loti made the point I’m about to make above, but appears to have taken it back; I’m not sure why, as it seem totally right.
Anyway: it’s certainly true that it doesn’t strictly follow from the fact that there are 75 times as many salespeople as librarians (and you know this) that you ought to be more confident that someone is a salesperson than a librarian, if all you know about them is that they are shy. However, that conclusion does follow on totally plausible assumptions about the frequency of shy people among librarians and the frequency of shy people among salespeople (and you having credences close to these frequencies). It follows, for instance, if four out of five librarians are shy, and only one in twenty salespeople are shy.
For it to not be the case that you should think the person is more likely be shy, given the base rate, you would have to think the frequency of shy people among librarians is 75 times higher than the frequency of shy people among salespeople. For that to be possible, the rate of shy people among salespeople would have to be less than or equal to one in 75. That is very low, I’d find that somewhat surprising. Even more surprising would be to find out that the frequency of shy librarians is close to 100%.
Maybe that’s the case; I don’t know. Probably Rob Bensinger doesn’t know for sure either; so yeah, he probably shouldn’t have been so categorical when he said that this is “a mistake”. But I think we can forgive Rob Bensinger here for using this as an example of base-rate neglect, because it’s pretty plausible that it is.
In fact, even if, as it happens, the numbers work out, and people get the right answer here, I expect most people don’t worry about the base rate at all when they answer this question, so they’re getting the right answer purely by luck; if that’s right, then this would still be an example of base-rate neglect.
loti made the point I’m about to make above, but appears to have taken it back; I’m not sure why, as it seem totally right.
Anyway: it’s certainly true that it doesn’t strictly follow from the fact that there are 75 times as many salespeople as librarians (and you know this) that you ought to be more confident that someone is a salesperson than a librarian, if all you know about them is that they are shy. However, that conclusion does follow on totally plausible assumptions about the frequency of shy people among librarians and the frequency of shy people among salespeople (and you having credences close to these frequencies). It follows, for instance, if four out of five librarians are shy, and only one in twenty salespeople are shy.
For it to not be the case that you should think the person is more likely be shy, given the base rate, you would have to think the frequency of shy people among librarians is 75 times higher than the frequency of shy people among salespeople. For that to be possible, the rate of shy people among salespeople would have to be less than or equal to one in 75. That is very low, I’d find that somewhat surprising. Even more surprising would be to find out that the frequency of shy librarians is close to 100%.
Maybe that’s the case; I don’t know. Probably Rob Bensinger doesn’t know for sure either; so yeah, he probably shouldn’t have been so categorical when he said that this is “a mistake”. But I think we can forgive Rob Bensinger here for using this as an example of base-rate neglect, because it’s pretty plausible that it is.
In fact, even if, as it happens, the numbers work out, and people get the right answer here, I expect most people don’t worry about the base rate at all when they answer this question, so they’re getting the right answer purely by luck; if that’s right, then this would still be an example of base-rate neglect.