"The trouble with the world is that the stupid are cocksure and the intelligent are full of doubt." -- Bertrand Russell

Friday, March 23, 2012

A Polemic Against The Wager

We are told that we should worship God because if we do not, we risk burning in Hell. This is something called Pascal's Wager; that we should bet on God existing, because the potential consequences of not believing are so large.

This fails in a number of ways.

First, is a god worthy of our worship? One that holds you hostage, who is so egotistical, that if you do not acknowledge his existence he will torture you forever? Wasn't our country founded on the idea that tyranny is a poor way to lead a nation? Wouldn't the cosmic tyranny of such a deity be even worse? In some religions, the mere thought that God does not exist is a crime from which there is no redemption. Even in mainstream Christianity, dieing as a non-believer warrants your entry to eternal pain and suffering. The most egotistical madman on Earth would never condemn you to such a fate; even those who suffered in Nazi concentration camps, at Darfur, or in Somalia were eventually released to death. Their suffering was finite.

When you say that such a god is just, you are saying that people like me deserve a fate worse than the worst suffering our world has ever known. Now, you might say that you are not condemning me there -- your god is. Very well, but then I ask whether you think that your god is either more or less just than you are. Obviously, if such a being is less just than you are, then I would rather worship you than it. But if you say that your god is more just than yourself, then condemning me to such a harsh fate should be something that you should strive for. If it's not something you strive for -- if you would condemn the person who would threaten me with such harm -- then you must condemn your god.

But wait! -- you say. It's not your god which threatens me with such harm; rather, I am condemning myself to such a place!

Well, let's think about that. Was it not God who set up the rules in the first place? Was it not God who is said to be all powerful and all knowing? In what sense, precisely, would one say that this being isn't responsible? What is it that He is not responsible for?

Indeed, if such a being existed, he would be responsible for all that is and could ever be.

But there are still at least 3 other ways in which Pascal's wager fails.

Let's suppose that such a god was worthy of my worship, for whatever reason. Which god would that be?

The Christians say that it is their god, while the Muslims say that it is theirs. The Jehovah's Witnesses think that God will cast everyone else -- even other Christians -- into Hell. In fact, name a religion in which non-belief is punishable by eternal suffering, and you can find someone who says that it is their deity we must oblige ourselves to worship. But note how this whole thing is constructed; it's construed as a bet to be taken without regard for evidence and only with regard to potential consequences. Therefore, in making a choice, we must list every such belief system and weigh their potential consequences off between each other.

What you find when you do this is that all such belief systems promise the same infinite rewards for belief and infinite punishments for non-belief. Worship the wrong deity, and that deity will surely cast you into Hell. At least that much is true of both Christianity and Islam.

This is some kind of stand still; we find ourselves unable to choose religions on this basis.

 But it gets worse.

Since we are simply weighing possibilities off against each other, we should weigh all possibilities. Even ones that don't reflect religions that you find in the world. After all, what basis do we have to decide that options we come up with right now are illegitimate?

Let's consider another God-concept, call it Fred. Now Fred created life in this universe to test our incredulity. If you believe in things for which there is no evidence -- such as Fred or other gods -- he will cast you into Hell. Surely it would be a mistake to worship Fred, but it would also be a mistake to worship any other gods. Because if you did worship other gods, then Fred could potentially punish you. Vis a vis Fred, you should worship no gods.

What this tells us is that the entire construction is illegitimate. We should not choose beliefs on the basis of their potential consequences alone; we need to break the tie by considering the various kinds of evidence and arguments either for or against all of these things.

Yet I find it worth mentioning that there is another way in which Pascal's Wager fails.

Suppose that all of the arguments I offered already didn't work, and that I really would be better off if I believed that your god existed.

Even then, how should I start believing? Belief is not entirely voluntary, if it ever even is. Certainly, the available evidence is either insufficient or directly undermines belief in a god. So convincing myself on the basis of evidence is out.

I couldn't simply profess belief either. You can't trick God, especially if he knows everything. And even if I could trick God, why should I trick the being who you claim is supposed to be the object of our love?

Maybe I could go around, doing various kinds of activities to compel myself to believe. But even if I could do that, wouldn't God see this as a deception and cast me into the flames nonetheless? I certainly wouldn't be coming to God wholeheartedly; I would be casting a bet for fear of perpetual torment.

