Pascal’s Wager and Newcomb’s Box

When I teach philosophy of religion to undergraduates, they consistently respond positively to Pascal’s Wager. I suspect it appeals to the practical, self-interested side of most young people, and that’s clearly what it’s designed to do. Pascal’s Wager is an argument in favor of belief in God on the basis of practical reason. Assuming that the theistic arguments are not rationally compelling, Pascal argues that the agnostic ought to believe in God for pragmatic, rather than evidential, reasons. In other words, one minimizes loss and maximizes gain by believing in God. After all, if we believe in God and are right we gain eternal reward. If we believe in God and are wrong, we ‘break even’ as it were. If we don’t believe in God and are right, we also ‘break even.’ But if we don’t believe in God and are wrong, we lose eternal reward and reap eternal damnation.

There are numerous arguments against the Wager, but most of them involve an appeal to considerations external to the Wager itself. I’m thinking specifically of the “other gods” challenge, in which the objector recalculates the odds on the basis of religious options other than atheism or Christian theism. While such an approach is interesting, I’m inclined to think that something like atheistic naturalism or something like Christian theism just are the live options, philosophically speaking. Now, I don’t have time to justify that assertion, but if the current state of the field is any indication, I think it’s a safe assumption. So let’s grant Pascal the point that these are the only live options available to us. How ought we to think about the Wager from the standpoint of rational decision-making? It occurs to me that we might usefully compare the Wager to another classic rational decision-making problem.

In my critical thinking course last semester, we had some fun with a thought experiment called “Newcomb’s Box.” This an interesting test case for rational decision-making models because philosophers, and students, disagree about what the most rational course of action is. It occurs to me that there are some similarities between Newcomb’s Box and Pascal’s Wager. But first, let’s outline Newcomb’s famous problem and then compare and contrast the two. Newcomb’s Box has various formulations. The one below is adapted from  Introduction to Philosophy, John Perry et al (Oxford University Press, 2010) “Newcomb’s Problem” pp 818 – 19.

Let’s say you’re participating in an experiement designed by a psychologist with a reputation for being brilliant and well-funded. On a table are two boxes. One of them, labeled A, is transparent; in it you can see an enormous pile of $100 bills. The other, labeled B, is opaque. She tells you that there is $10,000 in transparent box A and that in box B there is either $1,000,000 or nothing. She tells you that she is going to give you a choice between:

Taking just what is in box B.

Taking what is in both boxes.

She then informs you that she has made a sophisticated profile of your personality and character traits. On the basis of your profile, she made a prediction about what choice you would make, and she decided what to put in Box B on the basis of this prediction:

If she predicted you would take both, she put nothing in Box B.

If she predicted you would take only Box B, she put $1,000,000 in it.

At this point you ask her how accurate her predictions have been. She says that 1,000 participants have been given the choice, and she has only been wrong once. In all other cases, participants who chose both boxes got only $10,000, whereas those who chose only Box B got $1,000,000. You now have to choose.

In the case in which she was wrong, the participant either received $1,010,000 or nothing depending on whether s/he chose both boxes or Box B only. So if you choose both boxes and she’s right, you get $10,000. If you choose both boxes and she is wrong, you get $1,010,000. If you choose Box B only and she is right, you get $1,000,000. If you choose Box B only and she is wrong, you get nothing. These are the logical possibilities. Granted, not all outcomes are equally probable. But the probability of your getting $10,000 if you take both boxes is 1. So it’s the ‘safe’ bet. Most of my students recognized this and opted for both boxes.

Regarding the Wager, my students’ intuitions were that believing in God is the safe bet. However, thinking about both Newcomb’s Box and Pascal’s Wager, it seems to me that believing in God is analogous to ‘Box B only.’ You’re wagering on a big pay-off by foregoing the ‘sure bet.’ Now even assuming that the odds of that pay-off are very high, they aren’t 1. In fact, the odds of ‘Box B only’ paying off are significantly higher than the odds Pascal places on the existence of God (he estimates these to be no better than .5). Yet most of my students thought that ‘Box B only’ was a bad risk. However, when presented with the Wager, most thought that theism was a better bet than atheism.

Perhaps this has to do with the way the Wager is usually presented. It’s typically presented as having no cost up front. You simply believe or don’t believe, and believing is in your best interests. However, there is a cost involved in belief. Religious belief of the kind Pascal has in mind isn’t simply intellectual assent. It also involves certain commitments, the cultivation of certain virtues, and foregoing certain temporal pleasures (sleeping in on Sunday mornings and casual sex seem to rate pretty high among university students). Perhaps it would be nice if we could have our cake and eat it too (something analogous to taking the $10,000 and hoping there’s $1,000,000 in the other box), but that’s not the way the Wager works. You either opt for the religious life or you don’t. Agnosticism or nominal religiosity are not live options; they amount to practical atheism.

Since there is a cost involved in opting for the religious life (various spiritual disciplines and foregoing various temporal pleasures) and the odds in favor of theism (and the hypothetical pay-off) generously construed are no better than .5, should we reconsider the rationality of opting for theism on the basis of the Wager? Should we reason more on analogy with Newcomb’s Box? I’m inclined to think we should and I’m puzzled that people’s intuitions differ so widely in the two cases. I’d be interested in doing a more scientific study to see if the statistics bear out my informal experience. But then I’d be involved in some kind of social scientific enterprise that would seriously threaten my status as an armchair philosopher.

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