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Is Pascal’s Wager an Appropriate Use of Game Theory?

One of the more famous uses of game theory to support one decision over another in everyday life is Pascal’s Wager. This is a decision that physicist Blaise Pascal made, in the mid-1600’s, determining that given the choice between believing in God and not, believing is the better option every time. This turns out to be a very polemical decision and has turned a lot of debate between those that agree with it, and those who tend to refute it. This post will seek to point out the most salient flaws in Pacal’s Gambit, and explain why this application of game theory is not modeled perfectly.

For those who are unfamiliar with the decision, it goes something like this. First off, the following crucial components must be understood. While there is no one that is able to prove either side of the argument (that God does or does not exist) for sure, only one of these options can be true while the other is false: God either exists or does not exist. Therefore, it stands to reason that everyone must make a decision regarding this- in other words- the wager is not optional. Everyone must make a definite explicit choice to believe in God or not. Now that the background of Pascal’s logic in his wager has been explored, let’s delve into the game theory aspect of his decision. Pascal determined that if you wager that there is a God, and you are correct, then you gain an infinite amount of benefit. This benefit can be from being able to live an eternal afterlife in heaven, or from being rewarded for believing in God one’s whole life. He also reasoned that if one was to believe in God, and God was to not exist, then there is nothing to lose out on.  The conclusion, as Pascal saw it, came from realizing that while what you risk is finite (living life believing in a false God), what you stand to gain if infinite, spending an eternity after death with that God in heaven.

Something that can be added on to the Wager (although it was not explicitly stated by Pascal) is that if you do not believe in God and you are incorrect (God exists), then you stand to suffer an infinite amount of loss (hell or punishment). Additionally, if you choose to disbelieve and you are correct, there is nothing to gain from this, as there is no afterlife waiting for atheists proven correct. Therefore, the final payoff matrix familiar to the class can be written as:

God Exists (E) God Does Not Exist (~E)
Believe (B)  +Infinity  0
Disbelieve (~B)  -Infinity  0

It can clearly be seen from this payoff matrix that believing in God (B) is a dominant strategy (although not strictly dominant, since the payoff if God does not exist for either option is the same for both choices B and ~B).

There are many obvious flaws with this theory. What if people do not follow a monotheistic Christian faith and they choose to believe in a different God and not the Christian God (The Christian God was the one Pascal used in his approach)? This payoff matrix would involve as many Gods as there are faiths, and would get quite messy. Also, what about those who follow Pascal’s Wager in a very strict sense- they believe in God just because they think that believing is better than not believing, and not because they are actually true to the faith? God should be able to sort out these untruthful followers, and therefore their benefit would not be heaven regardless of their “belief”. Also, simply believing in God, as Pascal puts it, does not grant you eternal benefit from heaven. According to the Christian faith, you need to be reverent and do the right thing in everyday life, and follow the religious codes. So the payoff of believing if there is a God is not necessarily heaven.

However, the primary argument that I will address in this post is the payoffs for ~E (God not existing) for either choice, B or ~B. Pascal decided that there is nothing to lose from believing and being incorrect, and that there is nothing to gain from not believing and being right. However, there are many costs to living a pious life, if it is all for nothing. Many devout followers of their faiths spend a lot of time and energy going to church, praying, attending rituals, etc. Many wars have been fought and people killed for their beliefs, as well as many people over time sacrificing themselves for their beliefs. Imagine if all this time and energy could have been put to use on activities that could improve our world. Additionally, many people cannot do some things that they enjoy in life because of their faith. Therefore, there is clearly a sizeable loss from being wrong in your belief, although it is not an infinite loss like hell is. Additionally, atheists who are correct do not suffer hell, but gained from not wasting the time and resources on the activities described above, and can live out their life in the way they wanted to (without having to live by God’s word). Therefore, there is an equal benefit to those disbelievers, should there be no God.  I suggest that the true payoff matrix should be seen as:

God Exists (E) God Does Not Exist (~E)
Believe (B)  +Infinity  -C
Disbelieve (~B)  -Infinity  +C

The variable ‘C’ in this payoff matrix is a finite number that weighs the costs and benefits described above. As can be seen from this new, more accurate, payoff matrix, there is no longer a dominant strategy to believe in God. Although the benefit of true believing is infinite, and the benefit from correctly disbelieving is only finite, there are still two Nash Equilibria from this payoff matrix. In this way, using the game theory analysis developed in class, Pascal’s Wager can be refuted and it could not be determined that believing in God is always a better option than not.’s_Wager




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November 2011