Ah, bugger. I’ve lost my link to Transparent Newcomb (TN).
From what I recall, Omega doesn’t let you play the game if you would one-box on normal Newcomb but two-box on TN. As a result, having the strategy ‘I will one-box on normal Newcomb but two-box on TN’ will probably result in you getting no money because when Omega psychoanalyzes you, he’ll almost always see this. So you lose, because you’re not yet past the filter.
In this problem, you were filtered out prior to birth by a Prometheus who only chose embryos that he believed would one-box. The line ‘I should one-box or I won’t get to exist’ doesn’t work because embryos can’t think. At the time at which you can first consciously consider this problem, you will be past the filter, and so are free to choose the most effective solution regardless of Prometheus’s preferences. So you two-box and win, ’cause you already exist.
The problem changes, of course, if there is any way in which Prometheus could punish you for two-boxing, causing you to lose >100$ in utility.
Edit: Changed a couple of details to properly refer to TN when Omega has a slight possibility of being wrong.
Wrong rules. Correct rules are as follows (named “Newcomb’s Problem with a Dual Simulation” in Drescher’s book):
Omega fills the large transparent box with $1,000,000 iff it predicts that you, when faced with (1) full box, and (2) empty box, would in both cases one-box. If it predicts that there’s a nontrivial chance that you’d two-box in either case, it leaves the transparent box empty.
Ah, bugger. I’ve lost my link to Transparent Newcomb (TN).
From what I recall, Omega doesn’t let you play the game if you would one-box on normal Newcomb but two-box on TN. As a result, having the strategy ‘I will one-box on normal Newcomb but two-box on TN’ will probably result in you getting no money because when Omega psychoanalyzes you, he’ll almost always see this. So you lose, because you’re not yet past the filter.
In this problem, you were filtered out prior to birth by a Prometheus who only chose embryos that he believed would one-box. The line ‘I should one-box or I won’t get to exist’ doesn’t work because embryos can’t think. At the time at which you can first consciously consider this problem, you will be past the filter, and so are free to choose the most effective solution regardless of Prometheus’s preferences. So you two-box and win, ’cause you already exist.
The problem changes, of course, if there is any way in which Prometheus could punish you for two-boxing, causing you to lose >100$ in utility.
Edit: Changed a couple of details to properly refer to TN when Omega has a slight possibility of being wrong.
What if we modify transparent Newcomb to say the Omega chose whether to fill the box before you were born?
Maybe Prometheus could predict your decision by running a simulation of you and putting “you” in that situation.
Bongo linked to it in response to my question about it.
Wrong rules. Correct rules are as follows (named “Newcomb’s Problem with a Dual Simulation” in Drescher’s book):