prints were found. In fact, lots of smeared, smudge, or partial prints were found. The prosecution's own expert witness on fingerprints, Giuseppe Privateri, testified he saw no sign of the place being wiped down for prints. There were lots of prints, just not a lot of usable ones, which is totally normal since the way we use our hands often causes the oils left behind to be smeared.

Also, to believe this theory of a clean-up, one has to believe that with Superman-like enhanced vision, Knox and Sollecito could see their fingerprints and DNA, and Guede's, and could selectively remove their without disturbing his. This seems far-fetched in the extreme.

In the bathroom, some of Kercher's blood was found mixed with Knox's DNA, probably from splashing onto a hair follicles or dead skin cell from Knox. Why didn't this happen in Kercher's room, where the orgy took place? No intermingling of sweat, saliva, or other bodily fluids- in an orgy?!?! It boggles the mind.

Last, a lamp from Knox's room, her only source of light, was found on the floor in Kercher's room, possibly put there by Guede as he tried to look for his possessions, or look for obvious signs. If Knox so carefully scrubbed Kercher's room she was able to eras every invisible spec of DNA, why would she leave her bedroom lamp behind?

Comment author: AnnaGilmour 15 December 2009 04:23:21PM 1 point [-]

The idea of a staged break in is unsubstantiated. There is a broken window. Mignini added the interpretation without evidence of such a thing. The two shards on top of the bed turned out to be polka dots on a piece of clothing.

Comment author: AnnaGilmour 14 December 2009 09:02:35PM *  5 points [-]

One thing to remember is that Mignini fired the coroner doing autopsy investigation when that person said it was the injuries of a single perpetrator. He then hired someone who said it was more than one perpetrator. If you would like, I can find a link to back it up. So the original report said one person caused the injuries.

Comment author: Eliezer_Yudkowsky 14 December 2009 09:16:51PM 2 points [-]

Huh. I wondered if something like this might be the case, but then wondered if I was being selectively skeptical of the prosecution and trying to dismiss all of their evidence. Next time I'll remember to (a) trust myself a little more, and (b) remember that reality itself is consistent rather than fair, i.e., Knox obviously didn't do it, thus if the coroner says it's more than one perpetrator, I should (b1) construct a model in which the coroner is pressured (or fired and redealt) and (b2) penalize the probability of that model because (hopefully) most coroners aren't pressured.

Comment author: MichaelVassar 15 December 2009 10:05:56AM 2 points [-]

I'm not sure how much hope fits into the Bayesian analysis. My impression is that doing things like pressuring coroners is routine in the US and probably in Italy as well. Of course, pressuring coroners is a special case of "doing things like pressuring coroners" and thus unlikely a-priori, but its not very unlikely a-priori and once the possibility is raised it doesn't call for much penalty.

Comment author: AnnaGilmour 15 December 2009 04:25:41PM 1 point [-]

The significant factor though is not that the coroner was fired and replaced by someone who would report multiple perpetrators. The significant factor is that the original, unprompted, unbiased, objective analysis was that it was a single perpetrator.

Comment author: komponisto 15 December 2009 02:37:50AM *  4 points [-]

The various evidence at the crime scene itself of a clean up and/or staged break-in, things like the bra being cut off or the body being moved

A bizarre or unexpected condition of the crime scene is not the explanandum here; Meredith's death is. One person is entirely sufficient to have killed Meredith, and the DNA evidence establishes with virtual certainty that Guede had the kind of contact with her necessary to accomplish this. Unless the evidence suggesting someone else was involved is of comparable power to the DNA evidence against Guede (something on the order of 30 bits), then (and this is the part people have trouble understanding) even paying attention to it at all is automatically hypothesis-privileging.

(EDIT: Eliezer corrects below. What I actually wanted to argue here was that, given the certainty of Guede's involvement, the lack of connection between him and Knox or Sollecito is strong evidence against their involvement -- probably enough on its own to outweigh the comparatively weak evidence against them provided by the alleged indications of multiple attackers at the crime scene.)

Yes, we might be curious about the unusual mechanics of the crime scene given only one person, but unless they are so strange that assuming someone else's guilt of murder (when we already have a suspect) would constitute a reasonable explanation for them, we have to regard the whole question as a distraction.

Comment author: Eliezer_Yudkowsky 15 December 2009 04:34:37AM 6 points [-]

Unless the evidence suggesting someone else was involved is of comparable power to the DNA evidence against Guede

Doesn't follow. You can have a lot of evidence for one true statement and then less evidence for another true statement.

Comment author: pete22 15 December 2009 04:47:03AM 2 points [-]

You're right, this is the part I have trouble understanding. Partly because I have trouble separating the facts of this particular case from the theoretical point you're making. So if you'll humor me for a second: let's say you're the chief of police somewhere, and one of your detectives comes back from a murder scene and tells you "we've arrested a prime suspect and we've got very strong evidence against him, including an ironclad DNA match that ties him to the murder. but we don't think he acted alone, because of X, so we want to keep looking for another suspect."

It sounds like for almost any X, your response would be "Don't waste your time. Case closed. Your hypothesis that there was another killer is unnecessary to explain the victim's death." Is that correct? What kind of X would suffice for you to let your detectives keep investigating?

Comment author: komponisto 15 December 2009 04:54:23AM *  1 point [-]

What kind of X would suffice for you to let your detectives keep investigating?

Two examples that come to mind immediately:

-Similarly incriminating DNA from someone else in addition to the prime suspect.

-Information acquired from the prime suspect himself that points to accomplices.

Comment deleted 15 December 2009 05:02:29AM [-]
Comment author: komponisto 15 December 2009 05:13:49AM 1 point [-]

Maybe. But remember that reality is consistent: If two people were at the scene committing the crime, why would there be vastly more evidence of one than the other?

Once you have the suspect, you can interrogate him to find out who he knows.

Comment author: AnnaGilmour 15 December 2009 11:57:50PM 0 points [-]

I don't believe there was a staged break-in, but even if there was, how does one logically go from "staged break-in" to Amanda staging it? I detect a logical gap.

Comment author: AnnaGilmour 16 December 2009 12:58:49AM 1 point [-]

I am new to this site. Can someone elucidate for me why the statement above might have been seen as a minus? Just curious. I was asking for the logical link between the condition of the room and Amanda. One hasn't been provided, not even by the prosecution.

Comment author: captcorajus 19 December 2009 03:19:08PM *  9 points [-]

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.

Comment author: komponisto 15 January 2010 08:59:34PM *  5 points [-]

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 is distinct from legally admissible evidence, arguing that I chose "the wrong prior" (as opposed to just coming out and accusing me of failing to update on piece of evidence X), etc.

(2) Claims that I am too dismissive of psychological evidence.

(3) Object-level arguments from a few people who (still) think there is a significant chance Knox and Sollecito are guilty.

Here are some general responses, divided up into three separate (threaded) comments for ease of reading (and possibly replying):

(1) Bayesian pedantry.

In the first version of the post, when I wrote "there is for all intents and purposes zero Bayesian evidence that Amanda and Raffaele are guilty", I thought that "for all intents and purposes" was enough of a disclaimer; but really, of course, what I should have written was: "there is for all intents and purposes zero net Bayesian evidence...". Obviously there is some (weak) evidence of K and S's guilt; but (I claim) it is cancelled out by the evidence of their innocence to such an extent that the posterior probability is close to (not necessarily literally equal to) the prior probability.

