The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom
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 less 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 months 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: explaing 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 (524)
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.
(Beginning thread for a debate with Rolf Nelson. Others also welcome to comment, of course.)
Okay, Rolf, so to get things started, I'd like to get your numbers out on the table. So, if you wouldn't mind, please tell me, first of all, your current posterior probability estimates for the guilt of:
(I expect we'll mainly focus on Knox and Sollecito, since that's obviously where our main disagreement is; I've included Guede for the sake of comparison.)
Next, I'd like to know your priors for Knox and Sollecito (and 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).
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.
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.
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.
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.
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 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.
The disagreement most likely stems from the reliability of the Micheli Report for accuracy and comprehensiveness.
Posterior probability estimates:
Priors:
Is that the sort of thing you are asking? I don't know if I attributed correctly.
Anna: for the context of this, see here.
You may want to remember that 0 and 1 are not probabilities. Also, I must say I don't understand your extremely high prior of 0.5 for Guede. (The evidence against him is such that the prior could be much, much lower and he would still have a very high probability of guilt.)
The thing that I am trying to point out is that I believe Amanda and Raffaele were wrongly included in the class called "suspects".
Yes indeed -- our term for that here is privileging the hypothesis.
(Although I do find the point more salient when it is described explicitly rather than by reference to jargon. )
Wasn't trying to enforce the use of jargon so much as classify the fallacy.
After all, the point is even more salient when you can relate it to a whole category of error found in many other contexts.
I find the term useful. I think it is what a lot of the media has done. Since Amanda and Raffaele are in discussion and named in the theory, there must be something to it and they have equal weights of measure for concern as the third suspect, Rudy. When in fact, they are very lightweight and the (heavy) weight should be attributed to the method by which they became suspects. The term helps me to say "Oh that's what is going on." Like komponisto said, a whole category of error. (Not to mention all the contexts apart from this specific case, the topic at hand, indeed.)
Quite right. It's actually amazing how little attention was paid to Rudy Guede in the media coverage of this case, particularly in the U.S. and U.K. media. (Numerous stories either omitted all mention of him altogether or else referred briefly and vaguely to "a third suspect" -- without any hint about the disparity in evidence.)
I am also pointing out that is a question pertaining to applied situation with a limited scope - the decision to convict or exonerate. For all intents and purposes, relative "knowing" is permissible in a legal case, since we are dealing with human events and activities of a finite nature - a court decision is a discrete (not continuous) matter. After a certain point, probabilties have to turn into decisions.
Therefore, I offered 0 in the spirit of Goedel's completeness theorem, yes, at the expense of consistency. Consistency will yield a perpetual motion situation. Completeness is required and can be appropriately reached through reasoning, logic, objectivity, etc. Something can only consistent OR complete. Not both.
In other words, his psychological profile and actions leading up to the murder do not indicate that he was above board and immune from a violent attack, especially an attack with a knife. He was also known around town to go too far in the direction toward harassment of females around town at the clubs and so forth. He was also known to do various drugs including aggression-increasing drugs such as cocaine. He was known to break and enter and steal, and that he carried a ten inch knife "for protection" (his words). It could be argued then that it was a matter of brief time for him to break and enter, steal, and encounter someone indoors in the process as was arguably such in the situation with Meredith, and "defend" himself when caught or interrupted. This is the case that I would start to make as for a high prior.
It is true that a high probability of a prior is not necessary for probability of guilt.
It is also true, however, that it doesn't mean that he didn't have a high prior. I could drop it to .3 though. With the actions in the previous weeks, a case could be made that he was in an escalating pattern of behavior, which is why I gave him a .5 prior.
Thank you. Yes I've seen the post by Rolf Nelson.
I don't understand (though I admit for expediency's sake did not fully read the 0/1 link which I should do if I post here) how there cannot be an absolute for innocence. I didn't assign 1 to Rudy Guede for the reason you mention. But in terms of innocence, we know for example that Princess Diana didn't kill Meredith and that the mayor of Seattle at the time did not kill Meredith, so how can it not be zero? I wrote zero for a specific reason. I wanted it to indicate that gap between reasonability of arrest and no reasonability of arrest. To assign even a small possibility at this point seems inaccurate to me. Although, you make a good point, in actuality, so I would amend them to .001. Is that a proper probability quotient in terms of the question?
