This experimental outcome will not produce a disagreement between Alice and Bob. As long as they are following the same anthropic logic.
When saying Bob’s chance of survival is 100% according to MWI, the statement is made from a god’s eye view discussing all post-experiment worlds: Bob will for sure survive: in one/some of the branches.
By the same logic, from the same god’s eye view, we can say, Alice will meet Bob for sure: in one/some of the branches, if the MWI is correct.
By saying Alice shall see Bob with a 0.1% chance no matter if MWI is correct, you are talking about the specific Alice’s first-person perspective, which is a self-locating probability according to MWI. As in “what is the probability I am the Alice who’s in the branch where Bob survives?”.
By taking the specific subject’s perspective, Bob’s chance of survival is also 0.1% according to MWI. As in “what is the probability that I am actually in the branches where Bob survives?”
As long as their reasonings are held at the same level, their answers would be the same.
The real kicker is whether or not they should actually increase their confidence in MWI after the experiment ends (especially in the case where Bob survives). The popular anthropic camps such as SIA seem to say yes. But that would mean any quantum event, no matter the outcome would be evidence favouring MWI. So an armchair philosopher could say with categorical confidence that MWI is correct. (This is essentially the same problem as Nick Bostrom’s Presumptuous Philosopher but in the quantum worlds) So SIA supporters and Thirders have been trying to argue their positions do not necessarily lead to such an update (which they called the naive confirmation of the MWI). Whether or not that defence is successful is up for debate. For more information, I recommend the papers by Darren Bradley and Alastar Wilson.
On the other hand, if you think finding oneself exist is a logical truth, thus has 100% probability, then it is possible to produce disagreement against Aumann’s Agreement Theorem. And the disagreement is valid and can be logically explained. I have discussed it here. I think this is the correct anthropic reasoning. However, this idea does not recognize self-locating probability thus fundamentally incompatible with the MWI. Therefore if Alice and Bob both favour this type of anthropic reasoning, they would still have the same confidence in the validity of MWI, 0%.
This experimental outcome will not produce a disagreement between Alice and Bob. As long as they are following the same anthropic logic.
When saying Bob’s chance of survival is 100% according to MWI, the statement is made from a god’s eye view discussing all post-experiment worlds: Bob will for sure survive: in one/some of the branches.
By the same logic, from the same god’s eye view, we can say, Alice will meet Bob for sure: in one/some of the branches, if the MWI is correct.
By saying Alice shall see Bob with a 0.1% chance no matter if MWI is correct, you are talking about the specific Alice’s first-person perspective, which is a self-locating probability according to MWI. As in “what is the probability I am the Alice who’s in the branch where Bob survives?”.
By taking the specific subject’s perspective, Bob’s chance of survival is also 0.1% according to MWI. As in “what is the probability that I am actually in the branches where Bob survives?”
As long as their reasonings are held at the same level, their answers would be the same.
The real kicker is whether or not they should actually increase their confidence in MWI after the experiment ends (especially in the case where Bob survives). The popular anthropic camps such as SIA seem to say yes. But that would mean any quantum event, no matter the outcome would be evidence favouring MWI. So an armchair philosopher could say with categorical confidence that MWI is correct. (This is essentially the same problem as Nick Bostrom’s Presumptuous Philosopher but in the quantum worlds) So SIA supporters and Thirders have been trying to argue their positions do not necessarily lead to such an update (which they called the naive confirmation of the MWI). Whether or not that defence is successful is up for debate. For more information, I recommend the papers by Darren Bradley and Alastar Wilson.
On the other hand, if you think finding oneself exist is a logical truth, thus has 100% probability, then it is possible to produce disagreement against Aumann’s Agreement Theorem. And the disagreement is valid and can be logically explained. I have discussed it here. I think this is the correct anthropic reasoning. However, this idea does not recognize self-locating probability thus fundamentally incompatible with the MWI. Therefore if Alice and Bob both favour this type of anthropic reasoning, they would still have the same confidence in the validity of MWI, 0%.