If you can inspect and analyze your own prior (using your own prior, of course) you can notice that your prior is not reflectively consistent, that you can come up with other priors that your prior expects to get better results. Humans, who are not ideal Bayesians but have a concept of ideal Bayesians, have actually done this.
(Though reflective consistency does not guarantee effectiveness. Some priors are too ineffective to notice they are ineffective.)
If you have a concept of prior (2), and wish to get better at acting according to it over time, then (2) is your real prior. It is what you (try to) use to make your decisions. (3) is just a tool you employ in the meantime, and you may pick a better tool, judging with (2). I don’t know what (1) means (or what (2) means when (1) is realized).
(1) is the prior I would have if I had never inspected and analyzed my prior. It is a path not taken from prior (3). The point of introducing it was to point out that I really believe (2) is better than (3), as opposed to (2) is better than (1) (which I also believe, but it isn’t the point).
Does “your prior” refer to (A) the prior you identify with, or (B) the prior that describes your actual beliefs as you process evidence, or something else?
If (A), I don’t understand:
This might be a process of figuring out what your prior is, but the approximations along the way are not your prior
If (B), I don’t understand:
If you have a concept of prior (2), and wish to get better at acting according to it over time, then (2) is your real prior.
If you can inspect and analyze your own prior (using your own prior, of course) you can notice that your prior is not reflectively consistent, that you can come up with other priors that your prior expects to get better results. Humans, who are not ideal Bayesians but have a concept of ideal Bayesians, have actually done this.
(Though reflective consistency does not guarantee effectiveness. Some priors are too ineffective to notice they are ineffective.)
This might be a process of figuring out what your prior is, but the approximations along the way are not your prior (they might be some priors).
I see three priors to track here:
The prior I would counterfactually have had if I were not able to make this comparison.
The ideal prior I am comparing my approximation of prior (1) to.
My actual prior resulting from this comparison, reflecting that I try to implement prior (2), but cannot always compute/internalize it.
I have prior (3), but I believe prior (2) is better.
If you have a concept of prior (2), and wish to get better at acting according to it over time, then (2) is your real prior. It is what you (try to) use to make your decisions. (3) is just a tool you employ in the meantime, and you may pick a better tool, judging with (2). I don’t know what (1) means (or what (2) means when (1) is realized).
(1) is the prior I would have if I had never inspected and analyzed my prior. It is a path not taken from prior (3). The point of introducing it was to point out that I really believe (2) is better than (3), as opposed to (2) is better than (1) (which I also believe, but it isn’t the point).
Does “your prior” refer to (A) the prior you identify with, or (B) the prior that describes your actual beliefs as you process evidence, or something else?
If (A), I don’t understand:
If (B), I don’t understand: