I think pre-commitment is irrelevant if you assume Omega can actually read your decision algorithm and predict it deterministically. You want to be the type of person that would give Omega $1k if the fair coin toss didn’t go your way; if you’re not that type of person once the coin has been tossed, it’s too late; and not being that type of person is only a good thing if it wasn’t actually a fair coin.
Please provide an example or a link to a somewhat realistic situation where this approach (distinguishing between actual and counterfactual precommitment) loses money.
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.
I think pre-commitment is irrelevant if you assume Omega can actually read your decision algorithm and predict it deterministically. You want to be the type of person that would give Omega $1k if the fair coin toss didn’t go your way; if you’re not that type of person once the coin has been tossed, it’s too late; and not being that type of person is only a good thing if it wasn’t actually a fair coin.
What if I’m the type of person who does not honor counterfactual precommitment, only actual one?
Then expect to lose :-)
Lose what?
Lose money, at least in expectation, if ever these issues come up!
Please provide an example or a link to a somewhat realistic situation where this approach (distinguishing between actual and counterfactual precommitment) loses money.
Oh, you are being difficult, aren’t you! :-P
Well, there is this interesting claim:
http://lesswrong.com/lw/1zw/newcombs_problem_happened_to_me/
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.