St. Peter and St. Petersburg Paradox: Faith as a Gamble

This post uses the general idea of the St. Petersburg Paradox to explain faith. The paradox can be summed up like this: How much should a person be willing to wager in a lottery with a potential payout of infinity dollars? The answer is infinity dollars (minus one). Of course this is not the answer people give. Most people would not be willing to wager more than a meager sum because the probability of winning that lottery is essentially zero, despite the actual expected value of the lottery being much, much higher than fathomable.

If this idea is extrapolated to the promises of many religions, this modified version* of the paradox might be settled. How much of your life would you be willing to wager to participate in a lottery with a potential payout of infinite life? The answer is any amount necessary up to infinity minus one.

When we talk to our devoutly religious brother and sisters, I think we can see this line of reasoning. Despite the probability of winning this lottery being essentially zero, many devoutly religious people find no discrepancy between how much they are willing to wager and how much they expect to win. A wager of an entire lifetime is a very low price to pay for an expected value of ∞, and most would be willing to wager as many lifetimes as necessary to achieve the expected payout.

The new paradox—if this is true—is, however, the discrepancy between how much they are willing to pay for this lottery and how much they are willing to pay to play numerous identical lotteries. A Christian is not going to wager anything in the Islamic lottery, despite an identical expected value of playing, and a Muslim is not going to wager anything in a Christian lottery. Etc., etc.

In other words, faith might be seen as a wager in a specific lottery where the longer you play the more likely you can win, despite the odds being almost infinity to one against winning.

So why don’t non-believers play this lottery? Because until someone can show us the money, we’re not going to risk what little we have on a fabled payout.

*This modified version assumes there are only two payouts (0 and ∞). In the real lottery there is an infinite number of possible payouts. My version does not perfectly reflect the logic behind the original lottery.

About Rayan Zehn

I'm a political scientist.
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