And yes, by "prior probability", I am entitled to mean the probability that Amanda Knox would commit murder, rather than the probability that Amanda Knox would commit murder given that a murder occurred in her house. I have not neglected to take into account the latter information, and indeed, the fact that her housemate was murdered obviously raises the probability that Knox is guilty of something to a level significantly above the background prior. However, this probability is lowered again by the information that Guede committed the murder -- and this is true despite the fact that evidence of Guede's guilt is not itself evidence of Knox's innocence. As Eliezer put it,

the fact that we know Guede did it means that there's no unexplained murder around for Knox to be convicted of.

The Bayesian structure of this inference is simple enough. Let H be the hypothesis that Knox killed Kercher, and let E be the datum that Kercher was killed. Obviously, H and E are not independent; in fact, H strictly implies E, which means that P(H&E) = P(H). Thus P(H|E) = P(H)/P(E), which is larger than P(H). Now, however, let E be the datum that Kercher was killed by Guede. Then H and E are much closer to being independent, i.e. P(H&E) is only slightly larger than P(H)P(E), which means that P(H|E) is close to P(H)P(E)/P(E) = P(H). As I argued in the post, this is Occam's Razor at work: P(H&E) = P(H)P(E) << P(E).

To those who gasped at my dismissal of the DNA evidence against Knox and Sollecito when it is my solemn Bayesian duty to consider all available information, I would put it that Bayesian rationality is supposed to be more accurate than legal reasoning, not less. The kind of legal rules of evidence that would come into play here exist because of known biases people have toward convicting defendants (others, not relevant here, exist as a reflection of society's willingness to let a few culprits go free in order to maintain a certain incentive structure on police and prosecutors). Thus, if when you put your Bayesian goggles on, you suddenly find that defendants are looking more guilty than they used to, you're probably doing something wrong. In any case, dismissing evidence is not an illegal Bayesian move; it simply constitutes an assertion that the likelihood ratio for the information in question is close to 1. In other words, the evidence is very weak. Which probably has something to do with why it might not be admissible in court.

Comment author: komponisto 15 January 2010 09:01:58PM *  4 points [-]

(2) Claims that I am too dismissive of psychological evidence.

Some folks appear to have misunderstood me as arguing that psychological evidence can be dismissed out of hand by its very nature, or that Amanda Knox shouldn't have been questioned by police despite being Kercher's roommate. Obviously, neither is the case. First of all, psychological evidence, strictly speaking, is physical evidence. In fact, all evidence is physical. The question, always, is about how strong a given piece of evidence is. In the post, I mentioned two rules for this: (i) the closer the spatiotemporal connection, the stronger the evidence -- something which follows from the laws of physics; and (ii) high-prior data is at most weak evidence of a low-prior hypothesis (or: thou shalt not postulate a strange thing to explain a less strange thing) -- an immediate consequence of Bayes' Theorem.

If a person's behavior were sufficiently unusual, it might constitute significant evidence they were involved in a homicide. And if a murder occurs in Knox's house, Knox is clearly one of the first people the police should interview. But the psychological evidence against Knox is in fact very weak: the causal linkage between Knox's cartwheels, phone calls, or speculation about Lumumba's involvement on the one hand, and a hypothetical murder committed by her on the other is very tenuous compared to the causal links between these things and more local factors which are likely to be largely independent of Kercher's murder. And yet, many people mistakenly believe the evidence is strong. Why? Because, for perfectly understandable evolutionary reasons, people are interested in psychology; it's salient in their minds, and they mistake this salience for evidentiary strength. They find it easy to imagine a guilty Amanda Knox doing cartwheels, and caught up in the narrative, forget to properly consider the ways in which an innocent Amanda Knox could also end up doing cartwheels. (In fact cartwheels were never something particularly unusual for Knox.) And, in continuing to consider such weak evidence against Knox after the strongest evidence in the case -- the evidence from Kercher's room -- has pointed decisively to the crime having been committed by Rudy Guede, they compound the error by privileging the hypothesis, or, in other words, overestimating the prior probability, of Knox's guilt.

Comment author: komponisto 15 January 2010 09:05:37PM *  4 points [-]

(3) Object-level arguments from a few people who (still) think there is a significant chance Knox and Sollecito are guilty.

There don't appear to be many LW regulars who assign high probabilities to Knox and Sollecito's guilt. There are a few who remain apprehensive about doubting the rationality of the jury or of people like Judge Micheli (the judge in the Guede case) to the extent of lowering the probability of guilt to single digits of percentage; but mainly, they agree that acquittal is called for. My remarks here will thus be directed mostly at people chancing upon this post from outside.

It is incorrect to assume, as some people have, that because I didn't mention various facts about the case in this post, that I am therefore unacquainted with them. On the contrary. However, I do assert that the essence of the case -- the decisive information -- is just what I presented here. Among my main points was that people have been distracted by various other details to the point of getting the wrong answer. The central case in point would be the eight members of the Perugian jury, who despite hearing all kinds of information over the course of nearly a year, were unable to sort out the clutter from the essential facts, which are these:

  • The prior probability of Knox and Sollecito having committed murder is extremely low; of having committed this particular kind of murder, even lower.

  • Since Guede is unquestionably responsible, the mere fact of Kercher's death does not need to be explained.

  • There is no evidence that Knox was in Kercher's room on the night of the crime, and almost no evidence that Sollecito was.

  • There is almost no evidence of any association between Knox and Guede, still less of any between Sollecito and Guede.

  • There is no evidence of antipathy toward Kercher on the part of Knox or Sollecito, or of any other plausible motive for the crime.

  • Every piece of apparently strong prosecutorial evidence has either been totally discredited or is subject to serious doubt (examples: footprints, "mixed" blood, knife, bra clasp, cleanup,...).

  • The remaining prosecution case consists of odd physical facts that are nowhere near as strange as Knox or Sollecito being guilty (broken window circumstances, apparent rearrangement of scene), dubious psychological inferences (inconsistencies => cover-up, cartwheels => not sad, not sad => guilty), and outright non-sequiturs (Knox named Lumumba & Lumumba innocent => Knox hiding something).

  • Knox and Sollecito (along with Lumumba) were suspects before Guede was; the basic theory of the crime was not revised when Guede was discovered.

The above facts are indisputable; there can be little question about which way the winds of evidence blow in this case. Yes, there are lots more detailed facts you can learn about the case (and I know a bunch of them), but as regards the question of who is guilty and who is not, the above is what you need to know, and the rest is noise.

Comment author: rolf_nelson 01 February 2010 08:41:25PM *  -1 points [-]

Point-by-point:

Given that AK's roommate is dead, a break-in was staged, and the coroner's report showed multiple attackers, the prior on AK being a murderer of Meredith is rather high. On the other hand, if we throw away all known evidence, the prior of AK (or Guede, for that matter) being a murderer of Meredith is less than one in a trillion. I claim the former approach, where you use evidence rather than ignore it when it's inconvenient, is preferable. [Edit: OK, that was too snarky. Let me instead say that you should start with a tighter prior rather than a looser prior where possible; it makes the math more tractable.]

That said, I think our main disagreement is on whether the prosecutorial evidence holds up.

  1. Why do you believe DNA evidence flies around so easily? Quick tests: Do you find your beliefs about DNA match up with how DNA is used to draw conclusions in any other court cases that you're familiar with? Why was RS and the other roommate's DNA not found in more areas? Google any video of a DNA testing lab. Are they wearing hazmat suits and, if not, why aren't the testers contaminating their own samples left and right?

  2. I disagree the five pieces of evidence you listed (footprints, DNA-mixed blood, knife, bra clasp, cleanup) are discredited. I am interested in hearing why you personally believe each of them is not strong evidence. [Edit: if you limit yourself to one item, my order of preference is DNA-mixed blood, then knife, then bra clasp.)]

