My initial argument was really a question “Is there any approach to anthropic reasoning that allows us to do basic scientific inference, but does not lead to Doomsday conclusions?” So far I’m skeptical.
The best response you’ve got is I think twofold.
Use SIA but please ignore the infinite case (even though the internal logic of SIA forces the infinite case) because we don’t know how to handle it. When applying SIA to large finite cases, truncate universes by a large volume cutoff (4d volume) rather than by a large population cutoff or large utility cutoff. Oh and ignore simulations because if you take those into account it leads to odd conclusions as well.
That might perhaps work, but it does look horribly convoluted. To me it does seem like determining the conclusion in advance (you want SIA to favour universes 1 and 2 over 3 and 4, but not favour 1 over 2) and then hacking around with SIA until it gives that result.
Incidentally, I think you’re still not out of the woods with a volume cutoff. If it is very large in the time dimension then SIA is start going to favour universes which have Boltzmann Brains in the very far future over universes whose physics don’t ever allow Boltzmann Brains. And then SIA is going to suggest that not only are we probably in a universe with lots of BBs, we most likely are BBs ourselves (because almost all observers with exactly our experiences are BBs). So SIA calls for further surgery either to remove BBs from consideration or to apply the 4volume cutoff in a way that doesn’t lead to lots of Boltzmann Brains.
Forget about both SIA and SSA and revert to an underlying decision theory: viz your ADT. Let the utility function take the strain.
The problem with this is that ADT with unbounded utility functions doesn’t lead to stable conclusions. So you have to bound or truncate the utility function.
But then ADT is going to pay the most attention to universes whose utility is close to the cutoff … namely versions of universe 1,2,3,4 which have utility at or near the maximum. For the reasons I’ve already discussed above, that’s not in general going to give the same results as applying a volume cutoff. If the utility scales with the total number of observers (or observers like me), then ADT is not going to say “Make decisions as if you were in universe 1 or 2 … but with no preference between these … rather than as if you were in universe 3 or 4”
I think the most workable utility function you’ve come up with is the one based on subjective bubbles of order galactic volume or thereabouts i.e. the utility function scales roughly linearly with the number of observers in the volume surrounding you, but doesn’t care about what happens outside that region (or in any simulations, if they are of different regions). Using that is roughly equivalent to applying a volume truncation using regular astronomical volumes (rather than much larger volumes).
However the hack to avoid simulations looks a bit unnatural to me (why wouldn’t I care about simulations which happen to be in the same local volume?) Also, I think this utility function might then tend to favour “zoo” hypotheses or “planetarium” hypotheses (I.e. decisions are made as if in a universe densely packed with planetaria containing human level civilisations, rather than simulations of said simulations).
More worryingly, I doubt if anyone really has a utility function that looks like this ie. one that cares about observers 1 million light years away just as much as it cares about observers here on Earth, but then stops caring if they happen to be 1 trillion light years away...
So again I think this looks rather like assuming the right answer, and then hacking around with ADT until it gives the answer you were looking for.
Thanks again for the useful response.
My initial argument was really a question “Is there any approach to anthropic reasoning that allows us to do basic scientific inference, but does not lead to Doomsday conclusions?” So far I’m skeptical.
The best response you’ve got is I think twofold.
Use SIA but please ignore the infinite case (even though the internal logic of SIA forces the infinite case) because we don’t know how to handle it. When applying SIA to large finite cases, truncate universes by a large volume cutoff (4d volume) rather than by a large population cutoff or large utility cutoff. Oh and ignore simulations because if you take those into account it leads to odd conclusions as well.
That might perhaps work, but it does look horribly convoluted. To me it does seem like determining the conclusion in advance (you want SIA to favour universes 1 and 2 over 3 and 4, but not favour 1 over 2) and then hacking around with SIA until it gives that result.
Incidentally, I think you’re still not out of the woods with a volume cutoff. If it is very large in the time dimension then SIA is start going to favour universes which have Boltzmann Brains in the very far future over universes whose physics don’t ever allow Boltzmann Brains. And then SIA is going to suggest that not only are we probably in a universe with lots of BBs, we most likely are BBs ourselves (because almost all observers with exactly our experiences are BBs). So SIA calls for further surgery either to remove BBs from consideration or to apply the 4volume cutoff in a way that doesn’t lead to lots of Boltzmann Brains.
Forget about both SIA and SSA and revert to an underlying decision theory: viz your ADT. Let the utility function take the strain.
The problem with this is that ADT with unbounded utility functions doesn’t lead to stable conclusions. So you have to bound or truncate the utility function.
But then ADT is going to pay the most attention to universes whose utility is close to the cutoff … namely versions of universe 1,2,3,4 which have utility at or near the maximum. For the reasons I’ve already discussed above, that’s not in general going to give the same results as applying a volume cutoff. If the utility scales with the total number of observers (or observers like me), then ADT is not going to say “Make decisions as if you were in universe 1 or 2 … but with no preference between these … rather than as if you were in universe 3 or 4”
I think the most workable utility function you’ve come up with is the one based on subjective bubbles of order galactic volume or thereabouts i.e. the utility function scales roughly linearly with the number of observers in the volume surrounding you, but doesn’t care about what happens outside that region (or in any simulations, if they are of different regions). Using that is roughly equivalent to applying a volume truncation using regular astronomical volumes (rather than much larger volumes).
However the hack to avoid simulations looks a bit unnatural to me (why wouldn’t I care about simulations which happen to be in the same local volume?) Also, I think this utility function might then tend to favour “zoo” hypotheses or “planetarium” hypotheses (I.e. decisions are made as if in a universe densely packed with planetaria containing human level civilisations, rather than simulations of said simulations).
More worryingly, I doubt if anyone really has a utility function that looks like this ie. one that cares about observers 1 million light years away just as much as it cares about observers here on Earth, but then stops caring if they happen to be 1 trillion light years away...
So again I think this looks rather like assuming the right answer, and then hacking around with ADT until it gives the answer you were looking for.