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ozziegooen comments on Creating a Text Shorthand for Uncertainty - Less Wrong
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Comments (29)
You want to translation from numbers to certainty to be
0->1/2=50%
1->2/3=67%
2->4/5=80%
3->8/9=89%
4->16/17=94%
5->32/33=97%
6->64/65=98.5%
7->128/129=99.2%
8->256/257=99.6%
9->512/513=99.8%
10->1024/1025=99.9%
n->2^n/(2^n+1)
Here, the percent p is given the number n, such that it would take n more bits of information to convince you that you are wrong than it would take to convince you that you are correct. These numbers are very natural, and for some purposes, it would be better to use these numbers than to use the percents.
Notice that this luckily (Maybe you planned this) fits with your number system, except that 99.9 is really really certain compared to what you would expect would come one number after 95%. I know that it would be very hard to get that kind of detail in the intermediate values between 4 and 5, but even if you only ever say 0, 1, 2, 3, 4, 10, I still think it is worth it to emphasize the big difference between 95% and 99.9%.
Very good point. I like how this could go higher or have in-between values quite easily. In retrospect an equation like this makes much more sense than an intuitive guess, what I wrote down was mostly to use as a start.
I'm not sure if this is exactly the perfect equation for this, given that I think I'd probably want them to be a bit more spaced out if they went to 10 (going further in confidence past 99.9% perhaps) ~i1.