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MatthewB comments on The Fundamental Question - Less Wrong
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A couple of points:
I could not tell from your post if you understood that Pascal's Wager is a flawed argument for believing in ANY belief system. You do understand this don't you (That Pascal's Wager is horribly flawed as an argument for believing in anything)?
Also, as Counsin it seems to be implying (And I would suspect as well), you seem to be exhibiting signs of the True Believer complex.
This is what I alluded to when I discussed friends of mine who would swing back and forth between Born-Again Christian and Satanists. Don't make the same mistake with a belief in the Singularity. One needn't have "Faith" in the Singularity as one would God in a religious setting, as there are clear and predictable signs that a Singularity is possible (highly possible), yet there exists NO SUCH EVIDENCE for any supernatural God figure.
Forming beliefs is about evidence, not about blindly following something due to a feel good that one gets from a belief.
Pascal's wager is not such a horribly flawed argument. In fact, I wager we can't even agree on why its flawed.
Later edit: I assume I am getting voted down for trolling (that is, disrupting the flow of conversation), and I agree with that. An argument about Pascal's wager is not really relevant in this thread. However, especially in the context of being a 'true believer', it is interesting to me that statements are often made that something is 'obvious', when there are many difficult steps in the argument, or 'horrible flawed', when it's actually just a little bit flawed or even controversially flawed. If anyone wants to comment in a thread dedicated to Pascal's wager, we can move this to the open thread, which I hope ultimately makes this comment less trollish of me.
Partially seconded. (I think most people agree that the primary flaw is the symmetry argument, but I don't think that argument does what they think it does, and I do see people holding up other, minority flaws. I do think the classic wager is horribly flawed for other, related but less commonly mentioned, reasons.)
I'll write a top-level post about this today or tomorrow. (In the meantime, see Where Does Pascal's Wager Fail? and Carl Shulman's comments on The Pascal's Wager Fallacy Fallacy.)
Thanks for the link to the Overcoming Bias post. I read that and it clarified some things for me. If I had known about that post, above I would have just linked to it when I wrote that the fallacy behind Pascal's wager is probably actually unclear, minor or controversial.
There aren't many difficult steps in refuting Pascal's wager, and I dont' think there's be much disagreement on it here.
The refutation of PW, in short, is this: it infers high utility based on a very complex (and thus highly-penalized) hypothesis, when you can find equally complex (and equally well-supported) hypotheses that imply the opposite (or worse) utility.
(Btw, I was one of those who voted you down.)
Again, is it the argument that is wrong, or Pascal's application of it?
(Can you confirm whether you down-voted me because it's off-topic and inflammatory, or because I'm wrong?)
It is always wrong to give weight to hypotheses beyond that justified by the evidence and the length penality (and your prior, but Pascal attempts to show what you should do irrespective of prior). Pascal's application is a special case of this error, and his reasoning about possible infinite utility is compounded by the fact that you can construct contradictory advice that is equally well-grounded.
I downvoted you not just for being wrong, but for having made such a bold statement about PW without (it seems) having read the material about it on LW. I also think that such over-reaching trivializes the contribution of writers on the topic and so comes off as inflammatory.
Are you saying, here, that it is wrong to factor in the utility of the hypothesis when giving weight to the hypothesis?
If he didn't consider all the cases, his particular application of the argument was bad, not the argument itself, right?
I have read the material, but I disagreed with it, and it's often not clear -- especially when the posts are old -- how I can jump in and chime in that I don't agree. Often it's just the subtext I disagree with, so I wait for someone to make it more explicit (or at least more immediate) and then I bring it up.
Thanks for your explanation about the down-voting.
No (assuming you mean the expected utility of the action given the hypothesis), just that you have to accurately weight its probability.
But his argument wouldn't somehow be improved by considering all the cases (not that it would be practical to even consider all the hypotheses of lengths up to that which implies high utility from faith in God!). Considering those cases would find hypotheses that assign the opposite utility to faith, and worse, some would be more probable.