  3. Outside of those five pieces of evidence, I also think you're being too dismissive of the other pieces of evidence. For example, why is Knox naming Lumumba a non-sequitur?

  4. If the basic theory was that multiple people, including at least one roommate, killed MK, then there was no reason to abandon that basic theory upon discovering Guede.

Am I correct in that one of our disagreements is this:

Observation: AK claimed she saw Lumumba kill Meredith. Lumumba was therefore detained by the police based on her affidavit, but Lumumba turned out to be innocent.

Your conclusion: The presence of this false accusation decreases the probability of AK's guilt (?!) (Because it somehow leads credence to a railroading theory? You may be buying into a false FoA meme that the prosecution merely replaced Lumumba with Guede to save face.)

My conclusion: The presence of this false accusation increases the probability of AK's guilt.

Comment author: Jack 01 February 2010 11:48:53PM 9 points [-]

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. Then when Lumumba was cleared and an actual suspect was found they kept AK in their hypothesis so as to not totally embarrass themselves. Indeed, this explanation is one of the few parts of the story where I feel like I can account for every single fact and where no other particularly different explanation makes sense. Even if Knox did kill Kercher I would still assign this kind of story a high probability.

Comment author: captcorajus 17 December 2009 03:51:44AM 5 points [-]

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 innuendo would be that she cleaned the crime scene, but see the logic problems posed by that below.

"Knox purchased bleach the morning of the murder, there are receipts." No receipts were presented at trial, but even if there were what how is that probative?

"The found the murder weapon in Sollecito's flat." They found his knife, in his flat, in his drawer. Logic alone makes it unlikely that this is the murder weapon, and the prosecution's own analysis reinforces this. See logic question below as to why.

"Meredith's bra had Sollecito's DNA on it." Left on the floor of Knox's flat for 47 days after the murder, a variety of DNA including Sollecito's was found on the seperated clasp, not the bra itself.

... and on and on. I offer no explanation in this article for these, but simply pose some logic questions that address conflicting and incompatible ideas with the facts. This approach certainly reveals some troubling problems with the case against Knox and Sollecito. The unspoken question at the end of each of these is simply, "If this is so, how is that possible?"

Logic problem 1: They had the temerity to properly dispose of their bloody clothes and shoes, but then took the murder weapon home, cleaned it thoroughly, and put it back in the drawer?

Logic Problem 2: They cleaned the knife so well that luminal had no reaction, no blood was found on the knife, but the low copy skin DNA of the victim somehow remained on the blade???

Logic Problem 3: With a mop and bucket they somehow managed to selectively clean the murder scene clean of their DNA and fingerprints but leave behind Rudy Guede's??

Logic Problem 4: The bra clasp collected 47 days after the murder had Sollecito's DNA on it, but the bra itself did not???

Logic Problem 5: Meredith Kercher's bedroom door was locked from the inside and had to be broken down to gain entry. How did Knox get in there and remove all of her and Sollecito's fingerprints and DNA and leave behind Rudy Guede's?"

I too have felt this case begs for the the application of Occam's Razor. You simply can't connect Knox and Sollecito to Guede, much less put them into some three way sexual tryst. My logic circuits implode at the prosecutor's inane theory, which to prove you would need significantly more evidence than what was presented at trial.

Comment author: wedrifid 13 December 2009 05:26:48AM 5 points [-]

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.)

Comment author: Yvain 13 December 2009 03:01:12PM 3 points [-]

...and why do you assert that? If you have good reasons, I'd like to see a top level post on the subject, since this is my natural response to a bunch of probability estimates given by different people with the same information who are rational enough that I care what they think.

Comment author: badger 13 December 2009 05:51:55PM 3 points [-]

Not a top level post because I don't think I have the definitive say on the matter, but I made an article in the wiki that illustrates why the mean of the log-odds makes more sense.

Unfortunately, the wiki appears to have issues with math right now, so the article has an ugly error message in it. The formula works fine in the Wikipedia sandbox. If anyone knows what is going on or has any other changes, feel free to edit.

Comment author: wedrifid 13 December 2009 09:52:02PM *  1 point [-]

...and why do you assert that?

Somebody with no information does not so effectively counterbalance ten people who can describe the positions of every atom on the planet.

I calculated an example involving 0.99, 0.5, 0.745 and (1-10^20) but then I noticed badger's link beat me to it.

Comment author: ciphergoth 13 December 2009 09:09:55AM 2 points [-]

What would the right thing look like? Averaging the log-odds ratio?

Comment author: dilaudid 13 December 2009 05:33:23PM 1 point [-]

That's what I would do. If one person is almost certain (say 1/(10^10^10)) then the strength of their view would be represented. Of course if anyone gives an irrationally low or high answer, or puts <=0 or >=1, then it overweights their views/blows up.

Comment author: [deleted] 13 December 2009 06:27:28AM 2 points [-]

I wonder what implications this has for the method of choosing priors I came up with that is "ask everybody in the world what they think the priors should be, normalize the invalid ones, and take the average of all of them".

Comment author: D_Alex 13 December 2009 06:54:17AM 8 points [-]

@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 calculation.

And this:

"3. About as high as the other two numbers are low. 0.999 as a (probably weak) lower bound."

Did your prior of "0.001 at most" apply to Guede as well?

I offer $50 to the AK defense fund if you can produce a defensible Bayesian probabilities calculation showing how you got from your priors to your final probabilities. A condition is that you must account for the fact that most (let us say 80% for the purposes of your calculation) persons convicted of a crime in a democratic society are in fact guilty of it, and that you use generally defensible assumptions.

Should you try to do so, Less Wrong readers can decide if you have succeeded by voting on the post containing your calculation.

D. Alex

Comment author: [deleted] 13 December 2009 07:30:18AM 4 points [-]

While I have a sort of vague sense of disagreement with this comment, I voted it up, because I would be very interested in an example of Bayesian reasoning applied to the real world without having a truckload of given probabilities to work with. In particular, I don't know how one would take into account D_Alex's 80% while also taking into account more specific factors.

Comment author: Tyrrell_McAllister 13 December 2009 05:13:11PM 5 points [-]

I had the same reaction. I'm strongly inclined toward the OP's position, but if you're going to excoriate everyone else for failing to "jettison [their] intuitive feelings in favor of cold, hard, abstract calculation", you should provide the actual cold, hard, abstract calculations supporting your own position.

Comment author: komponisto 18 December 2009 08:49:01PM *  1 point [-]

if you're going to excoriate everyone else for failing to "jettison [their] intuitive feelings in favor of cold, hard, abstract calculation", you should provide the actual cold, hard, abstract calculations supporting your own position.

I should have pointed this out earlier, but for the record: "cold, hard, abstract calculation" referred to the willingness to ignore quantitatively weak evidence even though it "feels important" to you; it did not refer to some specific back-of-the-envelope application of Bayes' Theorem.

(And "excoriate" is definitely not the right word here, at least with regard to the LW community.)

Comment author: Blueberry 13 December 2009 07:21:50AM 3 points [-]

A condition is that you must account for the fact that most (let us say 80% for the purposes of your calculation) persons convicted of a crime in a democratic society are in fact guilty of it

I'm curious where in the world you get this "fact". I don't believe that at all (and it seems essentially unverifiable). Also, remember that Knox isn't a random person convicted of a crime: most of them don't make international news. Also, Italy does not have the same rights and freedoms as the US: for instance, they don't have separation of church and state.

Comment author: ciphergoth 13 December 2009 09:14:39AM 2 points [-]

The only test I can imagine is: when a new technique, like DNA testing, comes along, test a random sample of cases to which it is applicable. Unfortunately the cases re-examined are very carefully chosen, so no such information is available.

