The rephrasing as frequencies makes it much clearer that the question is not “How likely is an [A|B|C|D|E] to fit the above description” which J thomas suggested as a misinterpretation that could cause the conjunction fallacy.
Similarly, that rephrasing makes it harder to implicitly assume that category A is “accountants who don’t play jazz” or C is “jazz players who are not accountants”.
I think similarly, in the case of the poland invasion diplomatic relations cutoff, what people are intuitively calculating in the compound statement is the conditional probability, IOW, turning the “and” statement into an “if” statement. If the soviets invaded Poland, the probability of a cutoff might be high, certainly higher than the current probability given no new information.
But of course that was not the question. A big part of our problem is sometimes translation of english statements into probability statements. If we do that intuitively or cavalierly, these fallacies become very easy to fall into.
Catapult:
The rephrasing as frequencies makes it much clearer that the question is not “How likely is an [A|B|C|D|E] to fit the above description” which J thomas suggested as a misinterpretation that could cause the conjunction fallacy.
Similarly, that rephrasing makes it harder to implicitly assume that category A is “accountants who don’t play jazz” or C is “jazz players who are not accountants”.
I think similarly, in the case of the poland invasion diplomatic relations cutoff, what people are intuitively calculating in the compound statement is the conditional probability, IOW, turning the “and” statement into an “if” statement. If the soviets invaded Poland, the probability of a cutoff might be high, certainly higher than the current probability given no new information.
But of course that was not the question. A big part of our problem is sometimes translation of english statements into probability statements. If we do that intuitively or cavalierly, these fallacies become very easy to fall into.