The various evidence at the crime scene itself of a clean up and/or staged break-in, things like the bra being cut off or the body being moved
A bizarre or unexpected condition of the crime scene is not the explanandum here; Meredith’s death is. One person is entirely sufficient to have killed Meredith, and the DNA evidence establishes with virtual certainty that Guede had the kind of contact with her necessary to accomplish this. Unless the evidence suggesting someone else was involved is of comparable power to the DNA evidence against Guede (something on the order of 30 bits), then (and this is the part people have trouble understanding) even paying attention to it at all is automatically hypothesis-privileging.
(EDIT: Eliezer corrects below. What I actually wanted to argue here was that, given the certainty of Guede’s involvement, the lack of connection between him and Knox or Sollecito is strong evidence against their involvement—probably enough on its own to outweigh the comparatively weak evidence against them provided by the alleged indications of multiple attackers at the crime scene.)
Yes, we might be curious about the unusual mechanics of the crime scene given only one person, but unless they are so strange that assuming someone else’s guilt of murder (when we already have a suspect) would constitute a reasonable explanation for them, we have to regard the whole question as a distraction.
Whether evidence is strong enough to justify attention is an absolute threshold. There is no “extremely weak by comparison”. There is just “extremely weak”.
It is extremely weak on its own, and its weakness is compounded and confirmed by the strength of evidence of someone else. The reason for this is that the strong evidence sets up a perameter, a reference point of what is possible for evidence left behind. It puts lines on the thermeter by which to read the murcury. This is because there is also no evidence of collusion, so the physical evidence has to carry most of the weight, if not all. Otherwise, the prosecution’s case operates via a tautology.
There will be some threshold of evidence below which a hypothesis ought to receive strictly zero attention. You could probably even formalize this in terms of bounded rationality.
Right, but I don’t need to claim that the anti-Knox evidence is below that threshold. Unless, that is, we’re talking about extremely imperfect less-than-Bayesian human minds, who can’t intuitively perceive the difference in weight that a perfect Bayesian would assign to 30-bit evidence vs. 10-bit evidence.
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?
That’s setting the bar pretty high. What about witnesses who claim to have seen two men running from the scene, or heard multiple voices at the time of the murder?
Maybe. But remember that reality is consistent: If two people were at the scene committing the crime, why would there be vastly more evidence of one than the other?
Once you have the suspect, you can interrogate him to find out who he knows.
Come to think of it, why would a further (unknown) DNA sample even be enough? You’ve got an explanation for the crime. Surely there are far more likely priors than a double murder that would explain a second DNA sample, right? “Similarly incriminating” might not really be possible; much of what made the first sample so incriminating is that it matched a guy who you already had reason to suspect. Or did you mean that an unknown DNA sample would not suffice, only one that matched another suspect?
OK, fair enough. I think I understand your standard better now. But let’s go back to the actual case. Here’s a quote from that truejustice site’s summary of the Micheli report:
2) Judge Micheli explains that blood evidence proves that Meredith was wearing her bra when she was killed. Nor is it just the blood on her bra which demonstrates this. It’s also where the blood isn’t on her body. He says that Meredith was wearing her bra normally when she laid in the position in which she died, and she was still wearing it for quite some time after she was dead. Her bra strap marks and the position of her shoulder are imprinted in the pool of blood in that position. Meredith’s shoulder also shows the signs that she lay in that position for quite some time.
He asks the question: Who came back, cut off Meredith’s bra and moved her body some time later? It wasn’t Rudy Guede. He went home, cleaned himself up and went out on the town with his friends. Judge Micheli reasons in his report that it could only have been done by someone who knew about Meredith’s death and had an interest in arranging the scene in Meredith’s room. Seemingly who else but Amanda Knox?
