Let Egalitarian Universalism (EU) be the doctrine that God exists and gives everyone infinite happiness, and that the quantity of this happiness is the same for everyone. The traditional formulation of Pascal's Wager obviously does not work in the case of the God of EU. What is surprising, however, is that one can make Pascal's Wager work even given the God of EU if one thinks that Bayesian decision theory, and hence one-boxing, is the right way to go in the case of Newcomb's Paradox with a not quite perfect predictor.
Here is how the trick works. Suppose that the only two epistemically available options are EU and atheism, and I need to decide whether or not to believe in God. Given Bayesian decision theory, I should choose whether to believe based on the conditional expected utilities. I need to calculate:
- U1=rP(EU|believe) + aP(atheism|believe)
- U2=rP(EU|~believe) + bP(atheism|~believe)
We'll need to use our favorite form of non-standard analysis for handling infinities. Observe that
- U1−U2=rc + something finite.
The argument works on non-egalitarian universalism, too, as long as we don't think God gives an infinitely greater reward to those who don't believe in him.
However, universalism is false and one-boxing is mistaken.