Comment author: retired_phlebotomist 13 December 2009 05:05:29PM 1 point [-]

"I offer $50 to the AK defense fund..."

Has the offer been amended from $50,000 to $50 since last night, or did I just misread it at 1:00 AM?

A shame, because I was looking forward to seeing the attempt.

Comment author: wedrifid 13 December 2009 05:04:03AM *  6 points [-]

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 commenters on your last post were off by no fewer than two orders of magnitude. Probability is subjectively objective. There is one correct estimate for you to have given what you know but this is not the same one that others should have. In fact, given that on average the commenters care less about the subject so did less research if they arrived at the same confidence as you then one of you would probably have to be wrong.

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!)

The task isn't to guess your password. The task is to assign probability estimates about the state of their timeline of universe. Their universe does not include the state 'it is <some completely arbitrary high probability> probable that Amanda is innocent'.

ETA: I totally agree with your main contentions and found your post both insightful and extremely well written. It is rare to see such well reasoned essays from people who are emotionally entangled with the topic.

Comment author: AnnaGilmour 15 December 2009 05:32:20PM *  4 points [-]

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 initially implicated her former boss;

3.Allegations of police intimidation and misconduct were not investigated;

4.DNA evidence appears shoddy, and is the sole source of evidence linking Knox in any way to the crime;

5.Mignini, the chief prosecutor, stands accused of criminal abuse of office;

6.Mignini threatened and began to carry out a rigged prosecution against a journalist whose coverage he disliked;

7.Press were allowed to influence jurors and judges in the case;

8.There is evidence police knowingly presented false evidence, fabricating unsubstantiated theories of the crime;

9.There are questions about the legitimacy of imprisoning Knox for two years before even bringing her to trial;

10.Jurors may have slept through defense testimony, flagrantly ignoring facts of the case that conflicted with prosecution claims;

11.The prosecutor openly announced his determination that the trial should be treated as a guilty unless proven innocent process: investigation of possible collusion between the prosecutor’s office and the presiding judges were never properly investigated."

Comment author: imgleader 06 March 2010 03:46:44PM 2 points [-]

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.

Comment author: adrienm 16 January 2010 01:08:52AM 2 points [-]

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 inconsistencies. In addition perspective was not used in evaluating the various items of evidence against likely events. By creating such a fantastical scenario of an extreme sexual it seems the prosecution managed to distract the jury away from their normal perception of what is likely or otherwise to have happened. Note I am not implying such extreme acts of sexual behaviour are that uncommon, however I believe that amongst 20 year old female exchange students with normal family backgrounds, such extreme sexual practices are so rare as to be nonexistent. If one takes this view point and only then looks for evidence to support an event with such a high degree of improbability, then one needs to look for evidence that supports the claim far beyond that of any reasonable doubt. Certainly the circumstantial evidence presented to date is far too insufficient to outweigh this.

Comment author: bigjeff5 02 March 2011 07:08:02PM 1 point [-]

Worse, there was no physical evidence of a forced sexual orgy, there was no evidence that Knox or Sollecito were interested in such an orgy, there wasn't even any evidence that they had the slightest inclination toward that kind of behavior.

In other words, it was a hypothesis drawn from nothing, created in order to support a larger hypothesis that was based on extremely weak evidence and made before a far more likely guilty party was known.

The massive amounts of evidence pointing to Guide should have made this possibility extremely unlikely, and without it there was absolutely no reason for Knox and Sollecito to be involved at all.

Comment author: gate 23 December 2009 07:58:18AM 2 points [-]

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.

Comment author: Feh 24 December 2009 09:04:15AM 2 points [-]

Rudy chose the "fast track" option, which allows for a one third reduction in prison term, and so that's why his sentence was reduced. I don't really understand their system enough to criticize it, but it seems to me that guilty criminals generally would choose the "fast track" option, and get reduced sentences, whereas the innocent generally would choose the full trial, and get full sentences.

Comment author: AnnaGilmour 16 December 2009 01:26:37AM *  2 points [-]

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

Comment author: LauraABJ 13 December 2009 09:41:26PM 2 points [-]

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- fantasies or how many fantasy writers are violent offenders?

3) Knox really wasn't able to give a consistent story about her whereabouts. (I discount this a lot more now knowing her testimony was given under duress, but can't dismiss it entirely.)

Now, this doesn't add up to all that much, but certainly more than the p = 0.001 you are claiming. I think the odds are higher that she talked with Guede i n passing before he raped and murdered kercher than that she was there when it happened (due to absence of evidence and failure of guede to implicate her).

Comment author: Blueberry 13 December 2009 09:45:08PM 2 points [-]

Knox wrote a story about the drugging and rape of a young woman.

Did she really? Link/cite please? Is the story available anywhere?

I realize it may affect probability calculations, but it just doesn't seem fair to use someone's fiction against him.

Comment author: Psychohistorian 23 December 2009 07:37:42PM 3 points [-]

It's doubly unfair in the context of an assignment. I wrote an incredibly gory horror story when I was in elementary school; I would probably have been sent to see the principle if it had happened today. It had nothing to do with me being a violent person and everything to do with me thinking that it was how one wrote an effective horror story.

More generally, deviant writing and fantasies tend to be way, way more common than you'd think (simply since people do a decent job of concealing them), so just because someone writes something unusual or has unusual fantasies, that does not strongly suggest that they actually engage in such behaviour.

As a simple example, people who run over hookers and take their money in Grand Theft Auto are probably much more likely to do so in real life than those who do not. However, the number of them who actually do so is so small that even this significant increase in probability is not very useful. Even if they are a hundred times as likely to do this, going from .0001% to .01% is not as big of an increase as, "They're a hundred times more likely!" sounds.

Comment author: LauraABJ 13 December 2009 09:56:29PM 2 points [-]

I can't find it- though the excerpts given in the NYTimes do sound more like a soap-opera than a rape-fantasy.

Comment author: Kevin 14 December 2009 04:29:51AM 3 points [-]

No link handy, but it was for a class assignment and Knox's story was by far not the most violent out of the stories written by her peers.

Comment author: wedrifid 14 December 2009 05:42:51AM 3 points [-]

No link handy, but it was for a class assignment and Knox's story was by far not the most violent out of the stories written by her peers.

"I can't do the assignment miss, because I don't want to be imprisoned for murder!" I'm going to have children just so I can recommend that excuse to them.

Comment author: JRMayne 16 December 2009 03:19:21AM 4 points [-]

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 times as he is bicycling home from work. Wife has an alibi - she was 30 miles away, on film, at the time. But wife, after 20 minutes of questioning, confesses to giving $3,000 in cash she had squirreled away to someone (a description, but no name and he's gone) to shoot Hubby, that she gave him Hubby's route, and she was mad at Hubby for his affairs, affairs investigators later confirm.

Is the confession noise? We have no physical evidence. That's somewhat dissimilar to your assertion, I understand. Let's take it back a step:

Let's keep Hubby shot dead, but Wife does not confess. However, she has a $45,000 withdrawal the day before. She says it was for "baking supplies," but she lost it somewhere and can't find the cash. She says that she dearly loved Hubby, but she has dates from match.com that she set up the week before. When the cops get there to tell her about Hubby 15 minutes after the shooting, all of Hubby's clothes and property are being placed in a Goodwill truck, and Hubby's car is on sale at E-bay and there's champagne on ice.

I don't think that's noise.

And I don't think Amanda Knox's behavior is valueless noise. The argument made that the lack of physical evidence is far more telling may be sound (depending on the actual evidence), but the behavior is evidence.

