Here’s a model of Sleeping Beauty under MWI. The universe has two apartments with multiple rooms. Each apartment has a room containing a copy of you. You have 50:50 beliefs about which apartment you’re in. One minute from now, a new copy of you will be created in the first apartment (in another identical room). At that moment, despite getting no new information, should you change your belief about which apartment you’re in? Obviously yes.
So it seems like your “conservation of expected evidence” argument has a mistake somewhere, and SIA is actually fine.
I’m just getting started with SIA, SSA, FNC and the like, so probably I’m missing some core understanding, but: A minute from now you do gain new information: One minute has passed.
should you change your belief about which apartment you’re in? Obviously yes.
Do you want the majority of your copies to be correct as to what branch of the multiverse they are in? Go SIA. Do you want your copies to be correct in the majority of branches of the multiverse? SSA, then.
This experiment doesn’t have branches though, it has apartments and rooms. You could care about being right in the majority of apartments, or you could care about being right in the majority of rooms, but these are arbitrary divisions of space and give conflicting answers. Or you could care about majority of copies being right, which is objective and doesn’t have a conflicting counterpart. You can reproduce it by creating three identical copies and then distributing them into rooms. So SIA has an objective basis and SSA doesn’t.
The next question is whether apartments are a good analogy for MWI, but according to what we know so far, that seems likely. Especially if it turns out that quantum and cosmological multiverses are the same.
Does MWI imply SIA?
Here’s a model of Sleeping Beauty under MWI. The universe has two apartments with multiple rooms. Each apartment has a room containing a copy of you. You have 50:50 beliefs about which apartment you’re in. One minute from now, a new copy of you will be created in the first apartment (in another identical room). At that moment, despite getting no new information, should you change your belief about which apartment you’re in? Obviously yes.
So it seems like your “conservation of expected evidence” argument has a mistake somewhere, and SIA is actually fine.
I’m just getting started with SIA, SSA, FNC and the like, so probably I’m missing some core understanding, but: A minute from now you do gain new information: One minute has passed.
Was that unexpected?
Do you want the majority of your copies to be correct as to what branch of the multiverse they are in? Go SIA. Do you want your copies to be correct in the majority of branches of the multiverse? SSA, then.
This experiment doesn’t have branches though, it has apartments and rooms. You could care about being right in the majority of apartments, or you could care about being right in the majority of rooms, but these are arbitrary divisions of space and give conflicting answers. Or you could care about majority of copies being right, which is objective and doesn’t have a conflicting counterpart. You can reproduce it by creating three identical copies and then distributing them into rooms. So SIA has an objective basis and SSA doesn’t.
The next question is whether apartments are a good analogy for MWI, but according to what we know so far, that seems likely. Especially if it turns out that quantum and cosmological multiverses are the same.