Same here. The reason I think so low of the self proclaimed Bayesianism is the sort of thinking where someone sees someone ugly accused and they're like, ha, I am going to be more rational than everyone else today, by ticking my estimate of the guilt up because they're ugly. Completely ignorant that it even makes a difference to the way you should apply Bayes rule that the police and the witnesses and the like had already picked the suspect with this sort of prejudice.
I mentioned duplication. That in 3^^^3 people, most have to be exact duplicates of one another birth to death.
In your extinction example, once you have substantially more than the breeding population, extra people duplicate some aspects of your population (ability to breed) which causes you to find it less bad.
The other observation that occurred to me is unrelated. It is about the idea of harm being nonlinear, which as I noted above is just plain not enough to invalidate the torture/specks argument by itself due to the ability to keep thwacking a nonlinear relationship with bigger numbers until it collapses.
Not every non-linear relationship can be thwacked with bigger and bigger numbers...
But does beauty influence our judgement in accordance with the correlation, or disproportionally so? It may be for example that ugly people are 10% more likely to commit crimes, 200% more likely to be villains in the movies, and 100% more likely to get flagged as suspects by the prosecutor, or get other massive penalty before you even think consciously about it.
Okay, let's go with your number... let's suppose hypothetically that you aren't beating or otherwise unduly coercing cute girls into saying what you want, and you started with the probability of 2.5%. Then your suspect tells you they were at the house covering their ears not to hear the screams as their big black boss murdered the victim. Now what happens to 2.5%? After you clear the big black boss, what happens?
I don't think you can claim base rate neglect without also claiming police brutality, coercion, and leading the witness (which would be a much bigger problem)
I think it'd be quite strange to claim that confessions don't ever correlate with guilt.
By the way what she did was she claimed she was at the scene of the crime covering her ears as Lumumba murdered Kercher (and no she didn't call the 112 about it or anything). If she as she says was coerced into making such a statement, yeah, that's not evidence of guilt. But if it is as police says it is, do you still think it's not evidence of guilt?
Picture an alternative universe. Bob, an exchange student from Australia, is being questioned as a witness. There's a minor discrepancy: Jake, his friend, withdrew his alibi for the night. Those things happen, you don't really think too much of it, but you have to question Bob. You're somewhat suspicious but not highly so. Without much of a prompt, Bob tells a story of how he was covering his ears as Peter, his boss, was murdering the victim.
Now what do you do with Bob, exactly? Let him go once you clear Peter? Keep him because he's not a cute girl?
Now, we aren't sure that this is how it went. Police claims that this is how it went and Knox claims that she got pretty much beaten into that statement, and it's one word against the other.
Her being psychopathic would have likely lead to other facts that a well funded persecution could uncover.
She's a foreigner, there's no budget for transatlantic flights to figure out if she had been cruel to animals as a child or the like, there's no jurisdiction, and you can't use that sort of stuff in a court anyway.
Well it's a fairly specific type of breaking down, to be accusing other people. There's other ways of breaking down, you know. And if her account of interrogation is false, and the police's account is true, that goes well beyond the lie about slapping. She said she was at the scene of the crime covering her ears as black owner of the bar she works at was murdering the victim, and if you know you didn't coerce the witness into making such a statement, that's very different from coercing a witness into such a statement.
While perhaps insufficient evidence in the court of law, the prosecutor is not the court of law, the prosecutor merely needs a strong suspicion for it to be their job to try to convict.
Ultimately we have Knox's words against the police's, and both sides have a coherent story that makes either side right.
Well, for what it's worth their wounds and bruises guy didn't think it was a single killer. And when someone's murdered at their own place in the dead middle of the night, often the cohabitants are involved.
An interesting piece of easily quantifiable Bayesian evidence could be phones being switched off overnight (dropping off the network) - how often did Knox do that? If she only did that once in many hundred days, on that night in particular, then that could be a very huge amount of evidence. Or she may have done that few times a week, in which case it's irrelevant.
I think you skip some details. Sollecito withdrew his alibi for Knox. Then Knox implicated Lumumba. And they really go after the guy. Interestingly they fail to railroad Lumumba in the way in which you think they railroaded Knox. Which to me is really interesting because it doesn't fit the 'evil police' story.
Knox of course claims it was extremely coercive, took hours, and some physical abuse from the police. Police denies abuse. We can't really tell either way, but prosecution ought to know how coercive they were. So that's another opportunity to really piss prosecution off.
edit: another thing, wounds and bruises on the body were interpreted as Kercher having been held by one person and stabbed by another. This is the reason why prosecution got so completely sure that more than one person was involved. Yeah, it's rather subjective and unreliable but people can be very sure in that sort of stuff.
There's all sorts of complicated details that are completely missing from the US coverage of the trials, which make the prosecution's position much more understandable. Perhaps the prosecution did not have sufficient evidence, but neither did the prosecution come up with some batshit insane theory out of the blue for no reason when they had everything explained with Guede.
edit: also, Guede was not some random robber, he knew people downstairs and met Knox before at least briefly. If he was random robber who never set his foot on the premises, then Bayesian wise it would have been a no-brainer: it's just unlikely that two independent groups of people who had no chance to pick eachother would be on board with murdering.
It seems to me that knowing only a little (and/or being bad at applied math) is kind of a pre-requisite for the level of enthusiasm involved in the use of it as a movement name. It's exciting to see all those bits of evidence and see yourself one-upping all those classy educated people that are dead set against use of those bits of evidence, or who even seen to use them in the completely wrong way. It's even more fun to do that with friends.
You know about little math, and it makes a huge difference to everything, that's exciting.
Or you spent years studying and/or working and all that math almost never matters - almost any evidence that's not overwhelmingly strong is extremely confounded with what's already been considered and/or with the chain of events bringing something to your attention.