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That's still base-rate neglect as you are picking and choosing what you want to look at and not conditioning on one of the more relevant variables.
What fraction of the pretty girls who lived with the victims turned out to be murderers? By looking at the genderless conditional probability ('somebody'), you're implying that women like Knox might have male-like murder levels, which is obviously wrong. And to the extent that pretty girls do not have differing patterns of murdering roommates from other women, you're making the exact same mistake, even (it doesn't matter whether you update on pretty girl then roommate or roommate then pretty girl).
Update on both living with the victim and being female and the small probability is bigger but... still small, since the still relatively low probability of a roommate murdering is penalized substantially by being female (female murder rates are like 1/10th male and that's the raw rates, not adjusted for age or SES or race etc). As the top comment says, "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".
No, male-like murder levels would be higher than genderless murder levels. And, if I understand correctly, most of the excess male murder rate involves gang-related violence, which in this case was pretty clearly not involved.
Anyway, I agree that if you are doing pure Bayesian inference you have to condition on all kinds of available evidence, including gender, race, social class, nationality, etc. But we can't expect courts to consider this kind of evidence, for good reasons (avoid creating self-fulfilling prophecies and avoid incentivizing crime within certain demographics).
No, the male murder excess rate is not gang-related. Why would you think so?
Right. According to this huffpo post less than 10% of homicides are gang-related, which makes it impossible that gang violence could explain the 10:1 (male:female) homicide offending ratio.
I was thinking that most murders are gang-related and most gang members are male, but I see that this is disputed. Unfortunately, all the sources I can find seem to take a partisan position in the gun control debate, hence I don't know.
Bad prior. Gang violence is a major murder statistic, but it's pretty far from being "most". Quick googling says: "1 in 6 murders". The most common motive, at 50% is "Argument". So.. men are more likely to escalate those to homocide?
Makes sense.
...and what do you think that implies about whether female murder levels are lower as I claimed?
Yeah, no. Think about that a little bit. (Also, please note the irony of responding to criticism about not conditioning by claiming it would be neutralized by further conditioning.)
If the updates on different kinds of evidence would likely cancel each other, it is an argument for avoiding conditioning too hard or privileging one kind of evidence while doing informal reasoning.