Wednesday, June 1, 2011

A box of smoking sin

Newcomb's problem is a funny little thought experiment that goes roughly like this: Suppose Omega, the alien superintelligence, comes up to you, scans your brain, and then leaves two boxes on the ground. One, box A, is transparent, and you can see it has $1,000 inside. You can't see what's inside box B. Omega tells you that you can take both boxes, or only box B. If Omega expects you to take both boxes, then it left box B empty, but if it expects you to take only box B, then it put $1,000,000 inside. You know Omega has done this thousands of times and has never made a mistake. Do you take one box, or two?

While I am no expert on decision theory, I know enough to explain how two ways of making the choice, causal decision theory and evidential decision theory, think about this problem.

When faced with Newcomb's, CDT reasons: The boxes are already on the ground in front of me. Whatever I choose now, can't make box B change its contents. Since the contents are fixed, if I two-box I get $1,000 plus whatever's inside box B, if I one-box I get whatever's inside box B. Thus, I am guaranteed to get more money by two-boxing, so I take both boxes. CDT predictably wins $1,000.

In the same situation, EDT reasons: If I look at the money people get by each strategy, one-boxers always get $1,000,000 and two-boxers always get $1,000. If I one-box, I have a probability of ~1 of getting $1,000,000 and ~0 of getting nothing. If I two-box, I have a probability of ~1 of getting $1,000 and ~0 of getting $1,001,000. Clearly, I win much more money on average by one-boxing, so I take only box B. EDT predictably wins $1,000,000.

Now, people first introduced to the problem are pretty split as to what they choose, so I'm not going to say "obviously you can see how X is wrong" about either. But it is worth remarking that a) EDT predictably walks out with more money, and b) there is a some consensus among decision theorists that the "rational" thing to do is to follow CDT and two-box.

Now, for those of my imaginary readers that have concluded that obviously EDT is right and CDT is stupid, consider smoker's lesion.

Smoker's lesion is another thought experiment, which goes like this: Suppose you live in a parallel universe where the correlation between smoking and cancer is not because smoking causes cancer. Rather, it's because there's a gene that makes people more prone to lung cancer and also makes them more likely to enjoy smoking. Suppose you like to smoke, but not getting cancer is far more important to you. In this parallel universe, do you smoke?

CDT reasons: Either I have the gene, or I don't. Smoking is not going to give me the gene, it'll just be doing something I enjoy and will have zero effect on my chances of getting cancer (in this parallel universe). So I should smoke.

EDT reasons: People who smoke are more likely to get cancer than people who don't. So, if I don't smoke, I'll be less likely to get cancer, and thus I shouldn't smoke.

I don't know how people's opinions split on this one, but I'd guess that most people realise EDT is wrong here. Not smoking doesn't change your genes! You're just missing out on something you enjoy (by the scenario's specification) in the delusion it'll lessen your chances of cancer, which it won't, since there's no causal relationship.

So yes, I smoke in smoker's lesion. Does that mean I should worry that I walk out of Newcomb's Problem with less money? I suppose one answer could be that I don't expect to find an alien superintelligence that can predict my decisions, but smoker's lesion-type situations are more likely. Or that Omega unfairly rewards irrationality and there's nothing I can do about that. (I've heard that last one plenty of times). But those answers are mistaken, for a variety of reasons. My answer is much simpler; you would be able to predict it if you had read the paper I link here (and if "you" actually existed instead of being one of my imaginary readers). I one-box.

Which is to say, I think CDT is wrong in Newcomb's, though I believe EDT is even wronger in smoker's lesion. It's not that I alternate based on convenience, rather, I think something else called timeless decision theory is correct. Again, see here.

Of course, this is hardly my own original thinking. Pretty much everything I said above is taken as obvious in some circles, at least to the extent I didn't make any mistakes. This post is here because of a third thought experiment, this one about sinning Calvinists, which I found here:

John Calvin preached the doctrine of predestination: that God irreversibly decreed each man's eternal fate at the moment of Creation. Calvinists separate mankind into two groups: the elect, whom God predestined for Heaven, and the reprobate, whom God predestined for eternal punishment in Hell.

If you had the bad luck to be born a sinner, there is nothing you can do about it. You are too corrupted by original sin to even have the slightest urge to seek out the true faith. Conversely, if you were born one of the elect, you've got it pretty good; no matter what your actions on Earth, it is impossible for God to revoke your birthright to eternal bliss.

However, it is believed that the elect always live pious, virtuous lives full of faith and hard work. Also, the reprobate always commit heinous sins like greed and sloth and commenting on anti-theist blogs. This isn't what causes God to damn them. It's just what happens to them after they've been damned: their soul has no connection with God and so it tends in the opposite direction.

