So maybe it’s worth saying explicitly what’s going on here: You’re comparing probabilities conditional on different information.
A = “Beth read my email to Alice”.
B = “Beth knows that my email to Alice mentioned the Dead Badger Cafe”.
I = “Beth told me she read my email to Alice”.
J = “Beth told me my email to Alice mentioned the Dead Badger Cafe”.
Now P(A&B|I) < P(A|I), and P(A&B|I&J) < P(A|I&J), but P(A&B|I&J) > P(A|I).
So there’s no contradiction; there’s nothing wrong with applying probabilities; but if you aren’t careful you can get confused. (For the avoidance of doubt, I am not claiming that Lumifer is or was confused.)
And, yes, I bet this sort of conditional-probability structure is an important part of why we find stories more plausible when they contain lots of details. Unfortunately, the way our brains apply this heuristic is far from perfect, and in particular it works even when we can’t or won’t check the details and we know that the person telling us the story knows this. So it leads us astray when we are faced with people who are unscrupulous and good at lying.
Um. I was just making a point that “we know P(A & B) ⇐ P(A)” is a true statement coming from math logic, while “if you add details to a story, it becomes less plausible” is a false statement coming from human interaction.
Not sure about your unrolling of the probabilities since P(B|A) = 1 which makes A and B essentially the same. If you want to express the whole thing in math logic terms you need notation as to who knows what.
[...] is a true statement coming from math logic, [...] is a false statement coming from human interaction
My reading of polymer’s statement is that he wasn’t using “plausible” as a psychological term, but as a rough synonym for “probable”. (polymer, if you’re reading: Was I right?)
P(B|A) = 1 which makes A and B essentially the same
No, P(B|A) is a little less than 1 because Beth might have read the email carelessly, or forgotten bits of it.
[EDITED to add: If whoever downvoted this would care to explain what they found objectionable about it, I’d have more chance of fixing it. It looks obviously innocuous to me even on rereading. Thanks!]
if you add details to a story, it becomes less plausible” is a false statement coming from human interaction.
I don’t care whether it’s false as a “human interaction”. I care whether the idea can be modeled by probabilities.
Is my usage of the word plausible in this way really that confusing? I’d like to know why… Probable, likely, credible, plausible, are all (rough) synonyms to me.
So maybe it’s worth saying explicitly what’s going on here: You’re comparing probabilities conditional on different information.
A = “Beth read my email to Alice”. B = “Beth knows that my email to Alice mentioned the Dead Badger Cafe”. I = “Beth told me she read my email to Alice”. J = “Beth told me my email to Alice mentioned the Dead Badger Cafe”.
Now P(A&B|I) < P(A|I), and P(A&B|I&J) < P(A|I&J), but P(A&B|I&J) > P(A|I).
So there’s no contradiction; there’s nothing wrong with applying probabilities; but if you aren’t careful you can get confused. (For the avoidance of doubt, I am not claiming that Lumifer is or was confused.)
And, yes, I bet this sort of conditional-probability structure is an important part of why we find stories more plausible when they contain lots of details. Unfortunately, the way our brains apply this heuristic is far from perfect, and in particular it works even when we can’t or won’t check the details and we know that the person telling us the story knows this. So it leads us astray when we are faced with people who are unscrupulous and good at lying.
Um. I was just making a point that “we know P(A & B) ⇐ P(A)” is a true statement coming from math logic, while “if you add details to a story, it becomes less plausible” is a false statement coming from human interaction.
Not sure about your unrolling of the probabilities since P(B|A) = 1 which makes A and B essentially the same. If you want to express the whole thing in math logic terms you need notation as to who knows what.
My reading of polymer’s statement is that he wasn’t using “plausible” as a psychological term, but as a rough synonym for “probable”. (polymer, if you’re reading: Was I right?)
No, P(B|A) is a little less than 1 because Beth might have read the email carelessly, or forgotten bits of it.
[EDITED to add: If whoever downvoted this would care to explain what they found objectionable about it, I’d have more chance of fixing it. It looks obviously innocuous to me even on rereading. Thanks!]
I’m not quite sure what the following means:
I don’t care whether it’s false as a “human interaction”. I care whether the idea can be modeled by probabilities.
Is my usage of the word plausible in this way really that confusing? I’d like to know why… Probable, likely, credible, plausible, are all (rough) synonyms to me.