Potential Bias Alerts: I'm a prosecutor. I have had my cases dissected in the press (one case may end up on TV) and not always accurately. Circumstantial cases with a high degree of detail are often difficult for the press to get right, in my experience. Highly-charged sex cases are often difficult for the press to get right, in my view. I have no experience with Italian authorities, and probably impute similarities to American justice that do not exist. I do give some value to the jury's verdict, because I do not believe that the time I've spent looking at the evidence is anywhere near sufficient.

Comment author: AnnaGilmour 16 December 2009 05:00:26PM *  1 point [-]

micio quoted:

"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 exploiting Knox's image only to the extent it lines up with the idea that she's "not the type" who could kill another human being in connection with an act of sexual violence"


After a while people will be accountable for the evidence they choose to acknowledge or not. Things like this are inconsequential and incidental. Stick to the evidence. Talk about that. You will be voting for civilization and the rule of law or rule by thugs.

What I am finding is that a few people who are commenting here are consistently making the mistake that komponisto described. They are not leaving their perceptual fallacies.

For instance this statement:

"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."

First of all, if the roommate question is enough to bring her in for questioning, then it should be on the same level as the inquiry toward the other two roommates, and this also puts Raffaele further out on the proximity scale. But these checks should be quick and cleared by the lack of physical evidence.

And this statement:

"Wife...confesses to giving $3,000 in cash she had squirreled away to someone (a description, but no name and he's gone) to shoot Hubby... Is the confession noise? We have no physical evidence. That's somewhat dissimilar to your assertion, I understand. Let's take it back a step..."

This has been checked as well. Given the lack of physical evidence, then evidence of conspiracy or collusion gets checked. There was no evidence of this either.

And the following statement:

"...but the behavior is evidence."

Not when there is no evidence of conspiracy, collusion, or physical evidence because then you are going back to the mistakes described by komponisto in the post.

Comment author: wedrifid 16 December 2009 08:48:47PM 2 points [-]

Use a '>' at the start of a paragraph that is a quotation

so it will look like this.

Comment author: Psychohistorian 13 December 2009 06:15:25AM 3 points [-]

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, as 5% is extremely reasonable doubt - think that if that were our normal standard, we could have hundreds of thousands of totally innocent people imprisoned. So if people are somewhat like me, they probably just picked a low number to show "not guilty" and left it at that.

Of course, this is largely your point: given the evidence, there's really no reason those numbers should too much higher than they are for a random inhabitant of the city, so our willingness to compromise is itself a flaw, though, in this context, a flaw without adverse effect, as we'd still acquit.

Comment author: MendelSchmiedekamp 13 December 2009 06:37:33AM 11 points [-]

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.

Comment author: brazil84 13 December 2009 10:44:50AM 2 points [-]

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.

Comment author: Jack 13 December 2009 12:00:49PM 6 points [-]

Can you make explicit your intuitions? What experiences in particular lead you to think this?

Comment author: brazil84 13 December 2009 12:37:20PM *  1 point [-]

Well I've learned as an attorney that in general when people engage in a big or concerted effort to conceal, destroy, or manipulate evidence it's usually because the evidence is (or is perceived to be) damaging to their interests. Here, it seems pretty clear that Amanda Knox staged a break-in to her residence. Why would she do that if she were not involved in the murder?

At a minimum, she must have known before the police came that her roommate had met with serious misfortune. And how would she have known that if she had not been involved in the murder?

Similarly, it seems pretty clear that Knox attempted to manufacture an alibi by spinning a web of lies. Which is difficult to do nowadays since there are various electronic forms of evidence (cell phone records, internet records, etc.) to catch you up, which appears to be what happened.

I suppose it's possible she did all of this because she was innocent but still afraid the police would put the blame on her. But that doesn't make much sense since she could have easily pointed the finger at the African.

Comment author: Jack 13 December 2009 03:31:01PM *  5 points [-]

I'm pretty sure everyone agrees that if it is the case that Knox staged a break-in, knew before the police came that something happened to her roommate or tried to manufacture an alibi by spinning a web of lies then she is likely guilty. And we probably don't need experience as attorneys to tell us that. The question is whether or not the evidence in favor of those things outweighs the absence of physical evidence or any motive, and the fact that female college students don't commit many sexually motivated throat slittings. What evidence for the former exists and how that evidence should be interpreted doesn't appear to be a settled matter. At this point I'm not clear on what was misinformation and what wasn't. But even if a break-in was staged we have no particular evidence tying Knox to the staging. And the so-called "web of lies" is hard to distinguish from the tale of a scared and confused girl abused by police. She must have known something bad had happened to her roommate? This is big news to a lot of us, explain.

Comment author: brazil84 13 December 2009 03:55:27PM *  4 points [-]

"I'm pretty sure everyone agrees that if it is the case that Knox staged a break-in, knew before the police came that something happened to her roommate or tried to manufacture an alibi by spinning a web of lies then she is likely guilty."

I'm not sure if that's true, since the original poster did not really address the staging issue. There is a lot of evidence one can consider, and each of us can make our own judgment about what evidence is more important and what evidence is less important.

Anyway, let's break things down a bit, since your 3 "ifs" are not logically independent.

  1. Do you agree that if Amanda Knox staged a break-in, then she was probably involved in the murder?

  2. Do you agree that the evidence does in fact suggest that a break-in was staged?

  3. Do you agree that if a break-in was staged, the likely perpetrator (of the staged break-in) was somebody who had lawful access to the residence?

Comment author: Jack 13 December 2009 04:37:57PM 1 point [-]

1, Yes. 2. Whoever was in there appears to have made some effort to make things look like a burglary (that is the best explanation for the strewn clothes and the fact that nothing was missing). But that doesn't mean the window breaking was staged. I find the argument that the window as inaccessible and that the glass was on top of the clothing unpersuasive. I don't know if forensics got good photos of the glass, how much there was or if we're just relying on the word of the roommate. 3. If the window breaking was staged then it was likely done by someone with lawful access- that could be Knox, someone with Knox's key, Sallecito, Guede invited up by Kercher, one of Kercher's friends, the landlord etc.

Comment author: Unknowns 13 December 2009 03:35:40PM 1 point [-]

The only evidence we have that she was abused by police are Amanda's own statements, which were also contradicted by the police. Given the multiple contradictions in her stories, her claims about the police might or might not be true, but are certainly not strong evidence of anything at all.

Comment author: [deleted] 16 June 2011 10:04:42AM 2 points [-]

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 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.)

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. If this intuition really is unreliable, then it ought to be possible to conduct some sort of experiment showing that it's unreliable. Until we see such an experiment, the best way to proceed is not by ignoring these intuitions, but by mere skepticism.

Comment author: komponisto 16 June 2011 11:03:27AM *  8 points [-]

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?

Comment author: brazil84 13 December 2009 10:57:19AM 2 points [-]

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.

Comment author: kodos96 14 December 2009 06:01:26PM 4 points [-]

What exactly do you think makes it "apparently staged"? All the evidence I'm aware of is that it looked like a burglary cause it was a burglary.

Comment author: SforSingularity 27 December 2009 08:05:16PM 1 point [-]

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 something? Have they never read Eckman, or at least Gladwell? Perhaps Less Wrong commenters are distrustful of their instincts to the point of throwing out the baby with the bathwater.

http://www.amandadefensefund.org/Family_Photos.html

Perhaps it is confusing to people that the actual killer is probably a scary looking black guy with a sunken brow. Obviously most scary looking black guys with sunken brows never kill anyone. So that guy's appearance is only very weak evidence of his guilt. But wholesome-looking apple-cheeked college girls don't brutally murder people ever, pretty much. So that is strong evidence of her innocence.

