Two-boxing, smoking and chewing gum in Medical Newcomb problems

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Jun 29, 2015

I am currently learning about the basics of decision theory, most of which is common knowledge on LW. I have a question, related to why EDT is said not to work.

Consider the following Newcomblike problem: A study shows that most people who two-box in Newcomblike problems as the following have a certain gene (and one-boxers don't have the gene). Now, Omega could put you into something like Newcomb's original problem, but instead of having run a simulation of you, Omega has only looked at your DNA: If you don't have the "two-boxing gene", Omega puts $1M into box B, otherwise box B is empty. And there is $1K in box A, as usual. Would you one-box (take only box B) or two-box (take box A and B)? Here's a causal diagram for the problem:

Since Omega does not do much other than translating your genes into money under a box, it does not seem to hurt to leave it out:

I presume that most LWers would one-box. (And as I understand it, not only CDT but also TDT would two-box, am I wrong?)

Now, how does this problem differ from the smoking lesion or Yudkowsky's (2010, p.67) chewing gum problem? Chewing Gum (or smoking) seems to be like taking box A to get at least/additional $1K, the two-boxing gene is like the CGTA gene, the illness itself (the abscess or lung cancer) is like not having $1M in box B. Here's another causal diagram, this time for the chewing gum problem:

As far as I can tell, the difference between the two problems is some additional, unstated intuition in the classic medical Newcomb problems. Maybe, the additional assumption is that the actual evidence lies in the "tickle", or that knowing and thinking about the study results causes some complications. In EDT terms: The intuition is that neither smoking nor chewing gum gives the agent additional information.

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I think UDT reasoning would go like this (if translated to human terms). There are two types of mathematical multiverse, only one of which is real (i.e., logically consistent). You as a UDT agent gets to choose which one. In the first one, UDT agents one-box in this Genetic Newcomb Problem (GNP), so the only genes that statistically correlate with two-boxing are those that create certain kinds of compulsions overriding deliberate decision making, or for other decision procedures that are not logically correlated with UDT. In the second type of mathematical multiverse, UDT agents two-box in GNP, so the list of genes that correlate with two-boxing also includes genes for UDT.

Which type of multiverse is better? It depends on how Omega chooses which gene to look at, which is not specified in the OP. To match the Medical Newcomb Problem as closely as possible, let's assume that in each world (e.g., Everett branch) of each multiverse, Omega picks a random gene look at (from a list of all human genes), and puts $1M in box B for you if you don't have that gene. You live in a world where Omega happened to pick a gene that correlates with two-boxing. Under this assumption, the second type of multiverse is better because the number and distribution of boxes containing $1M is exactly the same in both multiverses, but in the second type of multiverse UDT agents get the additional $1K.

I presume that most LWers would one-box.

I think the reason we have an intuition that we should one-box in the GNP is that when we first read the story, we implicitly assume something else about what Omega is doing. For example, suppose instead of the above, in each world Omega looks at the most common gene correlated with two-boxing and puts $1M in box B if you don't have that gene. If the gene for UDT is the most common such gene in the second multiverse (where UDT two-boxes), then the first multiverse is better because it has more boxes containing $1M, and UDT agents specifically all get $1M instead of $1K.

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Thank you for this elaborate response!!

Omega picks a random gene look at (from a list of all human genes), and puts $1M in box B for you if you don't have that gene

Why would Omega look at other human genes and not the two-boxing (correlated) gene(s) in any world?

Under this assumption, the second type of multiverse is better because the number and distribution of boxes containing $1M is exactly the same in both multiverses, but in the second type of multiverse UDT agents get the additional $1K.

Maybe I overlook something or did not describe the problem very well, but in the second multiverse UDT agents two-box, therefore UDT agents (probably) have the two-boxing gene and don't get the $1M. In the first multiverse, UDT agents one-box, therefore UDT agents (probably) don't have the one-boxing gene and get the $1M. So, the first multiverse seems to be better than the second.

I think the reason we have an intuition that we should one-box in the GNP is that when we first read the story, we implicitly assume something else about what Omega is doing. For example, suppose instead of the above, in each world Omega looks at the most common gene correlated with two-boxing and puts $1M in box B if you don't have that gene.

Yes, this is more or less the scenario, I was trying to describe. Specifically, I wrote:

Omega has only looked at your DNA: If you don't have the "two-boxing gene", Omega puts $1M into box B, otherwise box B is empty.

So, it's part of the GNP that Omega has looked at the "two-boxing gene" or (more realistically perhaps) the "most common gene correlated with two-boxing".

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Why would Omega look at other human genes and not the two-boxing (correlated) gene(s) in any world?