Yes, that would be more reasonable (indeed, it's about where my own estimate is).
Is it possible to show that it would be impossible for them to have been participants making it 0? Is there anyone in the world in that class - of 0? Trying to understand the parameters of "probability".
I agree with Alicorn - a probability of 0 or 1 can only be legitimately used as hyperbole.
(There's a technical explanation for why to exclude probabilities of 0 and 1, but it assumes you have studied and understood Bayes theorem and know how to think about probabilities in real life in Bayes terms.)
Exactly-0 isn't on the table at all. Close-enough-to-0-that-you-can-represent-it-that-way-without-too-much-disclaiming is reserved for propositions like "a square circle and Batman teamed up to, not kill, but kidnap and replace with a convincing inert android, Meredith". Princess Diana's odds of having killed Meredith are miniscule, but not zero or even compellingly zerolike, compared to those.
I don't know if this means I disagree with Eliezer but I'm pretty sure the probability of a contradiction has to be 0 and the probability of a tautology has to be 1. Else really weird things start happening and you can't do deduction. Like, what is the probability of A given A ^ B?
*cackles evilly and cracks metaphorical knuckles*
The circle is defined as the locus of points an equal distance from a center on a plane. A square is defined as a regular quadrilateral - i.e. a shape with four sides of equal length separated by four angles of equal magnitude. If you allow that "distance" may be generalized to be applicable to other geometries than Euclidean...
...what is the shape of a circle on a chessboard, where "distance" is measured by the number of king-moves?
I believe this is a useful object lesson in the difficulty of constructing properly impossible propositions.
Edited to make the square have four sides, not three. What was I thinking...?
And when you superimpose a middle finger onto Reimannian space...
Edit: But upvoted because it is always good to get this reminder.
Something can be metaphysically/logically impossible without it being okay to assign exactly-0 to it. Epistemic probability is what we're really representing here - I mean, even something as uncertain-to-me as the current weather conditions in the red spot on Jupiter is exactly one way. But it's not useful to represent that single-ness of weather conditions because I can't access them. I similarly can't usefully access absolute epistemic certainty about even simple math and logic. I'm a broken machine; I cannot handle perfect surety.
It isn't that simple. Most of the results we get from Bayes theorem we get by deduction. For example, the Dutch book argument, the most common justification given for Bayesian epistemology in the first place, relies on deduction. So does nearly every other important result we get from Bayes theorem. So when you say to someone: take this evidence and act rationally that may imply that that person not get her deductions wrong. This is why, afaict most Bayesians assume logical omniscience. See here. Apparently there have been attempts to weaken logical omniscience and maybe someone here has one in mind... but I haven't heard it. Obviously it is that case the humans, as a matter of psychological fact can screw up deduction. But this is basically like saying that as a matter of psychological fact humans aren't perfect Bayesian rationalists. The whole theory isn't supposed to be descriptive, it is an ideal to strive toward.
I have also seen Eliezer tempted to consider a '0' probability in response to a 'divide by infinity' situation. (I think there is a 'mathsy' way to represent that kind of '0'.)
That's called a limit. What's special is not the “zero” but the “infinity”: you don't talk about a value “infinity” (attempting to have one causes you to lose various other useful properties), but rather that as some input increases without bound, the output approaches zero.
“The limit of 1/x as x approaches infinity is zero."
Well, it is quite fascinating that no one gets a 0 probability. Just to ask, does Meredith get a 0 probability? I will move past understanding the exclusion of 0. I just want to make sure I understand. Anyway, when I say 0, I understand it to mean functionally 0, which is the same as .0000000001, which is also functionally 0, correct? Thank you for you patience.
Meredith could have committed suicide. She's probably more likely to be responsible for the death than Princess Diana. And she's much more likely than the team of Batman-and-square-circle.
Were there any fatal wounds that she could not have inflicted?
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).
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.
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 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.
(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.
(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.
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.
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?
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.)]
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?
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.
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.
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.
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).
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.
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.
Signaling may play a significant role in this.
As may microexpressions and other things of which we're not often consciously aware. This doesn't go to the level of a single photograph, but the (badly-named) truth wizards can "observe a videotape for a few seconds and amazingly they can describe eight details about the person on the tape."
