Pascal’s Wager

There is a famous theological argument known as Pascal’s Wager which, rather than making the usual appeals to morality and intuition, instead tries to show that believing in God and the afterlife is the logical, rational thing to do. While Pascal admitted that it is not always possible to “make yourself” believe in God (the Christian God, that is–what, you thought we were talking about some other God?), you should at least act as though you do until you are convinced. The core argument frames the question of whether one should be religious as a “wager” that you can’t opt out of: even if God isn’t likely to actually exist, the possibility of an infinite win (eternity in Heaven) justifies the merely finite cost of devoting yourself to religion–even if that cost is a lifetime of self-denial and asceticism. (This was back in the 1600s, when most folks thought getting into Heaven was really difficult and unpleasant, but the argument applies equally to anything a religion requires you to do that costs you time, effort, or money.)  Sounds pretty impressive, huh? Let’s go over the argument in a bit more detail–this time, with a few superficial modifications.

To start, let us imagine that a superintelligent race of aliens is invisibly orbiting our planet right now, monitoring the population for the purpose of an odd little game. The rules of the game are as follows: every time a human claps their hands, the aliens flip a coin. If the coin comes up heads, the human will be granted immortality and teleported to a boundless utopia, where they will spend eternity in perfect bliss. (We will suppose that the aliens leave a hologram or replica in the human’s place, to explain why none of the other humans are aware of the game.) However, if the coin lands on any of its other six million faces (it’s a multidimensional coin), the aliens do nothing. In other words: every time I clap my hands, I have a one in six million chance of being transported to paradise, whereas if I don’t clap my hands I forgo that chance.

To be sure, the likelihood that invisible aliens are currently playing such a bizarre and widespread game without our knowledge is miniscule–but if I am being a good rationalist, I must still admit that it is never exactly zero, so it is possible that in deciding what to actually believe I will make an error. There are two possible errors I can make: I can believe there are no aliens and do nothing, when in fact the aliens do exist (false negative), or I can believe in the aliens and clap my hands, when in fact there are no aliens (false positive). If the aliens don’t exist, and I clap my hands anyway, then I’ve incurred a small cost–a few calories expended, and perhaps some minor embarrassment–for no benefit. On the other hand, if the aliens do exist, and I choose not to clap my hands, then I’ve foregone the chance of infinite benefit: an eternity in paradise. Although the chance of gaining this benefit with each clap is small, and although the chance that the aliens exist at all is smaller still, an infinite benefit remains infinite no matter how small its probability–that’s just a simple fact of multiplication. Thus the expected value of a true positive (clapping and getting transported to paradise) overwhelms the finite cost of a false positive (clapping for no reason), no matter how small the probability of the former, and no matter how large the cost of the latter. It follows that the rational thing to do is assume the aliens exist, just to be on the safe side, and if you truly aspire to be rational then you will clap your hands as fast as possible for every waking minute of the rest of your life.

…Seems a bit off when you take out all that distracting religious stuff, doesn’t it?

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