I was trying to create a version of the problem that corresponds more closely to MNP, where the fact that a single gene correlates with both chewing gum and abscess is a coincidence, not the result of some process looking for genes correlated with chewing gum, and giving people with those genes abscesses.

Maybe I overlook something or did not describe the problem very well, but in the second multiverse UDT agents two-box, therefore UDT agents (probably) have the two-boxing gene and don't get the $1M. In the first multiverse, UDT agents one-box, therefore UDT agents (probably) don't have the one-boxing gene and get the $1M. So, the first multiverse seems to be better than the second.

Do you see that assuming Omega worked the way I described, then the number and distribution of boxes containing $1M is exactly the same in the two multiverses, therefore the second multiverse is better?

So, it's part of the GNP that Omega has looked at the "two-boxing gene" or (more realistically perhaps) the "most common gene correlated with two-boxing".

I think this is what makes your version of GNP different from MNP, and why we have different intuitions about the two cases. If there is someone or something who looked the most common gene correlated with two-boxing (because it was the most common gene correlated with two-boxing, rather than due to a coincidence), then by changing whether you two-box, you can change whether other UDT agents two-box, and hence which gene is the most common gene correlated with two-boxing, and hence which gene Omega looked at, and hence who gets $1M in box B. In MNP, there is no corresponding process searching for genes correlated with gum chewing, so you can't try to influence that process by choosing to not chew gum.

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Do you see that assuming Omega worked the way I described, then the number and distribution of boxes containing $1M is exactly the same in the two multiverses, therefore the second multiverse is better?

Yes, I think I understand that now. But in your version the two-boxing gene practically does not cause the $1M to be in box B, because Omega mostly looks at random other genes. Would that even be a Newcomblike problem?

I think this is what makes your version of GNP different from MNP, and why we have different intuitions about the two cases. If there is someone or something who looked the most common gene correlated with two-boxing (because it was the most common gene correlated with two-boxing, rather than due to a coincidence), then by changing whether you two-box, you can change whether other UDT agents two-box, and hence which gene is the most common gene correlated with two-boxing, and hence which gene Omega looked at, and hence who gets $1M in box B.

In EY's chewing gum MNP, it seems like CGTA causes both the throat abscess and influences people to chew gum. (See p.67 of the TDT paper ) (It gets much more complicated, if evolution has only produced a correlation between CGTA and another chewing gum gene.) The CGTA gene is always read, copied into RNA etc., ultimately leading to throat abscesses. (The rest of the DNA is used, too, but only determines the size of your nose etc.) In the GNP, the two-boxing gene is always read by Omega and translated into a number of dollars under box B. (Omega can look at the rest of the DNA, too, but does not care.) I don't get the difference, yet, unfortunately.

In MNP, there is no corresponding process searching for genes correlated with gum chewing, so you can't try to influence that process by choosing to not chew gum.

I don't understand UDT, yet, but it seems to me that in the chewing gum MNP, you could not chew gum, thereby changing whether other UDT agents chew gum, and hence whether UDT agents' genes contain CGTA. Unless you know that CGTA has no impact on how you ultimately resolve this problem, which is not stated in the problem description and which would make EDT also chew gum.

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Hm, this is a really interesting idea.

The trouble is that it's tricky to apply a single decision theory to this problem, because by hypothesis, this gene actually changes which decision theory you use! If I'm a TDT agent, then this is good evidence I have the "TDT-agent gene," but in this problem I don't actually know whether the TDT-gene is the one-box gene or the two-box gene. If TDT leads to one-boxing, then it recommends two-boxing - but if it provably two-boxes it is the "two-box gene" and gets the bad outcome. This is to some extent an "evil decision problem." Currently I'd one-box, based on some notion of resolving these sorts of problems through more UDT-ish proof-based reasoning (though it has some problems). Or in TDT-language, I'd be 'controlling' whether the TDT-gene was the two-box gene by picking the output of TDT.

However, this problem becomes a lot easier if most people are not actually using any formal reasoning, but are just doing whatever seems like a good idea at the time. Like, the sort of reasoning that leads to people actually smoking. If I'm dropped into this genetic Newcomb's problem, or into the smoking lesion problem, and I learn that almost all people in the data set I've seen were either bad at decision theory or didn't know the results of the data, then those people no longer have quite the same evidential impact about my current situation, and I can just smoke / two-box. It's only when those people and myself are in symmetrical situations (similar information, use similar decision-making processes) that I have to "listen" to them.

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Yes, all of this is basically correct. However, it is also basically the same in the original Newcomb although somewhat more intuitive. In the original problem Omega decides to put the one million or not depending on its estimate of what you will do, which likely depends on "what kind of person" you are, in some sense. And being this sort of person is also going to determine what kind of decision theory you use, just as the gene does in the genetic version. The original Newcomb is more intuitive, though, because we can more easily accept that "being such and such a kind of person" could make us use a certain decision theory, than that a gene could do the same thing.