But, again, I ask you whether a loving god would ever even put us in the position of making that sort of a decision. Is that the deity to whose allegiance you profess, or do you make a mockery of your own beliefs by using such a callous argument?


  1. Your first argument about such a god being unworthy of worship sounds more like an aesthetic judgement than a reason not to believe. Although I would rather be immortal, I still believe I am mortal.

    The second bit doesn't necessarily invalidate The Wager; it now depends on the probability distribution one assigns to the set of scenarios. Does it seem more likely that a god would adore or despise worship?

    On your final point, I'm not sure that your conception of belief is in agreement with empirical evidence of human belief. Perhaps it would be difficult for a cold, calculating, totally rational robot to decide to believe, but humans regularly adopt beliefs to conform to group narratives or to signal loyalties to beneficial allegiances.

  2. The first argument is about whether or not a God who holds such punishments over you is even worthy of our worship. I argue that such a being would likely not be worthy of our worship, though you might still want to for personal gain (i.e. to not meet it's wrath.)

    Since the utilities for heaven or hell are plus and minus infinity, respectively, in the decision theoretic construction of this argument, one can show that the probability distribution doesn't matter. If you would like, I can prove this for you.

    "Perhaps it would be difficult for a cold, calculating, totally rational robot to decide to believe, but humans regularly adopt beliefs to conform to group narratives or to signal loyalties to beneficial allegiances."

    I address this in the second to last paragraph.

    But, look, we should strive to form beliefs for *good* reasons. It might very well be an empirical fact that humans often form beliefs for *bad* reasons, but in so far as they do, that's a human fallibility. Using that as a defence is pretty silly for that reason.

  3. Re: Decision theory do you mean just because you can't calculate an expected value? Suppose you were offered a wager on the roll of a fair 6 sided die. You could either bet on 1 or not 1 (ie 2,3,4,5,6). If you win you get +inf and if you lose you get -inf. Would maximize your probability of a +inf outcome, or have no preference because of incomparable EV?

    Your second the last paragraph counters by arguing that a self interested desire to believe would not be a legitimate belief and that a god would see through it. I would contend that beliefs born of a desire to believe are just as legitimate as rational, justified beliefs. Meat brains are so messy that people often have no understanding of the true causes of their beliefs or how they've been influenced. There are tons of situations where people adopt beliefs just to fit in with their peers and yet they hold their beliefs with such conviction.

    When you say that humans should form beliefs for *good* reasons, I have a feeling you mean that we should form beliefs for rational reasons. But why should we? If I think that I can trick myself into adopting an advantageous belief (as empirical evidence suggests), why not do it? If that's not what you mean by *good*, then I would argue an advantageous false belief qualifies as *good*.

  4. "Re: Decision theory do you mean just because you can't calculate an expected value? Suppose you were offered a wager on the roll of a fair 6 sided die. You could either bet on 1 or not 1 (ie 2,3,4,5,6). If you win you get +inf and if you lose you get -inf. Would maximize your probability of a +inf outcome, or have no preference because of incomparable EV?"

    Not at all.

    Suppose that there are three possibilities -- deity A, deity B, or no deities. I am going to assume that if you bet on deity A, and B exists, then B will send you to hell and vice versa. Then, the expected payoff on betting that deity A exists would be:

    E(deity A) = p(AU~B)*(+ inf) + p(~AUB)*(- inf) + p(no deities)*n


    p(AU~B) = probability deity A exists but B does not
    (~AUB) = probability deity B exists
    p(no deities) = probability that no deities exist
    and n is whatever finite utility exists with there being no deities, and betting on deity A.

    But, now, we have a problem.

    This equation becomes:

    E(deity A) = (+ inf) + (- inf)

    But that equates to any finite number whatsoever. Similar problems obtain if we include the possibility of Fred.

    Notice that the probability of either A or B vanished; it doesn't matter how large or small those probabilities are so long as they were finite, non-zero, and non-negative (which *all* probabilities need to be by definition.) Thus, the probability of whatever deities we talk about doesn't matter.

    In fact, this is the reason why the argument would have worked had we left out deity B (or Fred, etc.) It wouldn't matter how small the probability of God's existence would be; we should still believe if we want to avoid Hell. But that's under the false dichotomy that Christianity and atheism are the only two options.