She was apparently the only person in Perugia that night who could gain entry to the cottage. And the clasp which was cut with a knife when Meredith’s bra was removed was found on November 2nd when Meredith’s body was moved by the investigators. It was right under the pillow which was placed under Meredith when she was moved by someone from the position in which she died. On that clasp and its inch of fabric is the DNA of Raffaele Sollecito and Amanda Knox. Micheli reasons in his report that Raffaele and Amanda seemed to have returned to the cottage some time after Meredith was dead, cut off her bra, moved her body, and staged the scene in Meredith’s room.
At what point exactly do you part ways with Judge Micheli in that chain of reasoning? To me, his reasoning starts to sound stretched around the middle of the second paragraph. But it sounds like you might have a problem with this logic from the very beginning …? Are you saying the evidence that the body had been moved is just not worth paying attention to?
Are you saying the evidence that the body had been moved is just not worth paying attention to?
If, starting from the premise of Guede’s involvement, there are reasons to infer the involvement of someone else, then that sort of thing may very well be worth paying attention to. If the trail through Guede goes utterly cold, however, there comes a point where you just have to declare that Guede’s actions + there’s-something-we’re-missing-about-that-other-”evidence” is a more parsimonious explanation of the data than Guede’s actions + someone-like-Amanda-Knox-is-guilty.
In this situation, we should suspect that, if we bothered to investigate further, we would find that we were missing something. And sure enough, by golly, that’s what often seems to happen.
OK, but why do you keep saying “if”? The judge is making an argument on your terms. He is trying not to privilege the hypothesis. He is starting from the premise of Guede’s involvement, and he does find a reason to infer the involvement of someone else. He does not conclude that the trail goes utterly cold, but instead that it leads convincingly to Raffaele and Amanda.
Now, you may disagree with this argument, but I still haven’t heard the substance of your disagreement. All you’ve done is gainsay it.
Don’t get me wrong—I think your original post was a very good explanation of some huge conceptual problems in the way the case against K&S has come together. If I came in believing they were guilty, you would have raised massive doubts in my mind. And that’s no small accomplishment on your part. But it doesn’t follow that no case against them remains. In order to convince me, or anyone else who’s around the average of 35%, that we should lower our odds to your 1-10% range, I think you have to address the facts more directly. It’s not enough to say “there comes a point when you just have to declare...” or that certain DNA evidence “doesn’t count.”
If you were a defense attorney and we were jurors, then you’re right, you’d have your acquittal. But it’s not a juror’s job to distinguish between a 1% and a 35% probability of guilt. To make that case, I don’t think you can just point out weaknesses here and there in the prosecution’s argument—you need to lay out the strongest version of the prosecution’s case, even if you have to put it together for them, and then show step-by-step why it doesn’t lead to a probability higher than 1-10%.
I don’t blame you for not doing that, because as I’ve been saying, the primary sources aren’t available to do it—at least not in objective, quality English translations. I’m just not sure how you can get to such low odds without taking a more granular approach. You’ve suggested that the correct prior is the (very low) odds of someone like Amanda committing homicide, and others have suggested that the correct prior is the (very high) odds of a convicted defendant in a modern legal system being guilty—but these are two ends of a spectrum, not binary alternatives. Finding the correct point on that spectrum is equivalent to assessing the strength of the prosecution’s case.
He is starting from the premise of Guede’s involvement
No he isn’t! He’s starting from the premise that some investigator found the condition of Meredith’s clothing and bloodstains to be unusual given the hypothesis of only one killer. As far as I can tell, he has failed to update properly on the lack of connection between Guede and anyone else who might be a suspect—not to mention the lack of other evidence (e.g. DNA) that would indicate two or more killers.
In order to convince me, or anyone else who’s around the average of 35%, that we should lower our odds to your 1-10% range, I think you have to address the facts more directly.
I’m starting to suspect that we may just have a disagreement about how strong the anti-Knox evidence is. Yes, I agree it isn’t literally zero. But that’s not the point. The point is that it is utterly dwarfed by the other evidence. Exactly how strong of a dwarfing is this? Well, that’s what seems to be the point of contention. I claim the net evidence of Knox’s guilt yields a probability of no more than 0.1; you’re uncomfortable going below 0.35. The only way to resolve this would be to do some sort of rigorous calculation of the inferential power of clothing-mechanics-analysis evidence—something which I think would take us too far away from our main topics here.
