I don’t think we’re on the same page. I imagine myself in a different situation in which there is a tails only coin.
How is it different? If you get zapped to Omega world, then you are in some deterministic universe, but you don’t know which one exactly. You could be in a universe where Omega was going to flip tails (and some other things are true which you don’t know about), or one where Omega was going to flip heads (and some other things are true which you don’t know about), and you are in complete ignorance as to which set of universes you now find yourself in. Then either Omega will appear and tell you that you’re in a “heads” universe, and pay you nothing, or appear and tell you that you’re in a “tails” universe, in which case you will discover that you don’t want to pay Omega $100. As would I.
Have you made the assumption that handing over the $100 proves that you have made a precommitment?
It proves that either:
a) you are literally incapable of doing otherwise
b) you genuinely get more benefit/utility from handing the $100 over than from keeping it, where “benefit” is a property of your brain that you rationally act to maximize.
c) your actions are irrational, in the sense that you could have taken another action with higher utility.
When I refer to “you”, I mean “whoever you happen to be at the moment Omega appears^W^W you make your decision”, not “you as you would be if pushed forward through time to that moment”.
How is it different? If you get zapped to Omega world, then you are in some deterministic universe, but you don’t know which one exactly. You could be in a universe where Omega was going to flip tails (and some other things are true which you don’t know about), or one where Omega was going to flip heads (and some other things are true which you don’t know about), and you are in complete ignorance as to which set of universes you now find yourself in. Then either Omega will appear and tell you that you’re in a “heads” universe, and pay you nothing, or appear and tell you that you’re in a “tails” universe, in which case you will discover that you don’t want to pay Omega $100. As would I.
It proves that either: a) you are literally incapable of doing otherwise b) you genuinely get more benefit/utility from handing the $100 over than from keeping it, where “benefit” is a property of your brain that you rationally act to maximize. c) your actions are irrational, in the sense that you could have taken another action with higher utility.
When I refer to “you”, I mean “whoever you happen to be at the moment Omega appears^W^W you make your decision”, not “you as you would be if pushed forward through time to that moment”.