    "There are tons of situations where people adopt beliefs just to fit in with their peers and yet they hold their beliefs with such conviction."

    This is, again, an empirical fact about humans. It's not a compelling reason to think that something is true, even if it arises out of social pressure.

    In Korea, there is a tremendous amount of social pressure to believe in fan death (look it up.) Does that mean that you or I should believe in fan death? Or even that Koreans should?

    In fact, if social pressure counts as a good reason to believe something, then all of our beliefs are suspect. I see that more as an argument for postmodernism than for theism. In fact, it seems to hurt the case for theism; you mean to tell me that the only reasons to be a theist are socially constructed? That there are no objective reasons to take on that belief, but it's simply constructed out of a need for social conformity? That sounds more like an excuse to be a sheep than it does a legitimate reason to think that a given proposition is true.

    Lastly, you've just assumed that the belief in question was advantageous. Even if I were to grant you all of your points (which I am not willing to do), we would be left only taking on beliefs for which we benefited. As some trivial decision theoretic analysis shows, the outcome is actually indeterminate. There is no more decision theoretic benefit to affirming belief in any god than there is to disaffirming belief in any god.

  5. And, lastly, I will say this. Everyone, everywhere, always should strive to be rational even if they cannot always manage to do so. What you're trying to do -- by rejecting rationality and replacing it with beliefs formed on the basis of social cohesion -- is to give an excuse for being irrational, silly, or insane. That's simply inexcusable.

  6. Re Decision Theory, this is what I meant by that we can't calculate an expected value. So coming back to my d6 question, do you believe it is rational to bet on 1, not 1, neither is superior, or something else?

  7. Vis a vis decision theory, the decision is indeterminate on utilitarian grounds. We need some other way to decide the issue, if there is a way to decide it.

  8. Because to make the analogy more realistic, you can't simply state it the way you did. The way you need to state it is that every number *could* give you +inf if you guessed correctly but would give you -inf if you guessed wrongly. Now, which way would *you* bet?

  9. I would bet on {2,3,4,5,6} and accept a 5/6 probability of inf payout.

    In situations like this, it's important to keep in mind the distinction between the map and the terrain. Standard decision theory is your map to negotiate the terrain of good decision making. The d6 question should be a fairly straightforward decision. That simple decision theory can't decide means there's a problem with the map, not that the terrain is undecidable.

  10. If you bet on {2,3,4,5,6}, this puts you into the position of accepting logical contradictions as true. Are you trolling me?

    This would be the same thing as calling yourself a Muslim-Hindu-Jewish-Christian-Zoroastrian-Buddhist. You can't put your bet on multiple numbers, especially if you can't take on a logically contradictory point of view.

    And, in fact, placing your bet on that set doesn't even give you a 5/6 probability of infinite payout. Since each member of the set punishes you for guessing wrongly, you would have receive the -infinity punishment. In the religion analogy, the corresponding deity of each religion punishes you for worshipping the others. That means that you don't get to go to Heaven simply by betting on every religion. That would be heretical in a large number of those religions.

    I don't know what you mean about the map/terrain distinction. There is no reason that I see for this to be a good fairly straightforward decision; to the contrary, I believe that I have proved otherwise.

  11. Forget about the religion stuff for a second and think about the d6 problem by itself. There's a lesson to be learned from it about the scope of problems that expected value can be meaningfully applied. To reiterate the problem, you must choose between 1 or 2:

    1) Bet on 1. You get +inf 1/6 of the time and -inf 5/6 of the time.

    2) Bet on not 1. You get +inf 5/6 of the time and -inf 1/6 of the time.

    EV is indeterminate. What do you do?

    The point about the map and the terrain is that the map is the model of reality in your mind while the terrain is reality. For example, let's say my method for calculating sqrt(n) was to gather n pebbles, arrange them in a square, and count the edge length. This would only work on the perfect squares. To fallaciously conclude that the sqrt(2) does not exist would be to mistake my map with the terrain. My pebble counting method is a way to calculate a sqrt, but a sqrt is not defined as the result of my method.

  12. Suppose I conceded to you (for the sake of argument) and said that I would bet on "not 1". Now what?

  13. Now what principle did you use to arrive at this decision? What are some candidate principles that might be used to reason where ev fails?

    We're going up a meta level to discuss how one ought to reason in this situation.