We communicate more than we think.
Link (1:44) for those interested in trying the video experiment on themselves in the present context.
For a much more extended sample, see here.
Welcome! Feel free to introduce yourself here.
And then:
Belief without evidence - that's irrationality, right there. You may be misunderstanding the meaning of "evidence" - especially as that word is used in this community.
I assume he means studies or 'scientific' evidence (as if there were some other kind).
The other kind is rational (Bayesian) evidence. That's what most people here mean by unqualified "evidence", I think.
Scientific evidence is Bayesian evidence, no? I was just implying that I didn't think there was a special category of evidence gathering delimited as 'science'.
Best I can tell, Science is just a particularly strong form (/subset) of Bayesian evidence. Since it attempts (when done well) to control for many potentially confounding factors and isolate true likelihoods, we can have more confidence in the strength of the evidence thus obtained than we could from general observations.
Yeah, though a lot of science is just building localized, domain specific ontologies (here's what kinds of fish there are, here's what kind of stars there are etc.) and I'm not sure this kind of scientific knowledge is much better than observations you or I make routinely. Also, some evidence gathering is every bit as powerful as science (or more so) and yet is rarely counted as a science ( advanced sports statistics or marketing studies for example).
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.
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...)
The idea was that anything over 15% was wildly unreasonable.
[citation needed]
Here's a correlation between ugliness and crime:
(30 seconds on Google.)
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.
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.
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?
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?
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).
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.
Right... I was a fool to miss that. You're perfectly right of course.
Which leads us to the question of what "natural category" to put Knox in. Should it be "a pretty woman out of all women" or "a pretty young woman out of all young women"? Or lots of other options, of course. (We use some category the moment we compare her to women and not to all humans.)
But I'm sure this has been discussed, I haven't read all of this subthread...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
In fairness, aren't you also starting with some or all of the following pieces of evidence?:
(1) A room in the crime scene apartment has been ransacked but no valuables (which were in plain view) were taken;
(2) A window in that same room has been broken with marks suggesting it was broken from the inside;
(3) the same window is on the second floor and can be seen from the street. Further, there is no obvious reason why a burglar would need to get in through an upper floor;
(4) Bloodstains indicate that the victim died with her bra on and the bra was removed a few hours later; and
(5) When the police arrived at the crime scene apartment, one of the victim's flatmates was standing there with her boyfriend and with a mop and a bucket.
brazil84's points 1, 2, and 3 are false in my opinion, I have insufficient knowledge about #4 (the allegedly postmortem removed bra) but my reaction is "so what?" and "how does the investigator know the bra wasn't removed post-cut rather than postmortem?"), and here is my take on #5, the mop and bucket...
The allegation that Amanda and Rafael were found with a mop and bucket outside the crime scene apartment is reported on truejustice.org (which has been accused of bias in some of the comments here.) Truejustice.org claims to be paraphrasing a judge's statements about pretrial hearings. This alleged fact apparently did not come up in the actual trial. In the actual trial, Rafael's maid said she found a mop and bucket underneath the sink at his apartment, and said he explained that they had cleaned up some leaked water. The maid testified that there was a clear liquid in the bucket. My wild guess at the truth here is that indeed Amanda and/or Rafael had taken a mop and bucket from Amanda's apartment to Rafael's apartment to clean up a leak, and the maid saw it when she came in the morning (she cleaned around 11:00 on certain days, as I recall.) And then, possibly, and unfortunately for them, Amanda or Rafael brought the mop back to Amanda's apartment shortly before the police arrived. But your guess is as good as mine.
One thing I stumbled across was this comment to a blog:
I think that's pretty funny, or at least it would be if the freedom of two individuals weren't at stake. No evidence of bleach, by the way.
1) Actually, Kercher's rent money was missing and Guede's DNA was found in her purse. After her murder he went clubbing and then hopped a train Milan. Where did he get the money to do that? To state there was no robbery doesn't jibe with the evidence. Knox had $2000 in her bank account, and Sollecito's parents are well off. Guede was a known drifter known for his money problems.
