Daisy isn’t in a loop at all. There’s apparently evidence for Dark and that is tempered by the fact that its existance indicates a failing on Dark’s part.
For Bob, to make an analogy, imagine Bob is wet. For you, that is evidence that it is raining. It could be argued that being wet is evidence that it’s raining for Bob as well. But generally speaking Bob will know why Bob is wet. Given the knowedge of why Bob is wet, the wetness itself is masked off and no longer relevant. If Bob has just had a bath, then being wet no longer constitutes any evidence of rain. If Bob was outside and water fell on him from the sky, it probably did rain, but his being wet no longer constitutes any additional evidence in that case either (well, ok, it has some value still as confirmation of his memory, but it’s orders of magnitude less relevant).
Similarly Bob should ask “Why do I believe in Bright?”. The answer to that question contains all the relevant evidence for Bright’s existance, and given that answer Bob’s actual belief no longer constitutes evidence either way. With that answer, there is no longer a loop for Bob either.
One final point, you have to consider the likelihood of belief in case 4. If you would expect some level of belief in sorcerors in Faerie even when there are no sorcerors, then case 4 doesn’t fall behind as much as you might think. Once you’ve got both Bob and Daisy, case 4 doesn’t just break even, it’s actually way ahead.
It seems like, at this level, thinking of things in terms of “evidence” and “priors” at all is no longer really relevant—Bayesian updating just a way of computing and maintaining “belief caches”, which are a highly compressed map of our “evidence” (which is itself a highly compressed map of our phenomenal experience).
Daisy isn’t in a loop at all. There’s apparently evidence for Dark and that is tempered by the fact that its existance indicates a failing on Dark’s part.
For Bob, to make an analogy, imagine Bob is wet. For you, that is evidence that it is raining. It could be argued that being wet is evidence that it’s raining for Bob as well. But generally speaking Bob will know why Bob is wet. Given the knowedge of why Bob is wet, the wetness itself is masked off and no longer relevant. If Bob has just had a bath, then being wet no longer constitutes any evidence of rain. If Bob was outside and water fell on him from the sky, it probably did rain, but his being wet no longer constitutes any additional evidence in that case either (well, ok, it has some value still as confirmation of his memory, but it’s orders of magnitude less relevant).
Similarly Bob should ask “Why do I believe in Bright?”. The answer to that question contains all the relevant evidence for Bright’s existance, and given that answer Bob’s actual belief no longer constitutes evidence either way. With that answer, there is no longer a loop for Bob either.
One final point, you have to consider the likelihood of belief in case 4. If you would expect some level of belief in sorcerors in Faerie even when there are no sorcerors, then case 4 doesn’t fall behind as much as you might think. Once you’ve got both Bob and Daisy, case 4 doesn’t just break even, it’s actually way ahead.
It seems like, at this level, thinking of things in terms of “evidence” and “priors” at all is no longer really relevant—Bayesian updating just a way of computing and maintaining “belief caches”, which are a highly compressed map of our “evidence” (which is itself a highly compressed map of our phenomenal experience).