Comment author: Eliezer_Yudkowsky 27 December 2009 08:27:31PM 7 points [-]

Girls with cute smiles like that don't brutally murder people.

[citation needed]

Comment author: gwern 27 December 2009 08:37:34PM 7 points [-]
Comment author: Bo102010 27 December 2009 10:44:33PM *  1 point [-]

Although "unattractive individuals commit more crime in comparison to average-looking ones, and very attractive individuals commit less crime in comparison to those who are average-looking" is evidence for SforSingularity's claim, his comment is absurd enough to be taken as satire.

Comment author: gwern 28 December 2009 12:53:24AM *  9 points [-]

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.

  • First off, the number of murders so ascribable are small: females make up half the population and if we limit pretty to the top 5% or so (a reasonable guess at % for 'pretty enough that a guy will actively note and think "pretty!"'), we're already down to less than 2.5% of the population.
  • Second, women in general commit far fewer violent crimes than men. http://www.ncjrs.gov/html/ojjdp/jjbul2002_10_1/page4.html mentions that for juveniles, at one point, the male:female ratio was 22:1. Let's be conservative and put the young adult ratio at 5:1; now we're down to 0.4%.
  • Third, attractiveness is correlated with IQ, and IQ is well-known to correlate with lower crime rates. (see Wikipedia for a few links; IIRC, WP understates the case but I can't be fashed to dig up the stronger correlations). Let's cut another 10% off the rate, down to 0.36%.
  • Fourthly, attractiveness correlates to higher socioeconomic status through multiple mechanisms, which cuts down violent crime even further. (I don't think I need to adduce any citations for that!)

And so on. I've missed many factors (eg. maybe happier & less stressed people are more attractive, and that too is correlated to less propensity for murder; maybe pretty women have fewer violence-inducing mental diseases and substance abuse habits; etc.). But I've already knocked their murder rate way down. I suspect it has much further to go in a true reckoning.

Does his comment still look satirical to you?

Comment author: DanArmak 28 December 2009 12:33:06PM *  5 points [-]

we limit pretty to the top 5% or so (a reasonable guess at % for 'pretty enough that a guy will actively note and think "pretty!"')

Interesting. When I read "pretty", I thought of a binary division (make guys judge "pretty or not") and I thought it would yield at least 30-40% as pretty. (Possibly much more, but I've a high degree of certainty that at least that much.)

Granted that your test is different than mine, what leads you to your 5% estimate, which looks low to me even with your test?

Comment author: Jack 28 December 2009 12:42:21PM *  5 points [-]

30-40% seems reasonable for Knox's age group (early twenties). Something closer to 5-10% seems reasonable for the entire female population. Keep in mind pretty people are almost certainly more visible than the non-pretty (especially if you have high socio-economic status).

Comment author: gwern 01 January 2010 11:20:43PM 1 point [-]

I think 30-40% is unrealistic: something like 20-30% of females in that age group are overweight or obese, leaving 70-80% in an attractive weight bracket; are we really going to call half of those 'pretty'?

It may just be my media-biased high standards, but I don't think I'd call half of all thin young women that.

Comment author: gwern 28 December 2009 02:12:03PM 1 point [-]

Here's one exercise: take your highschool yearbook, open one of the dense pages (with dozens of pics on it), and let your eye drift along the columns with no particular intent (this is hard); how many of the girls will actually catch your attention for being attractive and not for having, say, bizarre & outdated hairstyles? For me, it was less than 1 in 10. (One plain forgets about the bottom 50% and between that and 90% is the 'unoffensive' range.) Considering that my highschool was private and that selection effects were already operating, I have to revise the estimate further down; ~5% seemed good & is a nice round number.

Comment author: Technologos 28 December 2009 03:47:49PM 4 points [-]

For what it's worth, I remember a study on Stanford undergrads with what was essentially speed dating; men suggested their interest in a second date with ~90% of the women they met, and simultaneously their top criterion for that choice was attractiveness. Even granting that they had loose definitions caused by the study, I suspect that under Dan's metric (binary choice) a reasonably large minority might be tagged "pretty."

I also didn't get the impression from the photos on the website that anybody in the Knox case was pretty in the sense that you mean it--I think of your criterion as defining "remarkably pretty" rather than "pretty, if I had to choose," and I'd say you're probably right on <5% being remarkably pretty.

Comment author: Douglas_Knight 28 December 2009 09:22:41AM 3 points [-]

First off, the number of murders so ascribable are small: females make up half the population and if we limit pretty to the top 5%..., we're already down to less than 2.5% of the population.

That's like saying very few murders are committed by people named Amanda. That's OK, if you're very careful, but you have to, at least, weigh it against the very few murders by people named Rudy. 2-4 are OK, though.

Comment author: gwern 03 April 2013 06:00:51PM 0 points [-]

Reference class tennis. Being an attractive female with a (formerly) well-off family is far more important a reference class than being named Amanda; and the corresponding reference class for Rudy would be being an unattractive man who is a poor African immigrant.

Comment author: Douglas_Knight 03 April 2013 11:44:24PM 1 point [-]

Reread your comment. What is the point of your your first bullet point that pretty girls are rare? That tells you nothing, just as the fact that Amandas are rare tells you nothing. Points 2-4 about the relative propensity to murder are relevant. But I'm explicitly talking about point 1 in isolation.

Comment author: Bo102010 28 December 2009 01:14:46AM *  1 point [-]

I think the "My probability estimate of guilt was around 1%" bit is probably pretty spot on (for the reasons you state), and not absurd.

I think the "I only saw a photo of Amanda Knox's face. Girls with cute smiles like that don't brutally murder people" and "Perhaps it is confusing to people that the actual killer is probably a scary looking black guy with a sunken brow" bits are absurd-enough-to-be-satire.

Comment author: Alicorn 27 December 2009 08:26:31PM 5 points [-]

Via what mechanism does wholesome appearance and apple-cheekedness correlate with a disinclination to commit murder? For example, does a murderous disposition drain the blood from one's face? Or does having a cute smile prevent people from treating the person in such a way as to engender a murderous disposition from without? I wouldn't be exactly astonished to find a real, strong correlation between looking creepy and being dangerous. But I'd like to know how it works.

Comment author: SforSingularity 01 January 2010 02:28:44PM *  6 points [-]

Think about it in evolutionary terms. Roughly speaking, taking the action of attempting to kill someone is risky. An attractive female body is pretty much a guaranteed win for the genes concerned, so it's pointless taking risks. [Note: I just made this up, it might be wrong, but definitely look for an evo-psych explanation]

This explanation also accounts for the lower violent crime rate amongst women, since women are, from a gene's point of view, a low risk strategy, whereas violence is a risky business: you might win, but then again, you might die.

It would also predict, other things equal, lower crime rates amongst physically attractive men.

Comment author: Jack 29 December 2009 09:03:34AM 3 points [-]

One of the comments about the photos was mine I believe. I tried to avoid the photos of both Knox and Kercher (though I failed spectacularly). The fact that Knox is pretty and has a cute smile is worth updating on, perhaps. But for me it would be better to be told those facts rather than figure them out by staring at pictures. Millions of years of evolution have made attractive girls my age more bias inducing than just about anything else in my life. For the lonely I imagine the effect is considerably more dramatic. Surely we don't think the men who wrote Knox letters telling her how beautiful they thought she was are seeing things clearly and objectively.

And everyone is programmed to have their protection instincts kick in on the sight of a young, baby- like face (this is why the facial expression of fear resembles the face of a baby).

Comment author: RonnyRaygun 10 January 2010 09:02:49PM *  1 point [-]

Hello, everyone, my first post, and while I'm not sure it will be seen as entirely rational, here it is anyway :)

I don't know if attractive girls of Amanda Knox's age are more bias inducing. I would tend to think that cute faces do make people feel a certain protective, nurturing instinct. I also think, however, that SforSingularity has a point. I haven't seen any evidence to back it up, but I believe it is rare for "cute" girls to commit violent murder without severe provocation. That's not to say it doesn't happen.

From personal observation, it seems that people who look agressive are more likely to be agressive. Would this be due to the balance of testosterone / oestrogen in the womb, throughout childhood and adolescence, and into adulthood? It would be interesting to find out if studies have been done to prove or disprove this theory. Also, I certainly believe that the above assertions appear to be true in the animal kingdom. Agressive looking animals, almost without exception tend to be more agressive predators. We, both as individuals and as a species, are animals so I see no reason why the same shouldn't apply to us.

Finally, I recently read a study concerning the domestication of dogs. Dogs are known to have evolved from wolves (they can still interbreed very sucessfully) and the hypothesis was that humans selected the most docile wolves and bred them, as they would make better companions and would be easier to train.

To test this, a study was carried out on Russian Silver Foxes. For the last fifty years the most docile foxes have been selectively bred. The current generation is now incredibly docile, and actively seeks out human companionship, but more importantly, they look cute (i.e. they bring out a protective, nurturing instinct in their carers), and show little agression towards people or other animals.

Finally, I don't think any of the above has any bearing on the guilt of Amanda Knox. I am still absolutely amazed that a jury could have convicted her and Sollecito guilty based on the evidence provided.

Comment author: mattnewport 10 January 2010 09:23:18PM 2 points [-]

From personal observation, it seems that people who look agressive are more likely to be agressive. Would this be due to the balance of testosterone / oestrogen in the womb, throughout childhood and adolescence, and into adulthood? It would be interesting to find out if studies have been done to prove or disprove this theory.

I don't know of any studies specifically on aggression but this recent study found evidence that people are able to make significantly better than chance personality judgements based on a single photograph.

Comment author: ideclarecrockerrules 10 January 2010 09:29:46PM 2 points [-]

Signaling may play a significant role in this.

Comment author: Jack 10 January 2010 09:44:39PM 1 point [-]

Welcome! Feel free to introduce yourself here.

Comment author: komponisto 29 December 2009 07:11:09AM 1 point [-]

My probability estimate of guilt was around 1%. This makes me one of the few people in reasonably good agreement with Eli's conclusion.

As far as I am aware, all we know about EY's number is that it is bounded from above by 15%.

Since the average estimate was 35% (and that was before this post, after reading which some people said they updated downward, and no one said they updated upward), it's fair to say a lot of people were in reasonably good agreement with EY's conclusion.

Perhaps Less Wrong commenters are distrustful of their instincts to the point of throwing out the baby with the bathwater.

I don't know whether SfS's comment is to be taken as attempted satire or not, but I did wonder if a sort of "Spock bias" might result in reluctance to update on the sort of evidence presented here or here. As it turned out, that didn't seem to be so much of an issue here on LW (for all that character assassination of Amanda played a role in the larger public's perception). By far the biggest obstacle to arriving at probability estimates close to mine was that old chestnut: trusting in the fundamental sanity of one's fellow humans. (The jury must have known something we didn't, and surely Judge Micheli knew what he was doing...)

Comment author: Eliezer_Yudkowsky 29 December 2009 08:32:45AM 2 points [-]

The idea was that anything over 15% was wildly unreasonable.

Comment author: AnnaGilmour 15 December 2009 04:30:21PM 1 point [-]

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

Comment author: Feh 18 December 2009 09:24:14AM 1 point [-]

The above Youtube video is worth watching. If there is even one mistake like this by the police in a criminal investigation, I think they should be forced drop the investigation, rather than to risk putting innocent people in jail due to the police's incompetence or bias.

Comment author: wedrifid 18 December 2009 10:40:53AM 3 points [-]

If there is even one mistake like this by the police in a criminal investigation, I think they should be forced drop the investigation

Is that before or after they are arrested, stripped of their authority (and employment) and imprisoned? I have zero tolerance for that kind of abuse of power.

Comment author: mariz 14 December 2009 07:05:02PM 1 point [-]

Posts like this are the reason I read this blog. Great job.

Comment author: ChristianKl 13 December 2009 05:36:17PM 1 point [-]

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.

Comment author: Jack 14 December 2009 07:50:51AM 4 points [-]

Given the number of convicted people who were later exonerated by DNA evidence it isn't obvious to me that juries expecting physical evidence is a bad thing. One thing entailed by komponisto's discussion of the emphasis humans put social and mental facts is that the pre-CSI judicial system assigned too much weight to such facts and likely imprisoned innocent people. And it turns out they really did imprison innocent people. So maybe it is the judicial system's bias, not komponisto's...

Comment author: wnoise 13 December 2009 05:51:12PM 5 points [-]

They did find lots of crime-scene evidence in this case -- pointing toward Guede.

Comment author: komponisto 14 December 2009 07:24:07AM *  1 point [-]

In general (with a very few idiosyncratic exceptions), I despise crime shows, and have never seen an episode of CSI in my life.

Comment author: JohnBonaccorsi 02 February 2014 09:29:59PM 0 points [-]

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 understanding of the murder forever impossible. Sympathy for her is as much of a menace as she is.

If the comment has, in fact, been removed, the party who removed it will kindly tell me why. If it was objected to on the ground that it did not address the probability of guilt of Knox, Sollecito, or Guede, I'm not sure the removal was fair. Komponisto's essay to which the comments here are a response is itself not quite limited to that probability question. It expresses and, in a sense, advocates sympathy for Knox and thus opens the door, as a lawyer might say, for a comment such as the one I posted.

Comment author: V_V 02 February 2014 10:13:41PM 1 point [-]

It hasn't been removed.
When a comment score becomes lower than a certain threshold, the forum auto-collapses it and its subthread. You can still read it by clicking on the [+] button on the right.

Comment author: JohnBonaccorsi 02 February 2014 10:25:33PM 1 point [-]

Got it. Thank you.

Comment author: wedrifid 04 April 2013 09:05:35AM 0 points [-]

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 be) extradited from the USA then that is a problem with the legal system of the United States of America, not just of Italy. The USA is a place I may consider returning to so isn't so easily written off. The prospect of extradition means visiting a country carries all the risks of flaws in that country's legal system as well as all flaws in any country with which it has extradition treaties (subject to whatever filtering the details of those treaties entail).

I am also interested in whether the criticism of the wikipedia coverage is accurate. Wikipedia is a source that I frequently rely on for information. Anything which should increase or decrease the amount of trust I place in wikipedia as a source is useful to me.

Comment author: TimS 04 April 2013 02:39:47PM 2 points [-]

Briefly, the Italians would have to request extradition. If they did, the US would hold a hearing to determine if there was sufficient evidence to extradite. The standard at that hearing is roughly "Is P(guilty) > .25 ?"

Here is a news / opinion article that suggests the Italians are unlikely to ask for extradition, and the standard for extradition probably could not be met. It sounds basically right.

Comment author: V_V 03 February 2014 12:35:25AM *  2 points [-]

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 be) extradited from the USA then that is a problem with the legal system of the United States of America, not just of Italy. The USA is a place I may consider returning to so isn't so easily written off. The prospect of extradition means visiting a country carries all the risks of flaws in that country's legal system as well as all flaws in any country with which it has extradition treaties (subject to whatever filtering the details of those treaties entail).

Isn't that a bit of an overreaction?

