Given the stakes, it seems to me the most rational thing to do here is to try to convince the other person that you should both cooperate, and then defect.
The difference between this dilemma and Newcomb is that Newcomb's Omega predicts perfectly which box you'll take, whereas the Creationist cannot predict whether you'll defect or not.
The only way you can lose is if you screw up so badly at trying to convincing him to cooperate (i.e. you're a terrible liar or bad at communicating in general and confuse him), that instead he's convinced he should defect now. So the biggest factor when deciding whether to cooperate or defect should be your ability to convince.
If you don't think you could convince him to cooperate then you still defect because he will, and if you cooperate 0 people are saved. Cooperating generates either 0 or 2 billion saved, defecting generates either 1 or 3 billion saved. Defect is clearly the better option.
If you were going to play 100 rounds for 10 or 20 million lives each, cooperate by all means. But in a single round PD defect is the winning choice (assuming the payout is all that matters to you; if your utility function cares about the other persons feelings towards you after the choice, cooperate can become the highest utility)
I spoke yesterday of the epistemic prisoner's dilemma, and JGWeissman wrote:
To which I said:
And lo, JGWeissman saved me a lot of writing when he replied thus:
I make one small modification. You and your creationist friend are actually not that concerned about money, being distracted by the massive meteor about to strike the earth from an unknown direction. Fortunately, Omega is promising to protect limited portions of the globe, based on your decisions (I think you've all seen enough PDs that I can leave the numbers as an excercise).
It is this then which I call the true epistemic prisoner's dilemma. If I tell you a story about two doctors, even if I tell you to put yourself in the shoes of one, and not the other, it is easy for you to take yourself outside them, see the symmetry and say "the doctors should cooperate". I hope I have now broken some of that emotional symmetry.
As Omega lead the creationist to the other room, you would (I know I certainly would) make a convulsive effort to convince him of the truth of evolution. Despite every pointless, futile argument you've ever had in an IRC room or a YouTube thread, you would struggle desperately, calling out every half-remembered fragment of Dawkins or Sagan you could muster, in hope that just before the door shut, the creationist would hold it open and say "You're right, I was wrong. You defect, I'll cooperate -- let's save the world together."
But of course, you would fail. And the door would shut, and you would grit your teeth, and curse 2000 years of screamingly bad epistemic hygiene, and weep bitterly for the people who might die in a few hours because of your counterpart's ignorance. And then -- I hope -- you would cooperate.