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Kevin P's avatar

> We know that someone participates in at least one bad activity but know nothing else about them. What is the probability they are a bastard?

>

> It’s quite low. About 20% I think.

No, it's over 50%.

You said that 10% of the population participate in each bad activity, and 90% of those are bastards.

With 20 bad actions, the absolute maximum number of non-bastards taking part will be 20*10*10% = 20% of the total population. In reality it will be noticeably lower because of overlap.

But practically all of the bastards will have done at least one bad thing. Their chance of doing any individual bad thing is 9%/20% = 45%, so with 20 independent things the chance of doing none at all would be (1-45%)^20, or less than one in 100,000. So the number of bastards in your "at least one bad thing" sample is roughly 20% of the total population.

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Bistromathtician's avatar

I think your Jerrow and Wenes scenario is not as clear-cut in terms of who should be considered "worse" as you're making it out to be (or perhaps here are some complications which explain why conventional morality gets the result it does). One complication is that Jerrow is a (mild) "sex pest," and sexual ethics is partly based on "sacred" values, so its taboos and complications are not evaluated purely logically. For the same reason rape is now considered more villainous than murder in Western countries, comparing sex(-adjacent) offenses against other offenses will often lead to strange conclusions. Another complication is the ease of "defending" your moral judgement to outsiders. Even though the group deciding between the two guys are all vegans, they still (in their head at least), are "justifying" why they don't want to be associated with someone. For the vegans, both men are objectional, and casting either out of the group would be a defensible call. But if a non-vegan asks why they don't like Wenes, they have to be prepared to argue the moral case of veganism, but if they ask the same question of Jerrow, the vegans can simply say "he's a sex pest." Even though the vegans have their own moral framework, they are still comparing the two fellows against "average social morality," and coming down harder on the one whose behavior more people outside their group would find more objectional.

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