Even the point about other people knowing the results or using certain reasoning is the same. If you find an Omega in real life, but find out that all the people being tested so far are not using any decision theory, but just choosing impulsively, and Omega is just judging how they would choose impulsively, then you should take both boxes. It is only if you know that Omega tends to be right no matter what decision theory people are using, that you should choose the one box.

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I am not entirely sure, I understand your TDT analysis, maybe that's because I don't understand TDT that well. I assumed that TDT would basically just do what CDT does, because there are no simulations of the agent involved. Or do you propose that checking for the gene is something like simulating the agent?

This is to some extent an "evil decision problem."

It does not seem to be more evil than Newcomb's problem, but I am not sure, what you mean by "evil". For every decision theory, it is possible, of course, to set up some decision problem, where this decision theory loses. Would you say that I set up the "genetic Newcomb problem" specifically to punish CDT/TDT?

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The general mistake that many people are making here is to think that determinism makes a difference. It does not.

Let's say I am Omega. The things that are playing are AIs. They are all 100% deterministic programs, and they take no input except an understanding of the game. They are not allowed to look at their source code.

I play my part as Omega in this way. I examine the source code of the program. If I see that it is a program that will one-box, I put the million. If I see that it is a program that will two-box, I do not put the million.

Note that determinism is irrelevant. If a program couldn't use a decision theory or couldn't make a choice, just because it is a determinate program, then no AI will ever work in the real world, and there is no reason that people should work in the real world either.

Also note that the only good decision in these cases is to one-box, even though the programs are 100% determinate.

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You're describing regular Newcomb, not this gene version. (Also note that Omega needs to have more processing power than the programs to do what you want it to do, just like the human version.) The analogue would be defining a short program that Omega will run over the AIs code, that predicts what the AI will output correctly 99% of the time. Then it becomes a question of whether any given AI can outwit the program. If an AI thinks the program won't work on it, for whatever reason (by which I mean "conditioning on myself picking X doesn't cause my estimate of the prediction program outputting X to change, and vice-versa"), it's free to choose whatever it wants to.

Getting back to humans, I submit that a certain class of people that actually think about the problem will induce a far greater failure rate in Omega, and that therefore that severs the causal link between my decision and Omega's, in the same way as an AI might be able to predict that the prediction program won't work on it.

As I said elsewhere, were this incorrect, my position would change, but then you probably aren't talking about "genes" anymore. You shouldn't be able to get 100% prediction rates from only genes.

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It should be obvious that there is no difference between regular Newcomb and genetic Newcomb here. I examine the source code to see whether the program will one-box or not; that is the same as looking at its genetic code to see if it has the one-boxing gene.

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Upvoting: This is a very good post which has caused everybody's cached decision-theory choices to fail horribly because they're far too focused on getting the "correct" answer and then proving that answer correct and not at all focused on actually thinking about the problem at hand. Enthusiastic applause.

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I may as well repeat my thoughts on Newcomb's, decision theory, and so on. I come to this from a background in decision analysis, which is the practical version of decision theory.

You can see decision-making as a two-step, three-state problem: the problem statement is interpreted to make a problem model, which is optimized to make a decision.

If you look at the wikipedia definitions of EDT and CDT, you'll see they primarily discuss the optimization process that turns a problem model into a decision. But the two accept different types of problem models; EDT operates on joint probability distributions and CDT operates on causal models. Since the type of the interior state is different, the two imply different procedures to interpret problem statements and optimize those models into decisions.

To compare the two simply, causal models are just more powerful than joint probability distributions, and the pathway that uses the more powerful language is going to be better. A short attempt to explain the difference: in a Bayes net (i.e. just a joint probability distribution that has been factorized in an acyclic fashion), the arrows have no physical meaning--they just express which part of the map is 'up' and which is 'down.' In a causal model, the arrows have physical meaning--causal influence flows along those arrows only in directions with arrows, and so the arrows represent which direction gravity pulls in. One can turn a map upside down without changing its correspondence to the territory; one cannot reverse gravity without changing the territory.

Because there are additional restrictions on how the model can be written, one can get additional information out of reading the model.

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I have never agreed that there is a difference between the smoking lesion and Newcomb's problem. I would one-box, and I would not smoke. Long discussion in the comments here.

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Interesting, thanks! I thought that it was more or less consensus that the smoking lesion refutes EDT. So, where should I look to see EDT refuted? Absent-minded driver, Evidential Blackmail, counterfactual mugging or something else?

