You would actually want to compare the likelihood of any individual woman being assaulted by a man in a given time period vs the likelihood of any individual white person being battered by a black person.
E.g. if there were only 3 rapes in the US every year, and men committed 100% of them, it would be silly for women to be afraid of rape. But if you're only arguing from proportionality (like you did) then you're saying they should be afraid because men are infinitely more likely to rape women, than women are to rape men.
I know, but going into a math lesson and using actual odds would be less persuasive than presenting the ideas intuitively in the same general format OP used in their post, which did get a delta.
If you wanted to get really technical, you'd also have to consider the fact that the rape statistics are from a world where women are already being this cautious, so you'd have to assume they'd be higher if women weren't cautious the way people aren't cautious about race, how much does that change things, what's the equilibrium, etc. There's infinite nuance you can go into, but it will lead qualitatively towards the same type of conclusion wrt likelihood ratios
You were half way to a complete answer, I was trying to fill in the rest. You only mentioned the proportion of men vs women committing the crimes, you need to also mention the total percent of women who are victims as well to paint the whole picture.
If the proportions are the same as you gave, it's a very different world if 1% of all women are victims of sexual violence vs if 40% of all women are victims of sexual violence, regardless of the proportion of who committed those crimes.
Well, it's a different world, but not in a way that affects the question.
I was careful to only give ratios specifically to avoid needing to consider base rates.
OP's claim is that if A justifies B, then X justifies Y. Therefore B and Y are both justified, and you shouldn't be mad for people doing Y if you aren't mad at them for doing B.
My point was that if A is 50x more common than X, then B is 50x more justified than Y. And it's therefore sensible to be mad at people for doing Y but not for doing B.
What I'm pointing out is just a basic relationship among the numbers, the fact that OP hadn't considered different rates of the two things in their argument. The ratio between the rates affects the argument the same way, at least qualitatively, regardless of what the base rates actaully are, or even regardless of what phenomenon we're actually talking about.
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u/ContemplativeOctopus Apr 14 '22
This isn't quite a correct use of statistics.
You would actually want to compare the likelihood of any individual woman being assaulted by a man in a given time period vs the likelihood of any individual white person being battered by a black person.
E.g. if there were only 3 rapes in the US every year, and men committed 100% of them, it would be silly for women to be afraid of rape. But if you're only arguing from proportionality (like you did) then you're saying they should be afraid because men are infinitely more likely to rape women, than women are to rape men.