Why You Should Bet on God
4. Challenging the Decision Matrix
The argument for BG2 relies on a number of assumptions I made about how to fill in the decision matrix (Matrix 3.0): the range of possible options and outcomes, the likelihood of the different outcomes, and the relative goodness or badness of the different eventualities. Thus, one way of challenging BG2 is to insist that, in one way or another, I’ve constructed or filled in the decision matrix incorrectly. In this section, we’ll consider a variety of different challenges of this kind.
But before turning to that, let me quickly dispense with a different line of objection, which some readers may find tempting.
People sometimes object that the argument rests on some sort of conceptual error simply because it invokes the notion of infinity.
They say that it doesn’t make any sense to talk about infinity, or to compare infinite quantities with finite quantities, or something to that effect. But surely that’s not right. Suppose you’re choosing between two offers for free movie tickets. One gives you free entry to twenty movies. The other gives you limitless free entry: no matter how many times you go for free, you can always go for free
again. Do you throw your hands up and say “How could I possibly decide?? It makes no sense to talk about limitless tickets!”
No, you accept the second offer. And it makes perfect sense why you would: because the second offer, despite involving an infinite quantity, gives you more of a good thing than the first.
4.1 Wrong Probabilities
One might complain that I’ve grossly overestimated the probability that God exists, by assuming that it’s a 50/50 chance that he exists. Perhaps you think it’s extremely unlikely that God exists. Surely, though, you’ll admit that it’s at least possible that God exists. If you die and are ushered into God’s presence, you’ll be surprised, but not in the way that you’d be surprised if you were ushered into the presence of something you think is genuinely impossible, like a round square.
So, let’s say it’s a 1% chance that God exists (though the response I’m about to give will work even if you think it’s a .00000001% chance). In that case, we need to update a couple of the boxes in the original decision matrix:
Matrix 4.1
God exists
1%
God doesn’t exist 99%
Expected Utility
Believe in God ∞ 2 ∞
Don’t believe in God 1 3 2.98
Changing the probabilities required us to recalculate the expected utility of not believing in God. It shot up almost a whole point!
But the expected utility of believing in God doesn’t change at all.
Why is that? Let’s crunch the numbers. What’s .01 x ∞? In other words, what do you get when you have infinitely many things, and you take away 99 out of every 100 of them? Answer: ∞. Now add 1.98 (= .99 x 2) to that, and you get ∞. The expected utility of believing in God doesn’t change and is still greater than the expected utility of not believing in God. Thus, so long as there is some chance that God exists, however small it may be, the argument for BG2 still works.
4.2 Belief Isn’t Enough
You might object that believing in God isn’t all by itself enough to get into heaven. You might think that you also have to meet some further conditions, for instance that you led a good, moral life and followed God’s commandments. I might ask you how you know that, but then again you might ask me how I know that badly- behaved believers go to heaven. (Touché.) So, let me just grant the point for the sake of argument: only well-behaved believers get into heaven. What that means is that the original decision matrix is inadequate, since it runs together two importantly different options: being a well-behaved believer and being a badly- behaved believer.
The fix is to expand our matrix so that each of these options has a row of its own.
Matrix 4.2
God exists
50%
God doesn’t exist
50%
Expected Utility
Believe in God and be good ∞ 3 ∞
Believe in God and be bad 2 4 3
Don’t believe in God 1 5 3
The new row introduces new eventualities, which means we have to redo the rankings. I gave a 1 to the eventuality in which you don’t believe in God and yet he does exist, and a 2 to being a badly-behaved believer, on the assumption that God will punish you for that too but will be a little more lenient since you at least believed in him. I’ve scored being an atheist in a Godless world (5) higher than being a badly-behaved believer in a Godless world (4), and I’ve ranked both ahead of the life of a well-behaved believer in a Godless world (3). Finally, the eventuality in which you’re a well-behaved believer and God does exist gets ∞, since this is what will get you into heaven, and that’s infinitely better than any of the other eventualities.