  14. Haha. No, you don't get to strong man me into reasoning irrationally.

    I said that I would (for the sake of argument) bet on not 1. You don't then get to tell me that we can decide this without evidence; that's two separate propositions.

    I'm still waiting to see how any of this non-sense is relevant to the God issue.

  15. No need to be so paranoid, I'm trying to help you think more rationally. I'm not sure what you mean by deciding this without evidence.

    If we are choosing not1 over 1, there should be a principle we can use to decide. Is there a preference relation we can construct on probability distrs over R U {inf} U {-inf}? It should be transitive and complete.

    This relates to Pascal's Wager because you need to develop the proper machinery to analyze the problem. At the moment, you're a bit like the man with the sundial claiming time doesn't exist at night.

  16. I wasn't being paranoid.

    I never agreed that I would take the bet on not-1 over 1. I simply said that I would temporarily agree to it to see where you wanted to go. You then asked me how I would make that decision; but I wouldn't. I merely suspended my arguments against it temporarily to see where you were headed.

    You seem to want me to say that one should prefer not-1 over 1 in virtue of the fact that not-1 has a higher probability than 1 does and therefore I have a higher chance of receiving +inf.

    However, let's try going to the next step like I keep trying to get you to do. At the next step in the analogy, we assign each face of the die to a religion or belief system. But now we see that the analogy falls apart. We cannot bet on multiple religions (and, therefore, we cannot bet on "not-1"), and if we guess wrong, we get -inf. Your construction implicitly assumes that we can bet on multiple choices at once, something which the original problem explicitly forbids.

    It has occurred to me that you might be going with something else. Instead of each face of the die representing a different religion, perhaps the point of the analogy is that we should bet on the option that has the highest chance of giving us +inf. But then the analogy breaks down too, because as far as I can tell, most god concepts are equally likely (unless they are internally contradictory in some way.) You earlier told me that you thought Fred was less likely than some other god (like Yahweh). I disagree, although I see where the intuition might come from. Regardless, I think Yahweh and Allah are definitely equally as likely to exist, but betting on the wrong one of those would have negative consequences. Thus, again, the analogy breaks down. And let's not forget about Jehovah's Witnesses who think that everyone else -- including other Chrisitans -- will be going to hell. I cannot discern why their theology is more likely to be false than that of the Catholics, Methodists, Presbyterians, evangelicals, or any one else.

    Traditionally, Pascal's Wager is constructed with only one particular god in mind and is contrasted against atheism. In that model, even if atheism is vastly more likely, one is supposed to bet on a god existing due to the utility structure of the problem. Of course, this is a false dichotomy -- which is my entire point. But what I want to point out is that your construction explicitly goes against this typical formulation.

    Now, if there are other considerations that we need to use whereby the probability of a given deity is raised above that of the others, then we should no longer be thinking about Pascal's Wager. We should move on and analyse whatever arguments raise the probability of a given deity. In that case, we could reach a conclusion on non-utilitarian grounds and we needn't worry ourselves with Pascal's wager at all.

  17. I'm meandering towards something closer to your third paragraph. There are a lot of adaptations you can make to decision theory to get it working, and a fairly typical one would be to decide based on P(+inf) - P(-inf) with EV over finite payouts as a tie-breaker. Using this improved decision theory, the wager comes down to a question about the probabilities you assign to each god as I originally commented. Here atheism wins only if the probability of a tricky god is greater than or equal to a more traditional one.

    Technically I didn't say Fred would be less likely than whatever other god (I just asked you :P). Perhaps that is the case, but I don't think those things are very interesting to think about. To me, the stronger reply to Pascal's wager is that the space of potential gods to bet on is infinite. The probability of picking the right one is 0.

  18. Now I'd like to return to the earlier discussion about what it means to strive for *good* rational beliefs. Earlier you asserted that "Everyone, everywhere, always should strive to be rational" so clearly this is an important goal for you.

    I contend that there are two distinct types of rationality we should strive for. Epistemic rationality (ER) involves truth seeking and the desire to hold true beliefs. Instrumental rationality (IR) is the practice of optimal decision making.

    I'm not sure if I am understanding you correctly, but it sounds like you lean pretty hard towards ER over IR in situations where they could potentially conflict. Would you say that's accurate or am I off base with this?