Comment by dataflow
6 days ago
> In context, the "at least 16%" is responding to someone who said 8%, and 16 just happens to be exactly twice 8. I suspect (though I don't know) that Yudkowsky would not have claimed to have a robust way to pick whether 16% or 17% was the better figure.
If this was just a way to say "at least double that", that's... fair enough, I guess.
Regarding your other point:
> For what it's worth, I don't think there's anything even slightly wrong with using whatever estimate feels good to you, even if it happens not to fit someone else's criterion for being a nice round number
This is completely missing the point. There absolutely is something wrong with doing this (barring cases like the above where it was just a confusing phrasing of something with less precision like "double that"). The issue has nothing to do with being "nice", it has to do with the significant figures and the error bars.
If you say 20% then it is understood that your error margin is 5%. Even those that don't understand sigfigs still understand that your error margin is < 10%.
If you say 19% then suddenly the understanding becomes that your error margin < 1%. Nobody is going to see that and assume your error bars on it are 5% -- nobody. Which is what makes it a ridiculous estimate. This has nothing to do with being "nice and round" and everything with conveying appropriate confidence.
I'm not missing the point, I'm disagareeing with it. I am saying that the convention that if you say 20% then you are assumed to have an error margin of 5%, while if you say 19% you are assumed to have an error margin of 1%, is a bad convention. It gives you no way to say that the number is 20% with a margin of 1%. It gives you only a very small set of possible degrees-of-uncertainty. It gives you no way to express that actually your best estimate is somewhat below 20% even though you aren't sure it isn't 5% out.
It's true, of course, that if you are talking to people who are going to interpret "20%" as "anywhere between 17.5% and 22.5%" and "19%" as "anywhere between 18.5% and 19.5%", then you should try to avoid giving not-round numbers when your uncertainty is high. And that many people do interpret things that way, because although I think the convention is a bad one it's certainly a common one.
But: that isn't what happened in the case you're complaining about. It was a discussion on Less Wrong, where all the internet-rationalists hang out, and where there is not a convention that giving a not-round number implies high confidence and high precision. Also, I looked up what Yudkowsky actually wrote, and it makes it perfectly clear (explicitly, rather than via convention) that his level of uncertainty was high:
"Ha! Okay then. My probability is at least 16%, though I'd have to think more and Look into Things, and maybe ask for such sad little metrics as are available before I was confident saying how much more."
(Incidentally, in case anyone's similarly salty about the 8% figure that gives context to this one: it wasn't any individual's estimate, it was a Metaculus prediction, and it seems pretty obvious to me that it is not an improvement to report a Metaculus prediction of 8% as "a little under 10%" or whatever.)