2) No, evidence was NOT that window was broke from the inside. The glass was inside the room, and a rock was found. The dispute arises because some glass was below clothing in Filomena's room. However, Filomena was allowed into her room to retrieve personal effects, so the exact placement of clothing is suspect. Furthermore, the building itself is fairly isolated and traffic along the road is minimal.
3) There is a truss next to the window making access relatively easy. An investigator for the defense, dressed in a suite and tie easily scaled it. Rude Guede was an accomplished athlete and basketball player.
4) That's an evaluation of the judge who accepted the prosecutor's contention of the muti person scenario. Scientific testimony at trial contradicts this assertion. In either case, this is evidence open to interpretation. Even if that were true, there is still no evidence that Knox or Sollecito were involved in moving the body! Putting them in the room a SECOND time hours later further creates a logic problem because no evidence of their presence is in the room! What are they, ghosts?? Even if you prove there was more then one assailant, you still have to prove those additional assailants were Knox and Sollecito... which you can't You must UNLEARN what you have learned my friend. ;)
5) No such evidence was presented at trial, and even if it was so, its completely meaningless. How do you get from "a mop and bucket" to "a three way sex crime"? You must have something stronger in addition to the observation for it to have probative value of a crime! If they cleaned the crime scene how did they leave behind Guede's fingerprints and DNA? Either is all there, or its all gone. You can't selectively clean up microscopic evidence... much less with a mop and bucket. Its laughable.
As komponisto stated, it is difficult to be cold in your rational evaluation. You are assigning the mop and bucket a value almost equal to DNA inside the victim when in real comparison they are light years apart in real value.
Hold on a sec: Are we looking at things from the perspective of the initial evidence available to investigators? Or are we looking at all the evidence in its totality?
These are two separate but related questions:
(1) Does the initial evidence offer a reasonable basis to be suspicious of Knox and/or Sollecito?
(2) Does all the evidence in its totality indicate that Knox and Sollecito are guilty?
It seems to me you just jumped from discussing (1) to discussing (2). If you want to do that, fine, but in that case it's not fair for you to ignore later evidence which developed against Knox and Sollecito.
I'm not doing that at all. The mop and bucket are one initial piece of evidence which, when combined with other initial pieces of evidence, form a reasonable basis to be suspicious of Knox and Sollecito.
How is the mop and bucket evidence of a crime??? That's an emotional response, not a rational one. You must prove 1) the mop and bucket was used to clean up a crime scene, and 2) that Knox and Sollecito were the one that did it. No proof of 1 exists, so how can you prove 2?
1) I'm saying that if you follow the evidence, Knox and Sollecito never enter the picture as suspects. I do not assign behavior as evidence of a crime without strong physical evidence to cooberate it. All we have initially are the behaviors.
2) The evidence in totality can't connect them to the crime or Guede. Guede is completely connected by the evidence. So how can you prove guilt?
I'm saying this: If you START with the cold hard evidence, and proceed from there, Knox and Sollecito are NOT suspects. Since they are not suspect, their behavior isn't probative, and everything that follows: "Foxy Knoxy", Vibrators in the bathroom, sex on a train, cartwheels at the police station have 0 value as evidence of a crime. Get it?
I'm time warping. Starting with the evidence to find the people, not starting with the people and then trying to find evidence to implicate them. Its a thought exorcise.
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.
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.
It seems to me that most of those problems can be explained by postulating that (1) the prosecution's case is overstated; and (2) the prosecution's scenario of what happened is incorrect.
However, even if (1) and (2) are true, it does not mean that Knox and Sollecito are innocent or uninvolved in the murder.
By analogy, consider the OJ Simpson case. As I recall, there really were some serious questions about the prosecution's evidence in that case. Even so, it seems pretty clear (to me) that OJ was guilty.
Obviously the OJ Simpson case is very different from the Amanda Knox case. But the point is that police, prosecutors, and others are often tempted to try to turn a good case into a great case.
Of course one big difference with OJ Simpson is that the case fits into a very simple paradigm: the jealous ex-husband. So it's very easy for the prosecution to present a coherent theory (including a motive).
Perhaps a better analogy is the Annie Le case. It seems pretty clear who killed her, but it's not entirely clear why. Nevertheless, there will be pressure on the prosecutors to come up with a scenario for what happened and why.
