It’s an interesting account indeed, but hardly relevant to the point in hand, which is “you are guaranteed to lose this time if you precommit counterfactually, but should do it anyway”.
You’re guaranteed to lose if you precommit to giving Omega $1k, if this scenario ever comes up, yes.
However, a precommitment to giving Omega $1k if you lose, and gaining $1M if you win, has positive expected value, and it necessarily entails the precommitment to giving Omega $1k if you lose the coin toss. If you just precommit to giving Omega $1k (and also to refusing the $1M if he ever offers it), then yeah; that’s pretty dumb.
It’s an interesting account indeed, but hardly relevant to the point in hand, which is “you are guaranteed to lose this time if you precommit counterfactually, but should do it anyway”.
You’re guaranteed to lose if you precommit to giving Omega $1k, if this scenario ever comes up, yes.
However, a precommitment to giving Omega $1k if you lose, and gaining $1M if you win, has positive expected value, and it necessarily entails the precommitment to giving Omega $1k if you lose the coin toss. If you just precommit to giving Omega $1k (and also to refusing the $1M if he ever offers it), then yeah; that’s pretty dumb.
Well, I’m more in favour of “you should now precommit to everything of this type that could happen in the future”.
I precommit to precommit on all future setups with expected positive payoff except for unannounced setups where I am told that I have already lost.
What about unannounced setups where you are told that you have already lost—but where you would have had a chance of winning big, had you said yes?
Again, a realistic example of where such a situation occurs would help me understand your point.