Pascal’s Wager inverted: all atheists go to heaven?
Pascal’s Wager is one of the most famous arguments for belief in God. Pascal’s Wager does not offer proof or evidence for God. Instead, it is an exercise in probability that suggests belief in God is a better than non-belief.
But it turns out there are many flaws with Pascal’s Wager. There is a good summary of these in the Wikipedia entry for Pascal’s Wager.
This article intends to highlight another flaw (as a teaching device). It appears Pascal specified the game too broadly. When logically extended, Pascal’s Wager can be flipped on its head. The exact reason that theism has an infinite payout would also imply that many beliefs–including atheism–have an infinite payout.
First, let’s recap Pascal’s Wager and then go into the new interpretation which depends on analyzing beliefs and the infinite payout.
(The point here is not to support any particular belief, but rather to explore and teach game theory with the fun example of Pascal’s Wager. If this sort of discussion offends you, consider other reading).
Pascal’s Wager
There are many ways to state Pascal’s Wager. The argument usually goes like this:
“If you believe, and God exists, then you will be rewarded with an infinite payout. If you disbelieve, and God exists, then you lose out on the reward. If God does not exist, then either way nothing happens.”
The wager can be translated into the following decision table:
| God exists | God does not exist | |
| Belief | +infinity (gain all) | nothing |
| Disbelief | nothing | nothing |
The idea here is to consider the consequences of possible decisions. One can either choose to believe or not believe. The believer has everything to gain and nothing to lose. Therefore, if one has to wager, it would be better to act as though God existed and believe.
It is not so obvious why this logic is wrong. But it is, and here is one of the flaws that turns the wager on its head.
–The flaw: beliefs are probabilities, not absolutes–
Pascal’s Wager creates a false dichotomy between believing and not believing. In fact, beliefs are rarely absolutes. It is telling that beliefs, as defined in game theory, are probability distributions over states of the world or other players’ strategies.
It might seem strange to think about beliefs as probabilities, but it is something that most of us already do. When we say things like “I believe it will rain,” or “I believe he is innocent,” we are not speaking about absolutes. We are summarizing probability distributions over various states of the world. And as a rule of thumb, when we are uncertain, we rarely assign a zero probability to an event. We keep our beliefs open for updating.
The same logic can be extended to belief in God. An atheist who says, “I don’t believe in God,” is usually not saying God has a zero probability. He is summarizing his probability distribution over about various theories of the world, and he happens to think the probability for God is low. But the probability for God is not zero-typically an atheist does not summarily eliminate options but rather puts them at low probability.
Now consider Pascal’s Wager again. Realistic beliefs are not absolutes between the choices of believe or not believe. They are probability distributions, like “99 percent believe and 1 percent not” or “1 percent believe and 99 percent not.” I would argue that even faith is not 100 percent because theists typically question their faith from time to time.
And here is the kicker. The infinite payout of God rewarding believers will yield an infinite payout to almost all beliefs. That is, any non-zero belief in God will have an infinite payout. Therefore, an atheist who give a small but non-zero chance to God’s existence would also receive an infinite payout. This is an absurd conclusion, to be sure, but it is a consequence of the gambit Pascal set up.
This is one illustration of how an infinite payout is problematic. Although most theists would think a stronger belief in God should be rewarded, Pascal’s Wager does not specify this contingency. In the end, this assumption makes the wager lose much of its power.
In conclusion
Pascal’s Wager is an interesting idea, but this article illustrates some of its flaws. The two main problems are its assumption of absolute beliefs and its assignment of an infinite payout. These flaws ultimately turn the wager on its head to yield the opposite conclusion. This is yet another reason to reject Pascal’s Wager.
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