Pascal's Wager

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I've long held that Pascal's Wager is a completely absurd argument. Most people will know what Pascal's Wager is, but it's loosely speaking the argument that you should believe in God because doing so offers the possibility of infinite reward, whereas not doing so offers no reward at all.

There are obvious flaws in it, which apparently even Pascal recognised. The primary one I think, is that the reward for believing something does not lead to a mechanism by which you can genuinely accept that belief. If you offer me a £10,000,000 to believe that pigs can fly, I will not be able to start believing that pigs can fly just to gain a benefit.

For this obvious reason, if anyone mentions the Wager in any context other than an example of dubious logic, treat anything else they say with caution.

However, Pascal's Wager is not really the object of this post. What I'm going to discuss is instead (despite the blog title) Pascal's Mugging.
Pascal's Mugging is set out clearly in Nick Bostrom's post here.

Pascal's Mugging rephrases things so that we operate purely in terms of the payoff. We don't actually have to believe anything with any certainty, we merely have to offer enough credence to a proposition that it becomes a reasonable bet - in much the same way that paying £1 for a lottery ticket that has a 1 in 10,000,000 chance of paying out £100,000,000 is a reasonable thing to do, even though you never believe you will win that lottery.

Now, I think Pascal's Mugging contains a hidden flaw, in that you are asked to specify some credence for a possibility of some level of payout. If that payout is too small for that credence, so that you do not consider it a reasonable bet, the payout is increased until (the argument goes) that bet does become reasonable. I would argue that as the payout is increased, your credence must also decrease, and just because the payout is unbounded does not mean that it ever becomes a reasonable possibility. Take as an example the idea that I have a level of belief in an ability to payout an amount £x as 1/(10 x). My expected payoff is then always 1/10, and if I'm staking an amount greater than that it's never worth my while to pay, no matter what reward is offered. I could equally construct a credence function that decreases my expected payoff as x increases, no matter its size.

There's another excellent post on the matter here.

I would argue that if you ever fell for Pascal's Mugging then practically by definition your system of assigning credences is deeply flawed. I suspect it's possible to find an argument that constructs this in something like the context of Dutch Books - the idea that to have a consistent way of assigning beliefs you should never open yourself to wanting to engage in gambling that will leave you open to a guaranteed loss.

To finish up, lets look at a situation in contrast to both Pascal's Wager and Pascal's Mugging - the issue of climate change. If we consider the possibilities involved in the climate change debate, we either accept considerable economic penalty for the possibility of saving the planet or not, or we go on as we are and either come out doing well, or end up having incurred an even greater penalty for continuing to consume resources and pollute as we currently are. 

It's not entirely unlike the cost a religious person accepts (in terms of lost Sunday mornings or whatever) for the possibility of heaven, or spending your Sunday mornings in bed or doing something else you enjoy and risk ending up in hell. Now the relative probabilities and relative benefits and penalties are very different, but it again makes the difference to Pascal's Wager clear. Whether the planet gets destroyed or not depends on my actions, whereas my ability to get past the Pearly Gates depends perhaps partly on my actions, but predominantly on my beliefs. I can hold the view that anthropogenic climate change is real or not, but it does not directly impact the end condition of the planet - my carbon footprint does.

It also differs from Pascal's Mugging, in that unlike the latter where payoffs are allowed to change without limit, the payoffs in climate change are pretty much fixed and limited (even if potentially extreme). Our credence in climate change is also detached from the payoffs themselves. It's a case with superficial similarity, but in fact I would argue it's quite possible and quite likely that a strong case can be made that we should undergo the economic penalty in return for avoiding the much more severe cost if climate change occurs. Even if you don't believe as I do that climate change is real, the argument for acting as if it is is strong, and doesn't depend on you actually accepting as likely the possibility of climate change itself.

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8 Comments

Thanks for a very intelligent post (glad to read someone else who knows what a Dutch Book Argument is!) I agree with your fundamental point: people can reasonably buy insurance against their house burning down, even though they think it highly unlikely that it will actually happen. It would be daft to say we cannot pin down a time that the house will burn down, or that the certainty of fire might be less than 90%, therefore we shouldn't buy insurance.

Good stuff Edd :) I've always thought there was another argument on how religious person or a climate sceptic should have two very different answers to this problem, and it just boils down to social responsibility. Going to hell is very much your own problem, whereas sending the planet to hell has somewhat wider implications. Perhaps one could fold this into the penalty but this should _not_ be a debatable matter. i.e., some people may argue that going to hell for eternity is worse than condemning the planet for the _next_ generation, and act accordingly. I would argue that that one is not up for debate.

That looks like an utterly awesome blog indeed. Must drag myself away from that and this now - but there is something that tickles me about the argument above. More later.

(sorry.. I realise I took this post off-topic - hopefully this won't discourage anyone from posting on-topic, which is quite frankly much more interesting!)

There are two points here.

1. Concerning the point made in the post you linked to above - agreed. I wasn't aware of the hordes of two-boxers that are so desperately trying to rationalise their way through financial loss (mind you, I'm not aware of much at all!). And if I read you right, the relevance to my previous argument is that this _may_ give you (us) a strictly rational reason as to why our perspective (taken here as meaning that the larger benefit always trumps) should be self-evident. At least if we can be clever about what 'winning' means.

2. My point, however, was a bit off topic and, as you correctly point out, perhaps one more for the philosophers. You write as if the issue was social _empathy_, whereas I strictly meant social _responsibility_. Or in other words, it's not that you'd feel guilty (in some quantifiable way) if we all suffered because of you, it's because you simply have no right. A moral argument, I guess.

[...]

Now, to save you some trouble and myself some embarrassment I deleted the (exceedingly long) text just above where I managed to write myself into a descending spiral of doom. This is hard - I want to argue for (2) without using (1) because I _feel_ one should be able to do so based purely on moral premises but I'm finding myself in horribly shaky ground! This one requires some digging/reading/re-thinking. I may have learned something new today.

(I meant something new about myself - I literally learn multiple new things from all your posts!)

And it just dawned on me that today, incidentally, the answer to this question is suddenly very clear!

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This page contains a single entry by Edd published on March 8, 2010 12:00 PM.

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Edd works somewhere between astronomy and computing and has a general interest in science, skepticism and other related topics.

Opinions expressed in this blog are my own and not those of my employer.