Monday, April 12, 2021

Pascal's wager and decision theory

From time to time I find myself musing whether Pascal’s Wager doesn’t simply completely destroy ordinary probabilistic decision theory. Consider an ordinary decision, such as whether to walk or bike to work. There are various perfectly ordinary considerations in favor of one or the other. Biking is faster and more fun, but walking is safer and provides more opportunity for thought.

But in addition to all these, there are considerations having to do with one’s eternal destiny. It is hard to deny that there is a positive probability that we will have an eternal afterlife and that our daily choices will affect whether this afterlife is happy or miserable. But even tiny differences in the probability of eternal happiness infinitely swamp all the ordinary considerations in the decision whether to walk or bike. If the opportunity for more leisurely reflection afforded by walking even slightly increases one’s chance at eternal happiness, that infinite contribution to expected utility completely overcomes all the ordinary considerations. But on the other hand, biking would allow one to arrive at work earlier, and thereby take on a larger share of work burdens, which would lead to growth in virtue, and increase chances of eternal happiness. So in the end, it seems, many of our ordinary everyday decisions end up turning into exercises in balancing tiny differences in the probability of eternal joy, as these swamp all the other ordinary consdierations. And that seems wrong.

One move here is to say that the question of how ordinary approximately morally neutral decisions affect the afterlife is one that we have so little information on that we should bracket the infinities, and just focus on the finite stuff we know about. But on the other hand, does that make sense? After all, perhaps we should put all our mental energies into figuring out this stuff that we have so little information on, as the infinities in the utilities swamp everything else?


Tom said...

My first thought is that this is a false dilemma. In these kinds of scenarios, it seems that the naturally preferable option is ordinarily the one that, in virtue of the very fact that it is naturally preferable, will lead more likely to greater eternal happiness.

For instance, if I choose to bike because it is more fun, I am not directly thinking of virtue and eternal happiness. However, making time for fun is of course virtuous provided due measure is observed, etc. So in that case, I have made the right decision.

It may be that in these decisions, the options are often incomensurate in individual cases provided that I am living the appropriate kind of life. For example, if I am making an appropriate amount of time for fun and intellectual reflection, in an individual case whether or not I decide to bike or walk in order to enjoy the goods of fun or time for reflection, it may be the case that these choices are incomensurate.

Unknown said...

I think a common sense rendering of the wager will lead to common sense decisions in everyday life. The intuition evoked by your examples - the intuition that having eternal happiness in the forefront of our minds as the deciding factor in all of our everyday decisions is an unintuitive way to approach decision-making - goes away when you keep in mind that constantly focusing on eternal rewards is a virtue-inhibiting vice that may end up lowering your chances of gaining those rewards. Thus, it all balances out. Eternal considerations should lie at the bottom of our decision to bike to work, but eternal considerations should also lie at the bottom of our decision to not always be daydreaming about eternal considerations.

That said, there is a reductio for Pascalian reasoning that I do find more troubling. Suppose person X was born and raised in a cult, where unreasonableness was prized as a cardinal virtue. Assuming that X was never exposed to other religions, he naturally takes Pascal's wager and pledges never to bow down to reason again. If he ever fails in being totally irrational, X believes, he will suffer eternal conscious torment. In such a case, according to Pascalian reasoning, X could never rationally give up his irrationality, even if it were just for a moment to consider the virtues of other religious perspectives. But this seems wrong, so the wager must be wrong.

Still, on the basis that I could be wrong about this, Pascal's wager is still the guiding principle of my life.

Benjamin Stowell said...

Unknown: on the reductio: I suspect that the person in this scenario has much too high a credence to wager rationally in the first place. Any system that prizes unreasonableness will have a credence of 0% for myself personally because of its self-refuting nature. Case in point, the wagerer has to use reason to reject reason in this case, but can simply see by reason the contradiction of that.