That said, FYI I was kind of enlightened by this phrasing:
That is, in the multiple stage fallacy, someone who wishes to portray a proposition as unlikely can prey on people’s reluctance to assign extreme probabilities by spuriously representing the proposition as a conjunction of sub-propositions that all need to be true.
I’d been feeling sus about why the multiple stage fallacy was even a fallacy at all, apart from “somehow in practice people fuck it up.” Multiplying probabilities together is… like, how else are you supposed to do any kind of sophisticated reasoning?
But, “because people are scared of (or bad at) assigning extreme probabilities” feels like it explains it to me.
I think the larger effect is treating the probabilities as independent when they’re not.
Suppose I have a jar of jelly beans, which are either all red, all green or all blue. You want to know what the probability of drawing 100 blue jelly beans is. Is it 13100≈2⋅10−48? No, of course not. That’s what you get if you multiply 1⁄3 by itself 100 times. But you should condition on your results as you go. P(jelly1 = blue)⋅P(jelly2=blue|jelly1=blue)⋅P(jelly3=blue|jelly1=blue,jelly2=blue) …
Every factor but the first is 1, so the probability is 13.
That said, FYI I was kind of enlightened by this phrasing:
I’d been feeling sus about why the multiple stage fallacy was even a fallacy at all, apart from “somehow in practice people fuck it up.” Multiplying probabilities together is… like, how else are you supposed to do any kind of sophisticated reasoning?
But, “because people are scared of (or bad at) assigning extreme probabilities” feels like it explains it to me.
I think the larger effect is treating the probabilities as independent when they’re not.
Suppose I have a jar of jelly beans, which are either all red, all green or all blue. You want to know what the probability of drawing 100 blue jelly beans is. Is it 13100≈2⋅10−48? No, of course not. That’s what you get if you multiply 1⁄3 by itself 100 times. But you should condition on your results as you go. P(jelly1 = blue)⋅P(jelly2=blue|jelly1=blue)⋅P(jelly3=blue|jelly1=blue,jelly2=blue) …
Every factor but the first is 1, so the probability is 13.