Nick: Kahneman and Tversky actually mention the mechanism you describe as one cause of the conjunction fallacy, in their 1983 paper that Eliezer linked to. I agree that in the case where the people who see “X” and the people who see “X and Y” are different, this makes it rather unfair to call it a fallacy; K&T don’t seem to think so, perhaps because it’s clear that people in this situation are either underestimating the probability of X or overestimating that of X&Y or both, so they’re making a mistake even if the explanation for that mistake is reasonably non-embarrassing.
I think that Felix is mostly making fun of people who try to think mathematically and who try to answer the question they’re asked rather than some different question that they think might make more sense, rather than trying to make a serious point about the nature of biased coins.
Nick: Kahneman and Tversky actually mention the mechanism you describe as one cause of the conjunction fallacy, in their 1983 paper that Eliezer linked to. I agree that in the case where the people who see “X” and the people who see “X and Y” are different, this makes it rather unfair to call it a fallacy; K&T don’t seem to think so, perhaps because it’s clear that people in this situation are either underestimating the probability of X or overestimating that of X&Y or both, so they’re making a mistake even if the explanation for that mistake is reasonably non-embarrassing.
I think that Felix is mostly making fun of people who try to think mathematically and who try to answer the question they’re asked rather than some different question that they think might make more sense, rather than trying to make a serious point about the nature of biased coins.