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Peter_de_Blanc comments on Intuitive supergoal uncertainty - Less Wrong
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Can you give a reference? Because that strikes me as rather un-Jaynesian.
You say that the interval tells us something about how apt the estimate is to move in the face of new evidence. What does it tell us about that? Doesn't it depend on which piece of evidence we're talking about? Do you have to specify a prior over which variables you are likely to observe next?
The material I have in mind is Chapter 18 of PT:LOS. You can see the section headings on page 8 (numbered vii because the title page is unnumbered) here. One of the section titles is "Outer and Inner Robots"; when rhollerith says 72%, he's giving the outer robot answer. To give an account of how unstable your probability estimates are, you need to give the inner robot answer.
When we receive new evidence, we assign a likelihood function for the probability. (We take the perspective of the inner robot reasoning about what the outer robot will say.) The width of the interval for the probability tells us how narrow the likelihood function has to be to shift the center of that interval by a non-neglible amount.
No.
That is a strange little chapter, but I should note that if you talk about the probability that you will make some future probability estimate, then the distribution of a future probability estimate does make a good way of talking about the instability of a state of knowledge. As opposed to the notion of talking about the probability of a current probability estimate, which sounds much more like you're doing something wrong.
Second the question, it doesn't sound Jaynesian to me either.
I'm relieved that I'm not the only one who thought that. I was somewhat aghast to hear Jaynes recommend something that is so, well, obviously a bull@# hack.
It's curious to me that you'd write this even after I cited chapter and verse. Do you have a copy of PT:LOS?
I do have a copy but I will take your word for it. I am shocked and amazed that Jayenes would give such a poor recommendation. It doesn't sound Jaynesian to me either and I rather hope he presents a variant that is sufficiently altered as to not be this suggestion at all. You yourself gave the reason why it doesn't work and I am sure there is a better approach than just hacking the scale when it is near 1 or 0. (I am hoping your paraphrase sounds worse than the original.)
Best to give a probabilty density function - but two 2-S-F probabilites typically gives more information than one.
It is good to indicate the strength of your priors. Perhaps one could indicate how much you think your opinion is likely to change over some specified timescale - or in response to the next set of pertinent data points.