I suppose I can console myself with the fact that it’s good news for Amanda and Raffaele (and bad news for the prosecution) if what are probably the most intelligent and sophisticated discussions of their case on the whole Internet consist of vociferous arguments about whether the probability of their guilt should be 0.35, 0.1, or even lower.
That’s setting the bar pretty high. What about witnesses who claim to have seen two men running from the scene, or heard multiple voices at the time of the murder?
those would be the witnesses that appeared months later and whose testimony is doubtful. The running feet and scream women’s story cannot be true… a reenactment later showed them to be impossible and they were actually not sure if it was Halloween the night before when there would have been a lot more rowdy students around… And the eyewitness was also discredited.
Come to think of it, why would a further (unknown) DNA sample even be enough? You’ve got an explanation for the crime. Surely there are far more likely priors than a double murder that would explain a second DNA sample, right? “Similarly incriminating” might not really be possible; much of what made the first sample so incriminating is that it matched a guy who you already had reason to suspect. Or did you mean that an unknown DNA sample would not suffice, only one that matched another suspect?
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.
Not sure I understand the objection. The point is that the evidence is extremely weak by comparison; not strong enough to justify any attention.
Whether evidence is strong enough to justify attention is an absolute threshold. There is no “extremely weak by comparison”. There is just “extremely weak”.
It is extremely weak on its own, and its weakness is compounded and confirmed by the strength of evidence of someone else. The reason for this is that the strong evidence sets up a perameter, a reference point of what is possible for evidence left behind. It puts lines on the thermeter by which to read the murcury. This is because there is also no evidence of collusion, so the physical evidence has to carry most of the weight, if not all. Otherwise, the prosecution’s case operates via a tautology.
Huh? Attention isn’t binary, off-or-on; like evidence itself, it’s a quantifiable commodity. The stronger the evidence, the more attention. Right?
There will be some threshold of evidence below which a hypothesis ought to receive strictly zero attention. You could probably even formalize this in terms of bounded rationality.
Right, but I don’t need to claim that the anti-Knox evidence is below that threshold. Unless, that is, we’re talking about extremely imperfect less-than-Bayesian human minds, who can’t intuitively perceive the difference in weight that a perfect Bayesian would assign to 30-bit evidence vs. 10-bit evidence.
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.
That’s setting the bar pretty high. What about witnesses who claim to have seen two men running from the scene, or heard multiple voices at the time of the murder?
Maybe. But remember that reality is consistent: If two people were at the scene committing the crime, why would there be vastly more evidence of one than the other?
Once you have the suspect, you can interrogate him to find out who he knows.
Come to think of it, why would a further (unknown) DNA sample even be enough? You’ve got an explanation for the crime. Surely there are far more likely priors than a double murder that would explain a second DNA sample, right? “Similarly incriminating” might not really be possible; much of what made the first sample so incriminating is that it matched a guy who you already had reason to suspect. Or did you mean that an unknown DNA sample would not suffice, only one that matched another suspect?
If the victim’s body and surroundings contains DNA from two different individuals, that would suggest multiple attackers.
OK, fair enough. I think I understand your standard better now. But let’s go back to the actual case. Here’s a quote from that truejustice site’s summary of the Micheli report:
At what point exactly do you part ways with Judge Micheli in that chain of reasoning? To me, his reasoning starts to sound stretched around the middle of the second paragraph. But it sounds like you might have a problem with this logic from the very beginning …? Are you saying the evidence that the body had been moved is just not worth paying attention to?
If, starting from the premise of Guede’s involvement, there are reasons to infer the involvement of someone else, then that sort of thing may very well be worth paying attention to. If the trail through Guede goes utterly cold, however, there comes a point where you just have to declare that Guede’s actions + there’s-something-we’re-missing-about-that-other-”evidence” is a more parsimonious explanation of the data than Guede’s actions + someone-like-Amanda-Knox-is-guilty.
