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Being cautious of a strange man around a group of kids in a park is also, I think, an understandable reaction.
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Again, this kind of reaction varies tremendously from place to place. In northern Germany or coastal Croatia, for example, most people would laugh and think you're joking or crazy or just sick if the reason you're cautious is that you think the man might be a child molester. If you're cautious because you think he might be trying to steal her purse, then that would probably be seen as a more reasonable reaction. Or in Croatia if the reason was that you thought he was a Serb, then that would be an patently obvious reason for concern . . . . .
In any case, doing a male/female convict comparison test is logically not relevant to determining how rational it is to be cautious of males but not females. If you want to know whether A is a risk in and of itself, you don't ask what the risk of B is, and compare the two. You need to know the risk of A itself, absolutely. For example, you don't say "I'm not going to swim in pool A because it's 10x dirtier than pool B" when pool A has only 10 sand grains and B has one sand grain in it. If you don't swim in the pool, it's because it's too dirty absolutely, not in comparison to some other pool. Or you don't say "I'm not going to bother driving safely in town because it's 10x more likely that I die on the freeway than in town." (just making up numbers here)
Similarly, if someone decides not to be vigilant about females as child molesters, then the logical reason would be because the absolute risk
from females alone is too small to worry about, not because the risk from males is 10x higher, which is completely irrelevant because it's a female standing there, not a male. And the critical point here is that nobody knows even within an order of magnitude what the absolute risk is. So any decision one makes is without any concrete support whatsoever.
Here's a little thought experiment. We know that the overall rates of child molestation vary tremendously from place to place. Let's say that in state A the overall rate is 10x what it is in state B, but that the relative male/female perp ratio is 10 in both states. If all you're relying on is your comparison test, then you would have to conclude in both states to be vigilant of males but not females. That's because it's 10x more likely that a male be a perp than a female. But look: in state A the absolute female perp rate is the same as the absolute male perp rate in state B! Therefore to be logically consistent you need to be just as concerned about females in state A as you are about males in state B. But is anybody going to react like that? No. The vast majority of people are going to do the same male/female comparison test as you did and conclude in both states to be vigilant of men but not women.
That's why this reaction is irrational. There is utterly no known absolute risk to base it on, so people take the psychological path of least resistance and suspect men because they already know that men are "more likely than women" to be sexual predators. Suspecting women for most people creates too much cognitive dissonance, so it's avoided regardless of the absolute risk from women.
And finally, the comparison test is reducible to absurdity: if you eliminate women by making a male/female comparison, why stop there? Why not eliminate white men by noting that, within men, there are a disproportionate number of black and hispanic convicts? And why not also eliminate rich men, because there is a disproportionate number of poor convicts? It's logically the same: you're eliminating women because there are a disproportionate number of male convicts, so why stop there?
So if one is basing one's behavior on convict comparison tests alone, then to be logically consistent, the conclusion,
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Being cautious of a strange man around a group of kids in a park is also, I think, an understandable reaction.
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should be altered to read:
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Being cautious of a strange poor, black or hispanic man around a group of kids in a park is also, I think, an understandable reaction.
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And of course that is exactly how most people do react in reality, in general, for exactly the reasons that you give for focusing on men but not women.