To salvage the argument, one would have to not just consider more cases, but provide a lot more epistemic labor -- that is, make arguments that aren't part of PW to begin with.
All of your objections to PW seem to be about Pascal's application of the argument (the probabilities he inputted, the number of cases cases he considered) in which case we can agree that his conclusion wouldn't be correct.
When I read that Pascal's Wager is flawed as an argument, I interpret this as 'the argument does not have good form'. Did people just mean, all along, that they disagreed with the conclusion of the argument because they didn't agree with the numbers he used?
I think what they mean is, "If an argument allows you to claim an unreasonably huge amount of utility from actions not seemingly capable of that, then you have a complex enough hypothesis that you can find others with the same complexity and opposite conclusion".
PW-type arguments, then, refer to the class of arguments in which someone tries to justify a course of action through (following the action suggested by) an improbable hypothesis by claiming high enough expected utility. That class of arguments has the flaw that when you allow yourself that much complexity, you necessarily permit hypotheses that advise just as strongly against the action.
That is not something that you can salvage by using different numbers here and there, and so the argument and similar ones have bad (and unsalvageable) form.
That is still fine, because we know how to handle the hypotheses with negative utility. You just optimize over the net utilities of each belief weighted by their probabilities.The fact that there are positive and negative terms together doesn't invalidate the whole argument. You just do the calculation, if you can, and see what you get.
If you have the right numbers, and a simple enough case to do the computation, would you find PW an acceptable argument?
The reason I believe Pascal's wager is flawed is that it is a false dichotomy. It looks at only one high utility impact, low probability scenario, while excluding others that cancel out its effect on expected utility.
Is there anyone who disagrees with this reason, but still believes it is flawed for a different reason?
This is an argument for why the argument doesn't work for theism, it doesn't mean the argument itself is flawed. If you would be willing to multiply the utility of each belief times the probability of each belief and proceed in choosing your belief in this way, then that is an acceptance of the general form of the argument.
If you assume that changing your belief is an available action (which is also questionable), then the idealized form is just expected utility maximization. The criticism is that Pascal incorrectly calculated the expected utility.
Right, one flaw in the idealized form is that it's not clear that you can simply choose the belief that maximizes utility. But in some cases a person can, and does.
I think that an incorrect calculation, because one person considered 2 cases instead of N cases, is very different from being flawed as an argument.
PeerInfinity was writing about applying Pascal's wager to atheism -- so he must have been referring to the general form of the argument, not a particular application. Matthew B wrote that "Pascal's Wager is a flawed argument for believing in ANY belief system". Well, what about a belief system in which there are exactly two beliefs to choose from and the relative probabilities are (.4, .6) and the relative utilities of having the beliefs if they are true are (1000, 100) ? I would say the conclusion of the idealized form of Pascal's wager is that you should pick the belief that maximizes utility, even though it is lower probability.
I would distinguish between the general form and the idealized general form. One way to generalize Pascal's wager for belief B, is to compare the expected utilities of believing B and believing one contradictory Belief D in the conditions that B is true and that D is true. This is wrong no matter what belief B you apply it to.
Why would having the beliefs have utility? Isn't utility a function of actions, as a rule?
There's no contradiction in thinking "A is unlikely" and yet acting as if A is true - otherwise no-one would wear seat belts.
The utility of having a belief is what is being considered in Pascal's wager, and is quite different from the utility of the belief itself.
The utility of a belief itself wouldn't sway you to choose one belief over another. Suppose againyou have the two beliefs X and Y, and they each have a certain utility if they are true. If X is true, then you "get" that utility, independently of whether you believed it or not, by virtue of it being true. For example, if there is utility to God existing, then there is that benefit of him existing whether you believe in him or not.
In contrast, there is also utility for having a belief.
To complicate things, there is a component of the utility that is independent of whether the belief is true or not, and there is a component of the utility that depends on the belief being true. In the case of theism, there is a utility to being a theist (positive or negative, depending on who you ask) regardless of whether God exists, and there would also be an extra utility for believing in him if he does exist (possibly zero, if he doesn't care whether you believe in him or not).