In this situation, we should suspect that, if we bothered to investigate further, we would find that we were missing something. And sure enough, by golly, that’s what often seems to happen.
OK, but why do you keep saying “if”? The judge is making an argument on your terms. He is trying not to privilege the hypothesis. He is starting from the premise of Guede’s involvement, and he does find a reason to infer the involvement of someone else. He does not conclude that the trail goes utterly cold, but instead that it leads convincingly to Raffaele and Amanda.
Now, you may disagree with this argument, but I still haven’t heard the substance of your disagreement. All you’ve done is gainsay it.
Don’t get me wrong—I think your original post was a very good explanation of some huge conceptual problems in the way the case against K&S has come together. If I came in believing they were guilty, you would have raised massive doubts in my mind. And that’s no small accomplishment on your part. But it doesn’t follow that no case against them remains. In order to convince me, or anyone else who’s around the average of 35%, that we should lower our odds to your 1-10% range, I think you have to address the facts more directly. It’s not enough to say “there comes a point when you just have to declare...” or that certain DNA evidence “doesn’t count.”
If you were a defense attorney and we were jurors, then you’re right, you’d have your acquittal. But it’s not a juror’s job to distinguish between a 1% and a 35% probability of guilt. To make that case, I don’t think you can just point out weaknesses here and there in the prosecution’s argument—you need to lay out the strongest version of the prosecution’s case, even if you have to put it together for them, and then show step-by-step why it doesn’t lead to a probability higher than 1-10%.
I don’t blame you for not doing that, because as I’ve been saying, the primary sources aren’t available to do it—at least not in objective, quality English translations. I’m just not sure how you can get to such low odds without taking a more granular approach. You’ve suggested that the correct prior is the (very low) odds of someone like Amanda committing homicide, and others have suggested that the correct prior is the (very high) odds of a convicted defendant in a modern legal system being guilty—but these are two ends of a spectrum, not binary alternatives. Finding the correct point on that spectrum is equivalent to assessing the strength of the prosecution’s case.
No he isn’t! He’s starting from the premise that some investigator found the condition of Meredith’s clothing and bloodstains to be unusual given the hypothesis of only one killer. As far as I can tell, he has failed to update properly on the lack of connection between Guede and anyone else who might be a suspect—not to mention the lack of other evidence (e.g. DNA) that would indicate two or more killers.
I’m starting to suspect that we may just have a disagreement about how strong the anti-Knox evidence is. Yes, I agree it isn’t literally zero. But that’s not the point. The point is that it is utterly dwarfed by the other evidence. Exactly how strong of a dwarfing is this? Well, that’s what seems to be the point of contention. I claim the net evidence of Knox’s guilt yields a probability of no more than 0.1; you’re uncomfortable going below 0.35. The only way to resolve this would be to do some sort of rigorous calculation of the inferential power of clothing-mechanics-analysis evidence—something which I think would take us too far away from our main topics here.
I suppose I can console myself with the fact that it’s good news for Amanda and Raffaele (and bad news for the prosecution) if what are probably the most intelligent and sophisticated discussions of their case on the whole Internet consist of vociferous arguments about whether the probability of their guilt should be 0.35, 0.1, or even lower.
That’s setting the bar pretty high. What about witnesses who claim to have seen two men running from the scene, or heard multiple voices at the time of the murder?
those would be the witnesses that appeared months later and whose testimony is doubtful. The running feet and scream women’s story cannot be true… a reenactment later showed them to be impossible and they were actually not sure if it was Halloween the night before when there would have been a lot more rowdy students around… And the eyewitness was also discredited.
Come to think of it, why would a further (unknown) DNA sample even be enough? You’ve got an explanation for the crime. Surely there are far more likely priors than a double murder that would explain a second DNA sample, right? “Similarly incriminating” might not really be possible; much of what made the first sample so incriminating is that it matched a guy who you already had reason to suspect. Or did you mean that an unknown DNA sample would not suffice, only one that matched another suspect?