Consider two Calvinists, Aaron and Zachary, both interested only in maximizing his own happiness. Aaron thinks to himself "Whether or not I go to Heaven has already been decided, regardless of my actions on Earth. Therefore, I might as well try to have as much fun as possible, knowing it won't effect the afterlife either way." He spends his days in sex, debauchery, and anti-theist blog comments.

Zachary sees Aaron and thinks "That sinful man is thus proven one of the reprobate, and damned to Hell. I will avoid his fate by living a pious life." Zachary becomes a great minister, famous for his virtue, and when he dies his entire congregation concludes he must have been one of the elect.
If you were a Calvinist, which path would you take?
This problem I found a bit trickier than the previous two (though, to be fair, Newcomb's was much more confusing before I learned about TDT). So, in the interest of testing my understanding of the principles behind each decision, I ask myself: is this analogous to Newcomb's, or to smoker's lesion (or neither)? What makes them different? Why is it that I am certain that imitating the choice of those who end up better off in Newcomb's is a good idea, but I find it laughable in smoker's lesion?

Think about this: In Newcomb's, you want to be the kind of person who chooses to one-box, because one-boxers have a box with one million dollars there for the taking. (In fact, a CDT who knows in advance they will face Newcomb's problem, would choose to pre-commit to one-box if the option was available). In smoker's, you want to be the kind of person who doesn't smoke, but only to the extent that such a thing means you don't have the cancer-causing gene. Indeed, you could use, say, a nicotine patch to get rid of your desire to smoke, but it would be pointless as a cancer prevention measure and thus have no particular reason to do so.

Could something similar be said about Newcomb's? At first, it might appear that this would be equivalent to someone giving you a brain surgery to make you a one-boxer, but only after Omega left and the box's contents are fixed. But wait. Omega is a superintelligence who can perfectly (or near-perfectly) predict your decisions. If you had the choice to self-modify to one-box, then Omega would know of this, and also know if you would go with it or not, and fill the box appropriately. Perhaps if Omega Prime, the even more powerful superintelligence, had intervened and offered to make you a one-boxer but guaranteed that Omega didn't know of this, that would be analogous. But there's nothing in your own power you could do that would make you a one-boxer without also meaning that one-boxing was a viable strategy, since Omega would predict your self-modification.

This is key. In smoker's lesion, making yourself a non-smoker through any means other than changing your cancer-causing gene is pointless. In particular, choosing not to smoke falls under that category. In Newcomb's, making yourself a one-boxer through any means that are predictable by Omega is not pointless. In particular, choosing to just take box B falls under that category.

So, in Calvin, is choosing not to sin useless or not? Well, here I am unsure about the actual theology, so let it be clear that whatever I say applies to actual Calvinism only to the extent that it is correctly represented by the description of the problem. That aside:

The problem specifies that a sinning or virtuous nature are not the cause of damnation or blessing. God does not use his omniscience to see if I will be a sinner or saint and determine my eternal fate accordingly, rather he determines it based on something else entirely, or random chance, or whatever, and then as a result I act however it is I do. Thus, choosing to be virtuous will not mean that God predicted I would be virtuous, and dictated my fate accordingly. It just means I'm acting virtuous. If I was damned, I'm still damned, just wasting my time not sinning.

One caveat, though. The problem is specified in terms of always-never, the damned always sin, the virtuous always lead righteous lives. Which means that any universe in which I am simultaneously damned and not sinning is in contradiction. This is because the fact of whether I sin or not is, in the problem, specified not by my decision theory but by my connection to God. This, I contend, means it's not a problem where decision theory matters. If the problem simply said that there is a high probability of sinning (as high as you want except exactly 1), then you could use decision theory. This is not an attempt to weasel out;. my decision in both cases is to sin. It just happens that in the first case, my decision cannot affect my behaviour in that particular aspect, by the specifications of the problem.

And before you say the same is true of Newcomb's: The specification is that, out of thousands of tries, Omega has not yet made a mistake. This does not need to correspond to Omega being incapable of failing, only to its chance of failure being small (presumably less than one in several thousands). The same principles hold if Omega is right 90% of the time, or 60% of the time for that matter. (the average one-boxing payout would be 60% of $1,000,000, which is more than the average two-boxing payout, 60% of $1,000 + 40% of $1,001,000). Phrasing the problem in those terms doesn't change the decision-theoretic answer, but it requires a type of mathematical thinking some people tend to ignore.

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