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I assume that the one-boxing gene makes a person generically more likely to favor the one-boxing solution to Newcomb. But what about when people learn about the setup of this particular problem? Does the correlation between having the one-boxing gene and inclining toward one-boxing still hold? Are people who one-box only because of EDT (even though they would have two-boxed before considering decision theory) still more likely to have the one-boxing gene? If so, then I'd be more inclined to force myself to one-box. If not, then I'd say that the apparent correlation between choosing one-boxing and winning breaks down when the one-boxing is forced. (Note: I haven't thought a lot about this and am still fairly confused on this topic.)

I'm reminded of the problem of reference-class forecasting and trying to determine which reference class (all one-boxers? or only grudging one-boxers who decided to one-box because of EDT?) to apply for making probability judgments. In the limit where the reference class consists of molecule-for-molecule copies of yourself, you should obviously do what made the most of them win.

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But what about when people learn about the setup of this particular problem? Does the correlation between having the one-boxing gene and inclining toward one-boxing still hold?

Yes, it should also hold in this case. Knowing about the study could be part of the problem and the subjects of the initial study could be lied to about a study. The idea of the "genetic Newcomb problem" is that the two-boxing gene is less intuitive than CGTA and that its workings are mysterious. It could make you be sure that you have or don't have the gene. It could make be comfortable with decision theories whose names start with 'C', interpret genetical Newcomb problem studies in a certain way etc. The only thing that we know is that is causes us to two-box, in the end. For CGTA, on the other hand, we have a very strong intuition that it causes a "tickle" or so that could be easily overridden by us knowing about the first study (which correlates chewing gum with throat abscesses). It could not possibly influence what we think about CDT vs. EDT etc.! But this intuition is not part of the original description of the problem.

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I think we need to remember here the difference between logical influence and causal influence?

My genes can cause me to be inclined towards smoking, and my genes can cause me to get lesions. If I choose to smoke, not knowing my genes, then that's evidence for what my genes say, and it's evidence about whether I'll get lesions; but it doesn't actually causally influence the matter.

My genes can incline me towards one-boxing, and can incline Omega towards putting $1M in the box. If I choose to two-box despite my inclinations, then that provides me with evidence about what Omega did, but it doesn't causally influence the matter.

If I don't know which of two worlds I'm in, I can't increase the probability of one by saying "in world A, I'm more likely to do X than in world B, so I'm going to do X". If nothing else, if I thought that worked, then I would do it whatever world I was in, and it would no longer be true.

In standard Newcomb, my inclination to one-box actually does make me one-box. In this version, my inclination to one-box is just a node that you've labelled "inclination to one-box", and you've said that Omega cares about the node rather than about whether or not I one-box. But you're still permitting me to two-box, so that node might just as well be "inclination to smoke".

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In the original Newcomb's problem, am I allowed to say "in the world with the million, I am more likely to one-box than in the world without, so I'm going to one-box"? If I thought this worked, then I would do it no matter what world I was in, and it would no longer be true...

Except that it is still true. I can definitely reason this way, and if I do, then of course I had the disposition to one-box, and of course Omega put the million there; because the disposition to one-box was the reason I wanted to reason this way.

And likewise, in the genetic variant, I can reason this way, and it will still work, because the one-boxing gene is responsible for me reasoning this way rather than another way.

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In the original, you would say: "in the world where I one-box, the million is more likely to be there, so I'll one-box".

the one-boxing gene is responsible for me reasoning this way rather than another way.

If there's a gene that makes you think black is white, then you're going to get killed on the next zebra crossing. If there's a gene that makes you misunderstand decision theory, you're going to make some strange decisions. If Omega is fond of people with that gene, then lucky you. But if you don't have the gene, then acting like you do won't help you.

Another reframing: in this version, Omega checks to see if you have the photic sneeze reflex, then forces you to stare at a bright light and checks whether or not you sneeze. Ve gives you $1k if you don't sneeze, and independently, $1M if you have the PSR gene.

If I can choose whether or not to sneeze, then I should not sneeze. Maybe the PSR gene makes it harder for me to not sneeze, in which case I can be really happy that I have to stifle the urge to sneeze, but I should still not sneeze.

But if the PSR gene just makes me sneeze, then why are we even asking whether I should sneeze or not?

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I think this is addressed by my top level comment about determinism.

But if you don't see how it applies, then imagine an AI reasoning like you have above.

"My programming is responsible for me reasoning the way I do rather than another way. If Omega is fond of people with my programming, then I'm lucky. But if he's not, then acting like I have the kind of programming he likes isn't going to help me. So why should I one-box? That would be acting like I had one-box programming. I'll just take everything that is in both boxes, since it's not up to me."

Of course, when I examined the thing's source code, I knew it would reason this way, and so I did not put the million.

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