In my previous comment, I mentioned my worry that accepting observer self-sampling without self-indication means that you’ve been suckered into taking conscious observation as an ontological primitive. (Also, I’ve been careful not to use examples that involve the size of the cosmos.) I would like to suggest that instead of a prior over observer-moments in possible worlds, we start with a prior over space-time-Everett locations in possible worlds. If all possible worlds we consider have the same set of space-time-Everett locations, and we have a prior P0 over possible worlds, then I suggest that we adopt the prior over (world, location) pairs:
P((w,x)) = P0(w) / number of possible locations
(Actually, that’s not necessarily quite right: If the “amplitude as degree of reality” interpretation is true, Everett branches should of course be weighted in the obvious way.)
As with observer-moments, we then condition on all the evidence we have about our actual space-time-Everett location in our actual possible world, and call the result our “subjective probability” distribution.
Isn’t anthropic reasoning about taking into account the observer selection effects related to the fact that we are conscious observers? Sure, but it seems to me that any non-mysterious anthropic reasoning is taken care of just fine by the conditioning step. Any possible worlds, Everett branches and cosmic regions that don’t support intelligent life will automatically be ruled out, for example.
The above definition trivially implies the following weak principle of self-indication:
If all possible worlds we consider have the same set of locations, worlds that contain more locations consistent with our evidence will tend to be more likely after conditionalization. (To be precise, the probability of each world w is weighted by P0(w) * number of locations in w consistent with our evidence).
This principle is enough to support being a thirder in the Sleeping Beauty problem, for example (which was what originally suggested it to me, when I was wondering what prior Beauty should update when she observes herself to be awake).
In my previous comment, I mentioned my worry that accepting observer self-sampling without self-indication means that you’ve been suckered into taking conscious observation as an ontological primitive. (Also, I’ve been careful not to use examples that involve the size of the cosmos.) I would like to suggest that instead of a prior over observer-moments in possible worlds, we start with a prior over space-time-Everett locations in possible worlds. If all possible worlds we consider have the same set of space-time-Everett locations, and we have a prior P0 over possible worlds, then I suggest that we adopt the prior over (world, location) pairs:
(Actually, that’s not necessarily quite right: If the “amplitude as degree of reality” interpretation is true, Everett branches should of course be weighted in the obvious way.)
As with observer-moments, we then condition on all the evidence we have about our actual space-time-Everett location in our actual possible world, and call the result our “subjective probability” distribution.
Isn’t anthropic reasoning about taking into account the observer selection effects related to the fact that we are conscious observers? Sure, but it seems to me that any non-mysterious anthropic reasoning is taken care of just fine by the conditioning step. Any possible worlds, Everett branches and cosmic regions that don’t support intelligent life will automatically be ruled out, for example.
The above definition trivially implies the following weak principle of self-indication:
This principle is enough to support being a thirder in the Sleeping Beauty problem, for example (which was what originally suggested it to me, when I was wondering what prior Beauty should update when she observes herself to be awake).