SilasBarta has pointed out a relevant argument regarding that case.
You mean the case of the argument applied to theism? I would be willing to forfeit the applicability of the argument for this case, since I'm just interested in discussing the validity of the general argument.
Taboo "Pascal's wager", please.
Sure.
Here's an argument:
Suppose there is a dichotomy of beliefs, X and Y, their probabilities are Px and Py, and the utilities of having each belief is Ux and Uy. Then, the average utility of having belief X is Px*Ux and the utility of having belief Y is Py*Uy. You "should" choose having the belief (or set of beliefs) that maximizes average utility, because having beliefs are actions and you should choose actions that maximize utility.
What is the flaw in this argument?
For me, the flaw that you should identify is that you should choose beliefs that are most likely to be true, rather than those which maximize average utility. But this is a normative argument, rather than a logical flaw in the argument.
Normally, you should keep many competing beliefs with associated levels of belief in them. The mindset of choosing the action with estimated best expected utility doesn't apply, as actions are mutually exclusive, while mutually contradictory beliefs can be maintained concurrently. Even when you consider which action to carry out, all promising candidates should be kept in mind until moment of execution.
This is complicated in the case of religious beliefs where the deity will judge you by your beliefs and not just your actions.
It is also complicated in the case of religious beliefs where other human beings will judge you by your beliefs, which is one reason why abandoning religions is so hard. But that is off-topic, particularly as you can just lie.
While we're being off topic, I'm of the opinion that if you are someone who accepts you should one-box then you should also accept Pascal's wager. I think both are wrong but most people here seem to accept one-boxing is correct but not accept Pascal's wager. I don't care enough about either to work the argument out in detail though.
Newcomb's problem is just a case of making decisions when someone else, who "knows you very well" has already made a decision based on expectation of your decision. There are numerous real-world examples of this. Newcomb's problem only differs in that it takes the limit of the "how well they know you" variable as it approaches "perfect". There needn't be an actual Omega, just a decision theory that is robust for all values of the variable up to and including perfect.
Which sounds a lot like Pascal's wager to me, when your decision is whether to believe in god and god is the person who "knows you very well" and is deciding whether to let you into heaven based on whether you believe in him or not.
There are situations which I guess are what you would describe as 'Newcomb-like' where I would do the equivalent of one-boxing. If Omega shows up this evening though I will be taking both his boxes, because there is too big an epistemic gap for me to cross to reach the point of thinking that one-boxing is sensible in this universe.
I think you're mistaken, therefore I would like to see your proof. It would be a shame if I missed an opportunity to be more correct. ;)
They both have an element of privileging the hypothesis. If I had some reason to think I lived in a universe with an Omega/God then I might agree I should one-box/believe in god but since I don't have any reason to think I live in such a universe why am I wasting my time even considering this particular implausible scenario?
Good point, I edited my form of the argument to include 'sets of beliefs'. If having a set of beliefs maximizes your utility, then having the set is what you "should" do, I think, in the spirit of the argument.
Thank you. My response appears in another thread.
In chapter five of Jaynes, "Queer Uses for Probability Theory," he explains that although a claimed telepath tested 25.8 standard deviations away from chance guessing, that isn't the probability we should assign to the hypothesis that she's actually a telepath, because there are many simpler hypotheses that fit the data (for instance, various forms of cheating).
This example is instructive when using Pascal's Wager to minimax expected utility. Pascal's Wager is a losing bet for a Christian, because even though expecting positive infinity utility with infitesimal probability seems like a good bet, there are many likelier ways of getting negative infinity utility from that choice. Doing what you can to promote a friendly singularity can still be called "Pascal's Wager" because it's betting on a very good outcome with a low probability, but the low probability is so many orders of magnitude better than Christianity's that it's actually a rather good bet.
Obviously, you don't want to let wishful thinking guide your epistemology, but I don't think that's what PI's talking about.