I feel like this post is dated by the fact that it came before Pascal's Mugging discussions to the point of being fairly wrong. The problem with Pascal's Wager actually is that the payoffs are really high, so they overwhelm an unbounded utility function (and they don't precisely cancel out, since we do have a little evidence). On the other hand, I suppose the core point that you shouldn't dismiss things out of hand if they have a low (but not tiny) probability and a large payoff is sound.
I think you're confusing Pascal's Wager with Pascal's Mugging. The problem with Pascal's Mugging is that the payoffs are really high. The problem with Pascal's Wager is that it fails to consider any hypotheses other than "there is the christian god" and "there is no god".
I am not. The problem with Pascal's Wager is sort of that it fails to consider other hypotheses, but not in the conventional sense that most arguments use. Invoking an atheist god, as is often done, really does not counterbalance the Christian god, because the existence of Christianity gives a few bits of evidence in favour of it being true, just like being mugged gives a few bits of probability in favour of the mugger telling the truth. So, using conventional gods and heavens and hells like that won't balance to them cancelling out, and you will end up having to believe one of these gods. On the other hand, the actual problem is that you can keep invoking new gods with fancier and more amazing heavens and hells, so that what you really end up believing is super-ultra-expanded-time-bliss-heaven and then you do whatever you think is required to go there. Which is isomorphic to Pascal's (self-)Mugging.
(I should try practising explaining things in fewer words...)
I'm pretty sure that actually is the problem with Pascal's Wager. You even just committed it when you only included Christianity. What about Islam? You go to hell in Islam if you are either an atheist or believe that Allah had a son. And then there are the various heretical versions of Christianity where you lose out on eternal life for "worshipping a dead man" instead of learning true knowledge from his teachings.
There are so many other competing hypotheses to choose from besides just Christianity or atheism that this is the massive failing point in the wager.
No, it's not (at least if we take the generous view and consider the Wager as an argument for belief in some type of deity, rather than the Christian one for which it was intended), because after considering all the hypotheses, you will still have to choose one (or more, I guess) of them, and it almost certainly won't be atheism. I also feel like you completely missed the point of my previous comment, but I'm not sure why, and am consequently at a loss as to how to clarify.
because after considering all the hypotheses, you will still have to choose one (or more, I guess) of them, and it almost certainly won't be atheism.
Why is that?
While a belief having adherents may be evidence for that belief, other people believing differently will be evidence against it. When religions function as evidence against each other and lose probability mass, more of the lost probability mass goes to atheism than to other religions.
Sure, but it doesn't matter how much probability mass atheism gets, because the religions are the only ones offering infinities*, and we're probably interested in best expected payoff, not highest probability. If religions have 1/10^50 residual probability mass and atheism has all the rest, you'd still probably have to choose one of them if at least one is offering immense payoffs and you haven't solved Pascal's Mugging.
*I guess one could argue that a Solomonoff prior assigns a zero probability to truly infinite things, but I'm not sure that's an argument I'd want to rely on (also I know Buddhism offers some merely vast numbers, although I'm not sure they're vast enough, and some other religions do too, I'd imagine).
While apologetics have adopted the idea that going to heaven offers infinite utility, the actual descriptions of heaven in the texts from which Christianity is derived (what little there are,) don't describe anything like infinite utility, except if you accept that a finite utility times an infinite duration equals infinite utility. Given an infinitesimal chance of payout on Christianity, you'd probably be giving yourself better odds trying to achieve infinite utility by living infinitely long, even given the rather low odds of the fundamental laws of physics being amenable to that.
That's fair. I guess adopting exponential discounting is also good enough to rule out Christianity. Not about trying to live infinitely long, though - it would depend on how much believing in Christianity would hinder you in achieving that. (Same for other religions that don't promise sufficiently amazing bliss.)
I would think that a properly self consistent Christian would probably not try to live forever given the expectation of being able to go to Heaven and stay there forever after a lifespan of ordinary length.
On the other hand, Christians with sufficient alief to look forward to their own deaths are pretty rare.
Today's post, The Pascal's Wager Fallacy Fallacy was originally published on 18 March 2009. A summary (taken from the LW wiki):
People hear about a gamble involving a big payoff, and dismiss it as a form of Pascal's Wager. But the size of the payoff is not the flaw in Pascal's Wager. Just because an option has a very large potential payoff does not mean that the probability of getting that payoff is small, or that there are other possibilities that will cancel with it.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was What Do We Mean By "Rationality"?, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.