There is a lot of what I call "noise" in this case. Things that MAY apply, but not all of them carry the same weight, thus it becomes necessary to organize my thought processes. I start with the hard evidence FIRST, not the other way around. I do not look at the people and then find evidence to implicate them, I look at the evidence first and then find the people.
By "hard evidence", I mean that evidence that can be observed directly or by repeatable scientific methods.
I refine my thought process even further by using these principles which state: 1. The simplest explanation that fits the facts is usually the correct one. 2. the more outlandish a theory is the greater the amount of evidence is required to support it, and 3. The further away you move from a causal event the less accurate your observations will be.
With that as a guide, the DNA of Rudy Guede inside Kercher becomes a white hot beam of guilt, and Knox's cartwheels with the police has almost no luminescence at all.
Given how much evidence is in the room where Kercher was killed leads you directly to Rudy Guede. The bedroom is the key to this case as that is where the murder took place. As you move further away from the bedroom, you are less likely to find direct connection to the killer or killers, so as I move out of the bedroom other things like mixed DNA in a bathroom of people who co-habituate get less consideration.
Given the preponderance of evidence that there is of Guede, logically then, this must also be true for Knox and Sollecito if the prosecution's theory of the crime is to hold true. However, no such preponderance of evidence exists for them. Knox's presence is non existent according the the physical evidence, and Sollecito's hinges on a bra clasp found 47 days after the crime. The more outlandish a theory is the greater the amount of evidence is required to support it, ergo which version of the crime does the evidence and logic support:
That a known burglar, involved in three separate break-in incidents in the weeks prior to the murder broke in and robbed, assaulted and murdered Kercher.
Or
That new lovers Knox and Sollecito with no criminal history whatsoever, conspired with relative unknown Guede to involve Kercher in some sex game and inadvertently killed her?
This leaves Knox, Sollecito and Lumumba footnotes in this story. Stories about bleach purchases, hip wiggling, knives in a residence not connected to the scene, Myspace pages, emials and raunchy tabloid stories about an attractive American female and her Italian boyfriend are relatively benign compared to fingerprints in blood, feces in the toilet and DNA inside the victim.
Using THIS method, which is the traditional method of deduction leads you to the guilty party. Using disassociated bits of information that you then try to connect to hard evidence found latter only leads to confusion. Bragging about it only leads to a need for obfuscation when the hard evidence contradicts your theory.
"That a known burglar, involved in three separate break-in incidents in the weeks prior to the murder broke in and robbed, assaulted and murdered Kercher.
Or
That new lovers Knox and Sollecito with no criminal history whatsoever, conspired with relative unknown Guede to involve Kercher in some sex game and inadvertently killed her?"
Are those the only two possibilities? As an attorney, I can tell you I have seen many many cases where neither side's theory about events is very credible.
It seems pretty clear to me that the answer to my question is "no," but I would like to hear your take.
As an attorney you are asking a tangential question with the implication that it has more relevance than it does.
I remember when I started practicing law on my own I would be outraged when I caught the other side in numerous lies and yet the judge would still go against my client. At the time, it seemed to me that the judge was heavily biased against my client.
It took me a while to learn what I have tried to share in my last couple posts. In hindsight, I realize that most of those clients really did do pretty much what they had been accused of doing. And that in any event, the judge was (generally speaking) making a reasonable assesment as to my client's guilt or innocense.
The fact that the prosecution's case has holes in it doesn't necessarily mean that the Defendants were innocent or uninvolved in the murder.
But feel free to explain why you think my question is tangential or irrelevant and I will be happy to consider it.
Also, you might ask yourself if you are angry at me over our previous exchange and whether this anger is coloring your judgment.
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
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."
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
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.
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.
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.
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:
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.
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.
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.
Doesn't follow. You can have a lot of evidence for one true statement and then less evidence for another true statement.
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?
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.
"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?
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.
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.
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.
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.
Posts like this are the reason I read this blog. Great job.
Post now revised in light of comments.
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:
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.
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
Jeeze, how did I miss that. Do you have a link?
Edit: Also. New people! Welcome.
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.
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.
The Daily Mail is a British tabloid... frequently posting completely fraudulent information about football players, for example... check your sources friend...
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.)
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'?
