Here’s is how I think I intuitively interpret such statements:
“I am a pretty average cook” → Either
I have no particular evidence about my cooking ability and therefore on priors expect to be fairly typical, or
I fall roughly in the middle of the few people I know well, and have no particular reason to think those people are very unusual in terms of cooking-skill, and therefore on priors + a little data I expect my skills to be fairly typical
“I am an above average cook” → I am pretty good compared to the few people I know well, and I have no particular reason to think they’re unusually bad cooks, so on priors + a little data I expect my skills to be better than typical.
and have no particular reason to think those people are very unusual in terms of cooking-skill
Yeah, that’s what I was trying to get at with the typical-friend-group stuff. The people you know well aren’t a uniform sample of all people, so you have no reason to conclude that their X-skill is normal for any arbitrary X.
so you have no reason to conclude that their X-skill is normal for any arbitrary X
I mean, you have some priors, and priors are a totally valid thing to reason from even if you’re not taking a uniform random sample of all people.
In general, “I have a few samples of X, and I don’t have any particular reason to think they’re unusual samples, so on priors they’re probably typical” is a totally valid way to reason even if your samples aren’t uniform random from the population.
Here’s is how I think I intuitively interpret such statements:
“I am a pretty average cook” → Either
I have no particular evidence about my cooking ability and therefore on priors expect to be fairly typical, or
I fall roughly in the middle of the few people I know well, and have no particular reason to think those people are very unusual in terms of cooking-skill, and therefore on priors + a little data I expect my skills to be fairly typical
“I am an above average cook” → I am pretty good compared to the few people I know well, and I have no particular reason to think they’re unusually bad cooks, so on priors + a little data I expect my skills to be better than typical.
Yeah, that’s what I was trying to get at with the typical-friend-group stuff. The people you know well aren’t a uniform sample of all people, so you have no reason to conclude that their X-skill is normal for any arbitrary X.
I mean, you have some priors, and priors are a totally valid thing to reason from even if you’re not taking a uniform random sample of all people.
In general, “I have a few samples of X, and I don’t have any particular reason to think they’re unusual samples, so on priors they’re probably typical” is a totally valid way to reason even if your samples aren’t uniform random from the population.