Let Egalitarian Universalism (EU) be the doctrine that God exists and gives everyone infinite happiness, and that the quantity fo 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 (i.e., Nozick’s original formulation).
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)
where r is the infinite positive reward that EU guarantees everybody, and a and b are the finite goods or bads of this life available if atheism is true. If U1 is greater than U2, then I should believe.
We’ll need to use our favorite form of non-standard analysis for handling infinities. Observe that
since a God would be moderately to want people to believe in him, and hence it is somewhat more likely that there would be theistic belief if God existed than if atheism were true (and I assumed that atheism and EU are the only options). But then by Bayes’ Theorem it follows from (3) that:
Let c=P(EU|believe)-P(EU|~believe). By (4), c is a positive number. Then:
- U1âU2=rc + something finite.
Since r is infinite and positive, it follows that U1âU2>0, and hence U1>U2, so I should believe in EU.
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.)