In my scheme, what I'm really discussing is the probability distribution of probability estimates for a given statement.
OK, let's rephrase it in the terms of Bayesian hierarchical models. You have a model of event X happening in the future which says that the probability of that event is Y%. Y is a parameter of your model. What you are doing is giving a probability distribution for a parameter of your model (in the general case this distribution can be conditional, which makes it a meta-model, so hierarchical). That's fine, you can do this. In this context the width of the distribution reflects how precise your estimate of the lower-level model parameter is.
The only thing is that for unique events ("will AGI be developed within 30 years") your hierarchical model is not falsifiable. You will get a single realization (the event will either happen or it will not), but you will never get information on the "true" value of your model parameter Y. You will get a single update of your prior to a posterior and that's it.
Is that what you have in mind?
I think that is what I had in mind, but it sounds from the way you're saying it that this hasn't been discussed as a specific technique for visualizing belief probabilities.
That surprises me since I've found it to be very useful, at least for intuitively getting a handle on my confidence in my own beliefs. When dealing with the question of what probability to assign to belief X, I don't just give it a single probability estimate, and I don't even give it a probability estimate with the qualifier that my confidence in that probability is low/moderate/high. ...
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