So, what does this all mean? What it means is that—assuming that you have to be a well-behaved believer to get into heaven—
being a well-behaved believer has greater expected utility than either being a badly-behaved believer or not believing in God at
all. It’s still true, then, that the option with the greatest expected utility requires you to believe in God. So, we have not yet found a reason to reject BG2.
It may be that I haven’t gotten all the scores exactly right.
Maybe I’m wrong, and God gives exactly the same punishment to both nonbelievers and badly-behaved believers. In that case, you could make it a tie and change the 2 in the first column to a 1. Or maybe I’m wrong that the life of an atheist in a Godless world is more rewarding than the life of a believer in a Godless world.
Fine, we can lower the score for “God does not exist” in the bottom row. It doesn’t matter. The argument still goes through, since the expected utility of being a nonbeliever or a badly- behaved believer still comes out to be some finite number, whereas the expected utility of being a well-behaved believer will be infinite.
4.3 Heaven May Be Finite
The reasoning behind BG2 takes for granted that God rewards believers with something that’s infinitely valuable, for instance an eternal afterlife filled with an infinite amount of pleasure. But I haven’t offered any evidence or argument for that. For all we know, God rewards believers only with some finite amount of pleasure—maybe ten years in heaven. And one might object that this imperils the argument: if we can’t be sure that believers stand to receive something of infinite value, then there’s no guarantee that the expected utility of believing will be infinite, and thus no guarantee that it will come out greater than the expected utility of disbelief.
But that’s the wrong way to look at it. Let’s just acknowledge that we can’t be sure whether God is generous and rewards believers with something of infinite value or whether God is stingy and rewards believers with something of finite value. That means that Matrix 3.0 is oversimplified, and that we need to expand the decision matrix to include three columns: one for the possibility of a generous God who offers infinite rewards, one for the possibility of a stingy God who offers only finite rewards, and one for the possibility that there’s no God.
Matrix 4.3
Generous God exists
25%
Stingy God exists
25%
No God 50%
Expected Utility
Believe in God ∞ 1,000,000 2 ∞
Don’t believe 1 1 3 2
I’ve valued the eventuality in which you’re a believer and God turns out to be stingy at 1,000,000 to reflect the idea that it’s still many orders of magnitude better than the next best eventuality, in which you’re a nonbeliever and God doesn’t exist. Again, though, the exact values don’t really matter, nor do the exact probabilities. All that matters is the ∞ on the top left, since that’s going to ensure an infinite expected utility for believing in God.
So, even if we can’t be sure that God rewards anyone with an infinitely valuable afterlife, we still get the result that we ought to believe in God.
4.4 Many Gods to Choose From
Let’s consider one last objection to BG2. You might worry that getting into heaven isn’t simply a matter of believing in God.
You’ve got to believe in the right God. If the true God is the Christian God and you believe in Zeus (or vice versa), you’re going to hell. And the decision matrix can’t tell you which God is the right God to believe in.
I think that’s right. But it’s no objection to BG2. Once again, what this shows us is that Matrix 3.0 was oversimplified. We need additional rows reflecting the different gods we can choose to believe in, and additional columns reflecting the different gods that might turn out to exist. So, let’s rectify that:
Matrix 4.4
Christian God exists
25%
Zeus exists 25%
No God 50%
Expected Utility Believe in Christian
God
∞ 1 3 ∞
Believe in Zeus 1 ∞ 3 ∞
Don’t believe 2 2 4 3
Once again, I’ve done my best to assign probabilities and score the non-infinite eventualities, and once again it doesn’t much matter whether I’ve gotten the rankings of the non-infinite eventualities exactly right. And we can, if you like, expand the matrix to include more and more possible gods, but that shouldn’t affect the argument either.
What we get now is a tie for greatest expected utility. This means that the objection under consideration is right as far as it goes: we aren’t told whether to believe in the Christian God or whether to believe in Zeus. But notice that believing in some God or other continues to have greater expected utility than not believing at all. So, the decision matrix still tells us that the greatest expected utility is attained by (and only by) believing that there is a God. So, there is no successful challenge to BG2 here.