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.
http://news.ycombinator.com/item?id=993573
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.
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.)
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.
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?
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.
Agree completely. Now apply it both ways. Specifically:
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.
I was surprised at you dismissing the knife DNA evidence. The linked FOA page claims:
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.
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.
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."
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
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!
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.
Upvoted for making me feel good, after I was bummed out for having overstated my case. :-)
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.
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).
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.
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.
I can't find it- though the excerpts given in the NYTimes do sound more like a soap-opera than a rape-fantasy.
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.
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.
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.
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.
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.
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.
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
The Friends of Amanda site claims:
If that is true then it suggests to me that finding Sollecito's DNA as well is not very strong evidence for anything.
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.
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.
It seems to me that the prosecution's case against Sollecito relies quite heavily on the evidence they claim proves he was present at the crime scene since they have no other solid evidence against him.
The reasoning used by the prosecution is basically what Jaynes calls the 'policeman's syllogism' in Probability Theory: The Logic of Science. The reasoning is of the form:
Here A is (Sollecito was present at the crime scene) and B is (DNA tests on the bra clasp detected Sollecito's DNA). If we use C to stand for our background knowledge then by Bayes theorem:
The premise of the policeman's syllogism "If A is true, then B becomes more plausible" takes the form
And by Bayes theorem if this premise is true then:
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.
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.
Very well said.
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.
"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.
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.
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.
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....
"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.
You're absolutely correct. Not only that, but the Luminol footprints specifically tested NEGATIVE for the presence of blood. Every single one of them.
@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
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.
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.
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.)
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.
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.
http://www.ncpa.org/sub/dpd/index.php?Article_ID=14481
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.
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...
In general (with a very few idiosyncratic exceptions), I despise crime shows, and have never seen an episode of CSI in my life.
They did find lots of crime-scene evidence in this case -- pointing toward Guede.
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.
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.
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)
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.
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 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.
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.
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.
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.
Can you make explicit your intuitions? What experiences in particular lead you to think this?
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.
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.
"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.
Do you agree that if Amanda Knox staged a break-in, then she was probably involved in the murder?
Do you agree that the evidence does in fact suggest that a break-in was staged?
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?
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.
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.
Other evidence of mistreatment are Raffaele's and Patrick's prior statements of similar treatment. They said it before the defamation claim by the police, which by the way, was made much time after the incident and was the day before the closing arguments by the defense.
This is one reason why police record interrogations, to avoid people making false accusations of coercion to get out of confessions. Alas, first we were told the tape had gone missing. And then later told no tape had been made at all! We don't even have a transcript of the interrogation, just a signed statement Knox obviously didn't write herself. It really is a shame they lost the tape, er, I mean, that no tape was ever made. Then the Italian police could show the world that she was lying all along!
</sarcasm>... You're right of course that Knox isn't reliable. But coerced false confessions are fairly routine as I understand it and the police have every incentive to lie.
It is odd that after 4 days of taping all their phone calls and also the interviews during that time that they completely forgot to record the big one the night of the 5th & 6th. The one where Mignini was orchestrating the proceedings, and Giobbi was in the next room (presumably working his pseudo-science Behavioral Analysis Interview demeanor magic interpretation of the whole thing. 36 police were in the room along with Mignini...they all signed as witnesses... the typewritten Italian police legalese "spontaneous confession" doc.(why so many? to keep her company?) Mignini running out of time (he knew from the telephone calls that Amanda's mother was coming and that she might possibly get Amanda to the US embassy or out of the country. they had no grounds to hold her... they needed a confession and they knew they could get one and they did. The police had the investigator's hunch leading them to believe that they had a guilty person to break down... even though there was no physical evidence. And that was the problem they had the theory before any evidence and seem to have been stringing the interviews along while they waited for the strong evidence they were convinced was there... and yet no DNA, no fingerprints... nothing... but they were so sure... Giobbi the mindreading expert from Rome and Mignini the famous Prosecutor and the policewoman duo were so convinced and they set the tone and the rest of the police believed them... nobody was trying to railroad innocent people Miginini and the rest took off running based on a gut feeling and pseudo science. (and add to that an African hair sample and a misinterpreted text message from an African)
The police do tend to cut corners when they are convinced a person is guilty... that is when they can justify putting the screws on and they if they were really sure about someone they could make you or I or anyone seem "unreliable", a person who changes their story... a liar...
