Pascal's wager - an economic analysis

"There are little invisible elves who constantly build and maintain our universe from the stars to the crickets and they control everything that occurs. So, if you wake up at 4 a.m. every Tuesday and worship the elves, they will make things go your way; if not, you are assured less than good luck. You lose nothing from believing this except a good night's sleep on Tuesdays. However, if they are real, and you don't worship, your life is guaranteed to be worse off. Now I ask you, are you going to worship elves every Tuesday morning?" -- Thomas Anderson


Sometimes you can hear the argument from theists that it is better to follow their religion than being an atheist because if the atheist is right nothing happens, but if the theist is right he goes to heaven while the atheist goes to hell. This is called Pascal's wager after the French philosopher Blaise Pascal, who was the first to write about it. For several reasons the argument is not valid. One of them is that from a complete economical analysis you will have to prove many additional things. This is an account of why it is so, and what additional evidence has to be provided.

The analysis

(Moderated from a posting by Abner J. Mintz on alt.atheism)

If we divide Pascal's wager up without ignoring any options, we get four branches: christian beliefs being right (Probability, P1), christian beliefs being wrong but getting better reward than atheism (P2), christian beliefs being wrong and gettting same reward as atheism (P3), christian beliefs being wrong and getting worse reward than atheism (P4).

is right (P1)
Christianity is wrong,
but better (P2)
Both get the
same reward (P3)
Christianity is wrong
and worse (P4)
Atheism:0 -w0 -y

Now, when it comes to the gain, x is high (if you're a good member of your religion), y can be any value >0 depending on what turns out to be right, z is mildly negative (you wasted a lot of your life on religion), and w can be any negative value depending on what turns out to be right.

The graph for atheists is a mirror of this, except that the values are different for x' and z' (both of which are 0, as you get no reward as compared with holding a religious belief)."

So, the total reasonability of holding christian belief as opposed to atheism is (P1*x)+(P2*y)+(P3*z)+(P4*w) < - [(P2*w)+(P4*y)].

Theists who use Pascal's wager do the mistake of implicitly assuming that P2 and P4 are 0, which causes the equation to reduce to (P1*x) + (P3*z) > 0 ... Or, in other words, as long as P1*x (the probability of them being right times the reward for their being right) is greater than P3*z; usually they also assume that z (the negative effect of believing in a false religion and wasting some of your life if there were no afterlife) was 0, so for them the equation becomes P1*x > 0, or the result of Pascal's wager.

For someone who doesn't agree that z (the cost of theism) is 0, the results are already different. The equation is then P1*x > -P3*z, and you have to compare the probability of your religion being right times the reward with the probability of the atheists being right times the cost of following your religion. If P1 is small (in other words, if your religion doesn't seem likely), then Pascal's wager fails, as the atheist would just say that the odds of you being right were so low that the cost of following your religion wasn't worthwhile. You no longer have "it is obviously best to follow my religion" - instead, you have to convince them that the probability of you being right is high enough to overcome the cost of following your religion.

Once you take into account the possibility of other religions, the equation expands to its full form, and Pascal's wager collapses entirely. You've got the problem of there being a whole bunch of religions, a good many of which punish blasphemers even more than nonbelievers, so P1 doesn't seem likely to be high to an outsider (why should we believe your religion as opposed to all those other religions?) compared with P2 and P4, much less with P3 ... The atheist just decides that the right side of the equation probably has equal value to or greater value than the left side, and thus doesn't choose to believe any religion.

In order to convince an atheist, then, you need to convince him that P3 is low (that there probably is some supernatural force, and that that supernatural force probably doesn't treat atheists the same as people of your religion), that P4 is low (that that supernatural force probably doesn't treat people of your religion worse than atheists), and that either P1 or P2 is high enough to overcome the cost of following your religion in this life.

Pascal's wager just doesn't cut it - you need to provide evidence of the supernatural, and reasons to think that the supernatural significantly rewards people of your religion, if you really want to convince people using the Pascal's wager logic.

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