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Manfred comments on Probability, knowledge, and meta-probability - Less Wrong
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I think a much better approach is to assign models to the problem (e.g. "it's a box that has 100 holes, 45 open and 65 plugged, the machine picks one hole, you get 2 coins if the hole is open and nothing if it's plugged."), and then have a probability distribution over models. This is better because keeps probabilities assigned to facts about the world.
It's true that probabilities-of-probabilities are just an abstraction of this (when used correctly), but I've found that people get confused really fast if you ask them to think in terms of probabilities-of-probabilities. (See every confused discussion of "what's the standard deviation of the standard deviation?")
Isn't Chapman's approach and your approach completely identical?
As per OP's graphs, each point on the X axis represents a model and the height of the blue line as the probability assigned to that model.
Or did you just mean that your way is a better way to phrase it for not confusing everyone?
Right. It's good for not confusing new people, and sometimes also good for not confusing yourself.
Oh ok.
I misinterpreted because you said "better" (implying a difference), and "abstraction" is not necessarily the same as "identical".