Interestingly enough (to me, at least), I would live a life of sin, and yet one-box. Now I'm trying to come up with justifications for this gut reaction.
The best I can come up with so far is that I can see God having a "causal" relationship towards me. That is, I am exactly what I am because God made me that way. The Alien, however, isn't causal, merely observational. It didn't cause me to choose whether to one-box or two-box, it simply observes me and determines which I would do.
The reason I would sin is because it seems like the way the hypothetical situation is set up, we're assuming predestination, which seems to make me really not worry to hard about putting effort towards anything. If I was supposed to "fight" predestination, then things will turn out so that I do fight predestination. But until that happens, why not simply take the path of least resistance (especially since in a predestined universe, you cannot offer up any resistance at all) and enjoy whatever pleasures you wish? Language is failing me here, because I'm speaking as if I can actually make decisions or control my actions, but obviously I can't.
Also, it might be important to clarify that I would choose "sin" only in this hypothetical world where I somehow know with certainty that the universe was predestined. In reality, I'd be unsure about whether or not the universe was predestined, and thus wouldn't automatically choose "sin".
Contrast this with the Newcomb problem, where there is a possibility that I have "free will" or some sort of control over my actions. In this scenario, I want to be the type of agent whom the alien will reward, and I know the alien rewards one boxers, and so I choose to be a one boxer.
I can sense all sort of inconsistencies in my reasoning, and I can sense ways of making these inconsistencies more salient E.g. the alien is able to predict whether I will one-box or two-box before human life has evolved, and thus plants the two boxes somewhere on Earth during the dinosaur age in a location it knows no one will discover except for me (or perhaps plants it on Neptune, but sets up some chain of events so that the boxes will arrive to me by the time I'm in my mid-20s). Since the alien infallibly knew whether I would one-box or two-box, can I really in any sense say that my universe is not predestined?
Clearly there is confusion in my mind that I have to meditate upon and clear up.
Followup to: Simultaneously Right and Wrong
Related to: Augustine's Paradox of Optimal Repentance
"When they inquire into predestination, they are penetrating the sacred precincts of divine wisdom. If anyone with carefree assurance breaks into this place, he will not succeed in satisfying his curiosity and he will enter a labyrinth from which he can find no exit."
-- John Calvin
John Calvin preached the doctrine of predestination: that God irreversibly decreed each man's eternal fate at the moment of Creation. Calvinists separate mankind into two groups: the elect, whom God predestined for Heaven, and the reprobate, whom God predestined for eternal punishment in Hell.
If you had the bad luck to be born a sinner, there is nothing you can do about it. You are too corrupted by original sin to even have the slightest urge to seek out the true faith. Conversely, if you were born one of the elect, you've got it pretty good; no matter what your actions on Earth, it is impossible for God to revoke your birthright to eternal bliss.
However, it is believed that the elect always live pious, virtuous lives full of faith and hard work. Also, the reprobate always commit heinous sins like greed and sloth and commenting on anti-theist blogs. This isn't what causes God to damn them. It's just what happens to them after they've been damned: their soul has no connection with God and so it tends in the opposite direction.
Consider two Calvinists, Aaron and Zachary, both interested only in maximizing his own happiness. Aaron thinks to himself "Whether or not I go to Heaven has already been decided, regardless of my actions on Earth. Therefore, I might as well try to have as much fun as possible, knowing it won't effect the afterlife either way." He spends his days in sex, debauchery, and anti-theist blog comments.
Zachary sees Aaron and thinks "That sinful man is thus proven one of the reprobate, and damned to Hell. I will avoid his fate by living a pious life." Zachary becomes a great minister, famous for his virtue, and when he dies his entire congregation concludes he must have been one of the elect.
Before the cut: If you were a Calvinist, which path would you take?
Amos Tversky, Stanford psychology professor by day, bias-fighting superhero by night, thinks you should live a life of sin. He bases his analysis of the issue on the famous maxim that correlation is not causation. Your virtue during life is correlated to your eternal reward, but only because they're both correlated to a hidden third variable, your status as one of the elect, which causes both.
Just to make that more concrete: people who own more cars live longer. Why? Rich people buy more cars, and rich people have higher life expectancies. Both cars and long life are caused by a hidden third variable, wealth. Trying to increase your chances of getting into Heaven by being virtuous is as futile as trying to increase your life expectancy by buying another car.
Some people would stop there, but not Amos Tversky, bias-fighting superhero. He and George Quattrone conducted a study that both illuminated a flaw in human reasoning about causation and demonstrated yet another way people can be simultaneously right and wrong.
Subjects came in thinking it was a study on cardiovascular health. First, experimenters tested their pain tolerance by making them stick their hands in a bucket of freezing water until they couldn't bear it any longer. However long they kept it there was their baseline pain tolerance score.
Then experimenters described two supposed types of human heart: Type I hearts, which work poorly and are prone to heart attack and will kill you at a young age, and Type II hearts, which work well and will bless you with a long life. You can tell a Type I heart from a Type II heart because...and here the subjects split into two groups. Group A learned that people with Type II hearts, the good hearts, had higher pain tolerance after exercise. Group B learned that Type II hearts had lower pain tolerance after exercise.
Then the subjects exercised for a while and stuck their hands in the bucket of ice water again. Sure enough, the subjects who thought increased pain tolerance meant a healthier heart kept their hands in longer. And then when the researchers went and asked them, they said they must have a Type II heart because the ice water test went so well!
The subjects seem to have believed on some level that keeping their hand in the water longer could give them a different kind of heart. Dr. Tversky declared that people have a cognitive blind spot to "hidden variable" causation, and this explains the Calvinists who made such an effort to live virtuously.
But this study is also interesting as an example of self-deception. One level of the mind made the (irrational) choice to leave the hand in the ice water longer. Another level of the mind that wasn't consciously aware of this choice interpreted it as evidence for the Type II heart. There are two cognitive flaws here: the subject's choice to try harder on the ice water test, and his lack of realization that he'd done so.
I don't know of any literature explicitly connecting this study to self-handicapping, but the surface similarities are striking. In both, a person takes an action intended to protect his self-image that will work if and only if he doesn't realize this intent. In both, the action is apparently successful, self-image is protected, and the conscious mind remains unaware of the true motives.
Despite all this, and with all due respect to Dr. Tversky I think he might be wrong about the whole predestination issue. If I were a Calvinist, I'd live a life of sin if and only if I would two-box on Newcomb's Problem.