Oddly, this problem seems (to my philosopher/engineer mind) to have an exceedingly non-complex solution, and it depends not upon the chooser but upon Omega.
Here’s the payout schema assumed by the two-boxer, for reference:
1) Both boxes predicted, both boxes picked: +$1,000
2) Both boxes predicted, only B picked: $0
3) Only B predicted, both boxes picked: +$1,001,000
4) Only B predicted, only B picked: +$1,000,000
Omega, being an unknowable superintelligence, qualifies as a force of nature from our current level of human understanding. Since Omega’s ways are inscrutable, we can only evaluate Omega based upon what we know of him so far: he’s 100 for 100 on predicting the predilections of people. While I’d prefer to have a much larger success base before drawing inference, it seems that we can establish a defeasible Law of Omega: whatever decision Omega has predicted is virtually certain to be correct.
So while the two-boxer would hold that choosing both boxes would give them either $1,000 or $1,001,000, this is clearly IRRATIONAL: the (defeasible) Law of Omega outright eliminates outcomes 2 and 3 above, which means that (until such time as new data forces a revision of the Law of Omega) the two-boxer’s anticipated payoff of $1,001,000 DOES NOT EXIST. The only choice is between outcome 1 (two-boxer gets $1,000) and outcome 4 (one-boxer gets $1,000,000). At that point, option 4 is the dominant strategy… AND the rational thing to do.
Does that makes sense? Or am I placing unfounded faith in Omega?
If you look through the many subsequent discussions of this, you’ll see that indeed $1,001,000 is not in the outcome domain, but the classical CDT is unable to enumerate this domain correctly.
Oddly, this problem seems (to my philosopher/engineer mind) to have an exceedingly non-complex solution, and it depends not upon the chooser but upon Omega.
Here’s the payout schema assumed by the two-boxer, for reference: 1) Both boxes predicted, both boxes picked: +$1,000 2) Both boxes predicted, only B picked: $0 3) Only B predicted, both boxes picked: +$1,001,000 4) Only B predicted, only B picked: +$1,000,000
Omega, being an unknowable superintelligence, qualifies as a force of nature from our current level of human understanding. Since Omega’s ways are inscrutable, we can only evaluate Omega based upon what we know of him so far: he’s 100 for 100 on predicting the predilections of people. While I’d prefer to have a much larger success base before drawing inference, it seems that we can establish a defeasible Law of Omega: whatever decision Omega has predicted is virtually certain to be correct.
So while the two-boxer would hold that choosing both boxes would give them either $1,000 or $1,001,000, this is clearly IRRATIONAL: the (defeasible) Law of Omega outright eliminates outcomes 2 and 3 above, which means that (until such time as new data forces a revision of the Law of Omega) the two-boxer’s anticipated payoff of $1,001,000 DOES NOT EXIST. The only choice is between outcome 1 (two-boxer gets $1,000) and outcome 4 (one-boxer gets $1,000,000). At that point, option 4 is the dominant strategy… AND the rational thing to do.
Does that makes sense? Or am I placing unfounded faith in Omega?
If you look through the many subsequent discussions of this, you’ll see that indeed $1,001,000 is not in the outcome domain, but the classical CDT is unable to enumerate this domain correctly.