I mean, no matter how bad this miscarriage of justice seems to be, the probability of being wrongly convicted of murder while visiting Italy is low, certainly much lower than the probability of being hit by a car.
But being extradited to Italy while visiting the US for a wrong conviction of murder, even if you have never visited Italy before? Probably less likely than being hit by a meteoroid.

Comment author: wedrifid 03 February 2014 05:50:15AM 3 points [-]

Isn't that a bit of an overreaction?

I decline to go to Italy based on this and the other research it prompted. The nature of a power structure I am exposing myself to has significance to me even when I am relatively confident in my ability to keep myself self safe. For the same reason I would be unlikely to make a tourist visit a counter-factual USA which still kept all black people enslaved. I'm white so am unlikely to be enslaved but I would still hold what I see in contempt.

the probability of being wrongly convicted of murder while visiting Italy is low, certainly much lower than the probability of being hit by a car.

The information gained about the culture of Italy by the acceptance of ongoing public corruption is not limited to making predictions specific to whether I personally will be falsely convicted of murder.

Comment author: V_V 03 February 2014 11:10:33AM 0 points [-]

So you are not going to visit Italy, and possibly the US, as a form of political protest?

Comment author: Kevin 04 April 2013 10:00:20AM 1 point [-]

It's a possibility, I think, but it would be a very political issue if it happened, and I would expect the US Department of State to intervene to prevent it.

Comment author: AnnaGilmour 14 December 2009 07:41:08PM *  0 points [-]

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?

Comment author: AnnaGilmour 14 December 2009 07:46:14PM 1 point [-]

In other words, the Razor says that it was actively and intentionally ignored at best and fabricated at worst.

Comment author: [deleted] 13 December 2009 07:13:01AM 0 points [-]

. . . 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 coin, you need to both find a path and follow it, and the processes need to be intertwined; nevertheless, they are separate processes.

At least, that's the viewpoint that my experiences and intuitions have produced. I've often found myself having the subgoal of creating Friendly AI myself (and, in my defense, checking with Eliezer or someone before running it!), and Friendliness has always seemed more a matter of avoiding spiked pits than of actually finding gold coins.

I find myself needing to go into more detail about my thoughts than I was planning a couple of minutes ago. I've always hoped that we could build a Friendly AI out of two parts: a base built out of rationality, and then intelligence on top. The rationality base would prevent failures of Friendliness but be flexible enough to let rational actions shine through. Nevertheless, it would be very Neat and sound and pretty much immutable. The intelligence-on-top, on the other hand, could be Scruffy and ad-hoc, since it's going to go through loads of rapid modification anyway.

We have managed to come up with one perfect formal system of rationality: mathematics, in which you can be "absolutely certain" of a statement, as long as it can be expressed in a certain language and doesn't actually depend on any observations. We have also managed to come up with another perfect formal system of rationality: Bayesian reasoning, in which you can assign a probability to any statement whatsoever, and be completely correct, as long as you don't mind having to do an infinite amount of computation. Can we find a third perfect formal system of rationality, one in which you can still assign a probability to any statement, in which you don't end up strongly believing falsehoods more often than you should, in which Aumann's agreement theorem holds, in which you can be considered rational, in which you nevertheless don't have to perform an unreasonable amount of computation?

(Wow, this post has gone far from its original point.)

Comment author: Sebastian_Hagen 13 December 2009 07:11:11PM 3 points [-]

We have managed to come up with one perfect formal system of rationality: mathematics, in which you can be "absolutely certain" of a statement, as long as it can be expressed in a certain language and doesn't actually depend on any observations.

That's incorrect. As shown by Gödel's second incompleteness theorem, mathematical formal systems divide into three categories:

  1. Systems that are inconsistent.
  2. Systems that can't prove their own consistency.
  3. Systems that aren't particularly powerful.

When doing math, humans tend to assume that certain formal systems are consistent. But we can't actually prove it; it's ultimately an empirical question (and actually it would be even without the incompleteness theorem; if strong consistent formal system could prove their own consistency, that wouldn't make them any different from strong inconsistent formal systems).

Though as far as empirical questions go, the consistency of certain formal systems fundamental to human math does seem to be extremely probable.

Comment author: JohnBonaccorsi 03 February 2014 09:23:00AM *  1 point [-]

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 they'd stop if the suspect accused you. If the suspect caved, would you blame them for accusing you, or the government for making them do it?

I would hope my friends would know I would applaud their doing anything--even torturing me--to avoid being tortured themselves. That goes double for strangers.

PS At 02 February 2014 11:49:15PM, I wrote, with respect to Knox's accusation of Lumumba: "The utterance of such a false thing, outside, maybe, a literal torture chamber, is depraved." I withdraw the word "maybe."

PPS Let's consider your own personal experience, the stressful interrogation you underwent about the money you were suspected of taking. Were you tortured? Was Knox tortured? If Knox was of the view that she was tortured, she had a duty--not merely to herself but to everyone--to take the stand in her trial and say her story-changing and her accusation of Lumumba were products of torture.

Comment author: JohnBonaccorsi 05 February 2014 04:01:17AM 11 points [-]

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 me to consider, namely, that the interrogation of Knox was a disgrace. Moore's closing paragraph was as follows:

"This is an innocent college girl subjected to the most aggressive and heinous interrogation techniques the police could utilize (yet not leave marks.) She became confused, she empathized with her captors, she doubted herself in some ways, but in the end her strength of character and her unshakable knowledge of her innocence carried her through. It’s time that the real criminals were prosecuted."

In saying "the real criminals," Moore seems to have been speaking of the interrogators themselves. If that is, indeed, what he meant, I would say he used the right term.

Should the conviction of Amanda Knox be upheld, and should Italy request Knox's extradition from the United States, the U.S. government, I hope, will decline to extradite her. The U.S., in my estimation, should do much more that that to right the wrongs that have been done in this matter.

Comment author: komponisto 05 February 2014 05:24:52AM 6 points [-]

Congratulations on changing your mind!

You did it exactly right: you realized you lacked knowledge in a certain domain (interrogation, in this case), proceeded to learn something about it, and updated your previous opinions based on the information you received.

Less Wrong exists pretty much in order to help people become better at doing exactly that.

My hat is off to you, sir.

Comment author: JohnBonaccorsi 05 February 2014 06:30:31AM 3 points [-]

Thank you, komponisto. Congratulations to you on this fine essay. I think I must have first encountered it in December 2012, when I first learned of Less Wrong and came to see what the site was. Though I didn't do much to absorb the essay at that time, it stayed in my mind; the news the other day about Knox's re-conviction moved me to read it again. My mental process in response to that rereading has, in a sense, been recorded here, in my last few days' worth of exchanges with Less Wrong posters. When I posted my first comment in response to the essay, I wasn't sure it would be noticed, because the essay was more than four years old. Fortunately for me, Less Wrong's participants were paying attention.

Comment author: Quest4Truth 23 December 2009 09:15:56PM 1 point [-]

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.

Comment author: AnnaGilmour 16 December 2009 01:25:33AM 1 point [-]

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?

Comment author: Kevin 14 December 2009 08:20:44AM *  1 point [-]

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.

Comment author: Kevin 14 December 2009 07:25:31AM 1 point [-]
Comment author: Bo102010 14 December 2009 01:55:06AM 1 point [-]

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.

Comment author: komponisto 14 December 2009 07:59:57AM 2 points [-]

Upvoted for making me feel good, after I was bummed out for having overstated my case. :-)

Comment author: AnnaGilmour 15 December 2009 12:31:40AM *  4 points [-]

I don't think you overstated your case. The point was that there is an almost absolute disparity of evidence between Guede's guilt and Amanda or Raffaele's guilt.