Justin Li

# Pascal's Wager, Part 2

2010-05-04

I have written about Pascal's Wager before, but I never finished that post. A few days ago I came across a video, which finally closed the case on that argument for me.

The inspiration is this, which I found on Reddit. Most of the video is junk and doesn't hold up to my standards of reason. Something at the end caught my attention though, and I came up with the following argument.

Recall that the problem with Pascal's wager is that, unlike most arguments about God, it's a completely rational. It frames the problem in turns of expected utilities, which is the standard practice in decision theory. The following payoff matrix summarizes the wager:

God Exists God Doesn't Exist
Believe in God +Infinity 0
Don't Believe in God -Infinity 0

Richard Dawkin's argument, that believing in God has a cost while living, doesn't hold up, as any cost incurred while alive is only finite, and does not offset the infinite payoff of being in heaven.

Pascal's wager is that simple. The video over-complicates and sets up several straw men (eg. Pascal not knowing what God is but then contradicting himself) and ad hominem attacks (eg. Pascal's bias towards Christianity). While the claim that Pascal ignores other gods is true, his wager still works - as long as gods reward belief, the expected utility is still to believe in god(s). The existence of non-god systems (frog's dream, video game, etc), doesn't matter, as they don't offer any utility. The gem of the video is in a 3 second frame: for every unknowable idea that rewards a particular behavior, another unknowable idea will punish that very same behavior.

Here's my new argument. Pascal's wager depends on supposing a Christian god, with the payoff matrix above. Since, however, the existence of the Christian god is unknown, it is equally valid to posit a different god (let's call Him AntiPascal), with different payoffs. In particular, let's imagine a god that will send people to heaven only if they don't believe in any god, and will send people to hell if they do. What does the payoff matrix look like?

God Exists God Doesn't Exist
Believe in God(s) -Infinity 0
Don't Believe in God(s) +Infinity 0

That's right - everything looks almost exactly the same, except the signs on those infinities switched. By this payoff matrix, people should not believe in gods at all.

So which payoff matrix is right? We don't know. To properly calculate the expected utility of believing in god(s), we need to know the probability of each payoff matrix itself - that is, the probability that the Christian god is real (and has the payoff matrix specified), and the probability that the AntiPascal god exists. Both of these probabilities, it turns out, is unknowable - and therefore the expected utility of believing or not believe in god cannot be compared.

Given the odds, Pascal's wager is not one you want to bet on - there's simply no telling whether you win or lose. While this is no argument against the belief in god, it is no longer the purely rational argument for it either.

The funny thing is, although this argument is new to me, the reasoning behind it is not. As Richard Dawkins himself has said several times, most theists are in fact atheists to all other religions. Real atheists just go one further.