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.
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, even if your way of getting the estimate was sticking a finger in the air and saying the first number you thought of. You never make anything more accurate by rounding it[1], and while it's important to keep track of how precise your estimates are I think it's a mistake to try to do that by modifying the numbers. If you have two pieces of information (your best estimate, and how fuzzy it is), you should represent it as two pieces of information[2].
[1] This isn't strictly true, but it's near enough.
> 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.
My interpretation was that Yudkowski simply doubled Christiano's guess of 8% (as one might say in conversation "oh it's at least double that", but using the actual number)
I did mean 1%, not sure if I used the right term though, english not being my first language.
Wasn't 16% the example they were talking about? Isn't that two significant digits?
And 16% very much feels ridiculous to a reader when they could've just said 15%.
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.
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, even if your way of getting the estimate was sticking a finger in the air and saying the first number you thought of. You never make anything more accurate by rounding it[1], and while it's important to keep track of how precise your estimates are I think it's a mistake to try to do that by modifying the numbers. If you have two pieces of information (your best estimate, and how fuzzy it is), you should represent it as two pieces of information[2].
[1] This isn't strictly true, but it's near enough.
[2] Cf. "Pitman's two-bit rule".
> 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.
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My interpretation was that Yudkowski simply doubled Christiano's guess of 8% (as one might say in conversation "oh it's at least double that", but using the actual number)