Do you see that assuming Omega worked the way I described, then the number and distribution of boxes containing $1M is exactly the same in the two multiverses, therefore the second multiverse is better?

Yes, I think I understand that now. But in your version the two-boxing gene practically does not cause the $1M to be in box B, because Omega mostly looks at random other genes. Would that even be a Newcomblike problem?

I think this is what makes your version of GNP different from MNP, and why we have different intuitions about the two cases. If there is someone or something who looked the most common gene correlated with two-boxing (because it was the most common gene correlated with two-boxing, rather than due to a coincidence), then by changing whether you two-box, you can change whether other UDT agents two-box, and hence which gene is the most common gene correlated with two-boxing, and hence which gene Omega looked at, and hence who gets $1M in box B.

In EY's chewing gum MNP, it seems like CGTA causes both the throat abscess and influences people to chew gum. (See p.67 of the TDT paper ) (It gets much more complicated, if evolution has only produced a correlation between CGTA and another chewing gum gene.) The CGTA gene is always read, copied into RNA etc., ultimately leading to throat abscesses. (The rest of the DNA is used, too, but only determines the size of your nose etc.) In the GNP, the two-boxing gene is always read by Omega and translated into a number of dollars under box B. (Omega can look at the rest of the DNA, too, but does not care.) I don't get the difference, yet, unfortunately.

In MNP, there is no corresponding process searching for genes correlated with gum chewing, so you can't try to influence that process by choosing to not chew gum.

I don't understand UDT, yet, but it seems to me that in the chewing gum MNP, you could not chew gum, thereby changing whether other UDT agents chew gum, and hence whether UDT agents' genes contain CGTA. Unless you know that CGTA has no impact on how you ultimately resolve this problem, which is not stated in the problem description and which would make EDT also chew gum.