What are the circumstances under which we might expect the police to admit to abuse? I doubt their lack of confession there is strong evidence for anything either.
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.
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.)
...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.
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.
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".
What would the right thing look like? Averaging the log-odds ratio?
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.
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.
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.
Then why do I see the term "intuitive" used around here so much?
Hmm, I was told here by another lw user that the best thing humans have to truth is consensus.
Somewhere there is a disconnect between your post and much of the consensus, at least in practice, of LW users.
Made a claim that verdict used Bayesian inference and then failed to support it . It also overlooked elements of the verdict were composed of complete supposition that had no supporting evidence
How about this:
What are the odds that, given a murder in a shared accomodation, one of the occupants is involved if someone known to one of the occupants is known to be involved, more than one person is known to be involved, and that occupant is found to have a false alibi?
You are making an assumption, one exaggeration, and one statement of belief.
Assumption: More than one person is known to be involved. (Not established.)
Exaggeration: someone known to one of the occupants (He was known to the occupants in the cottage below and only only known of by one the occupants alleged to be involved.)
Belief: found to have a false alibi (There is no proof or acceptable evidence that that occupant has a false alibi.)
The means by which the prosecution set about to establish that more than person was involved is suspect. The means by which a false alibi was established is also suspect. You cannot accept those as viable fact. Something that has been shown in previous comments, if I am not mistaken.
It's worth mentioning that what is meant by "false alibi" in the first place is some trivial memory lapse, such as Sollecito misremembering the time when he was browsing websites, etc.
"If Amanda Knox and Raffaele Sollecito were to be in investigators' thoughts at all, they had to get there via Guédé -- because otherwise the hypothesis (a priori unlikely) of their having had homicidal intent toward Kercher would be entirely superfluous in explaining the chain of events that led to her death." They have fake alibi's, a crime scene they believed had been tampered with to conceal evidence, the whole Lumumba story from Knox and evidence from the body suggesting multiple people were involved in the murder. I'm not sure that these are things it's trivial to assign probabilities to in order to work out the odds of anybody's guilt or innocence.
"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." Again, the body appeared to show the work of multiple attackers. Knox and Sollecito had lied about their alibi; Guede appeared to have an alibi for the time the police believed the body was moved. Whoever cleaned up after the murder (which the police believed occurred) clearly made little attempt to hide evidence pointing to Guede.
What are the odds of these events given Amanda being innocent and Amanda being guilty? Can anybody tell within a couple of order of magnitude?
Given a murder in a shared house, what is the a priori probability that somebody from that house was involved? 0.1? 0.01?
Surely you are comparing the combined probability of various events whose individual probability you can only guess at and not all of which you may know, that have complex interdependencies and comparing that number against another number that you don't know with any certainty. The likelihood of being out by a very great margin in such a calculation is large.
"If Amanda Knox and Raffaele Sollecito were to be in investigators' thoughts at all, they had to get there via Guédé -- because otherwise the hypothesis (a priori unlikely) of their having had homicidal intent toward Kercher would be entirely superfluous in explaining the chain of events that led to her death." They have fake alibi's, a crime scene they believed had been tampered with to conceal evidence, the whole Lumumba story from Knox and evidence from the body suggesting multiple people were involved in the murder. I'm not sure that these are things it's trivial to assign probabilities to in order to work out the odds of anybody's guilt or innocence.
"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." Again, the body appeared to show the work of multiple attackers. Knox and Sollecito had lied about their alibi; Guede appeared to have an alibi for the time the police believed the body was moved. Whoever cleaned up after the murder (which the police believed occurred) clearly made little attempt to hide evidence pointing to Guede.
What are the odds of these events given Amanda being innocent and Amanda being guilty? Can anybody tell within a couple of order of magnitude?
Given a murder in a shared house, what is the a priori probability that somebody from that house was involved? 0.1? 0.01?
Surely you are comparing the combined probability of various events whose individual probability you can only guess at and not all of which you may know, that have complex interdependencies and comparing that number against another number that you don't know with any certainty. The likelihood of being out by a very great margin in such a calculation is large.