Why one-box?

Two-boxers think that decisions are things that can just fall out of the sky uncaused. (This can be made precise by a suitable description of how two-boxers set up the relevant causal diagram; I found Anna Salamon's explanation of this particularly clear.) This is a view of how decisions work driven by intuitions that should be dispelled by sufficient knowledge of cognitive and / or computer science. I think acquiring such background will make you more sympathetic to the perspective that one should think in terms of winning agent types and not winning decisions.

I also think there's a tendency among two-boxers not to take the stakes of Newcomb's problem seriously enough. Suppose that instead of offering you a million dollars Omega offers to spare your daughter's life. Now what do you do?

Basically: EDT/UDT has simple arguments in its favor and seems to perform well. There don't seem to be any serious arguments in favor of CDT, and the human intuition in its favor seems quite debunkable. So it seems like the burden of proof is on CDT, to justify why it isn't crazy. It may be that CDT has met that burden, but I'm not aware of it.

A. The dominance arguments in favor of two-boxing seem quite weak. They tend to apply verbatum to playing prisoner's dilemmas against a mirror (If the mirror cooperates you'd prefer defect, if the mirror defects you'd prefer defect, so regardless of the state of nature you'd prefer defect). So why do you not accept the dominance argument for a mirror, but accept it in the case of Newcomb-like problems? To discriminate the cases it seems you need to make an assumption of no causal connection, or a special role for time, in your argument.

This begs the question terribly---why is a causal connection privileged? Why is the role of time privileged? As far as I can tell these two things are pretty arbitrary and unimportant. I'm not aware of any strong philosophical arguments for CDT, besides "it seems intuitively sensible to a human," and see below for the debunking of those intuitions. (Again, maybe there are better arguments here, but I've never encountered one. Basically I'm looking for any statement of a kind of dominance principle over states of nature, which doesn't look completely arbitrary and is also at all plausible.)

B. A sophisticated interpretation of EDT (called UDT around here) seems to perform well in all cases we've considered, in the sense that an agent making good decisions will achieve good outcomes. I think this is strong evidence in favor of a theory which purports to say which actions are good, since good decisions ought to lead to good outcomes; I agree its not a knock-down argument, but again I know of no serious counterarguments.

C. It seems that EDT is supported by the simplest philosophical arguments. We need to choose between outcomes in which we make decision A vs. decision B. It makes sense to choose between outcomes which we consider to be possible (in which we make decision A or decision B). CDT doesn't do this, and considers outcomes which are inconsistent with our knowledge of the situation. This isn't enough to pin down EDT uniquely (though further arguments can), but it does seem like a strong point in favor of EDT over CDT.

D. An agent living in an environment like humans' will do fine by using CDT, because the only effects of their decisions are causal. CDT is much simpler to run than EDT because it doesn't rely on a strong self-model (doing EDT without a good self-model results in worse decisions than CDT in reasonable situations; this is basically what the claims that EDT performs badly in such-and-such a situation amount to, at least the ones I have seen). So it seems like we can pretty easily explain why humans have an intuition in favor of CDT, and it seems like extremely weak evidence against EDT/UDT.

There are no two-boxers in foxholes.

The intuition pump that got me to be a very confident one-boxer is the idea of submitting computer code that makes a decision, rather than just making a decision.

In this version, you don't need an Omega - you just need to run the program. It's a lot more obvious that you ought to submit a program that one-boxes than it is obvious that you ought to one-box. You can even justify this choice on causal decision-theory grounds.

With the full Newcomb problem, the causality is a little weird. Just think of yourself as a computer program with partial self-awareness. Deciding whether to one-box or two-box updates the "what kind of decision-making agent am I" node, which also caused Omega to either fill or not fill the opaque box.

Yes, it's wonky causality - usually the future doesn't seem to affect the past. Omega is just so unlikely that given that you're talking to Omega, you can justify all sorts of slightly less unlikely things.

So I'm turning to you guys to ask for help figuring out whether I should be a staunch one-boxer too.

Only if you like money.

The optimal thing would be to have Omega think that you will one-box, but you actually two box. You'd love to play Omega for a fool, but the problem explicitly tells you that you can't, and that Omega can somehow predict you.

Omega has extremely good predictions. if you've set your algorithm in such a state that Omega will predict that you one-box, you will be unable to do anything but one-box - your neurons are set in place, causal lines have already insured your decision, and free will doesn't exist in the sense that you can change your decision after the fact.

The problem is no free lunch. Any decision theory is going to fail somewhere. The case for privileging Newcomb as a success goal over all other considerations has not, in fact, been made.

[Saying same thing as everyone else, just different words. Might work better, might not.]

Suppose once Omega explains everything to you, you think 'now either the million dollars are there or aren't and my decision doesn't affect shit.' True, your decision now doesn't affect it - but your 'source code' (neural wiring) contains the information 'will in this situation think thoughts that support two-boxing and accept them.' So, choosing to one-box is the same as being the type of agent who'll one-box.
The distinction between agent type and decision is artificial. If your decision is to two-box, you are the agent-type who will two-box. There's no two ways about it. (As others have pointed out, this has been formalised by Anna Salomon.)

The only way you can get out of this is if you believe in free will as something that exists in some metaphysical sense. Then to you, Omega being this accurate is beyond the realm of possibility and therefore the question is unfair.

My problem with causal decision theory is that it treats the past different from the future for no good reason. If you read the quantum physics sequence, particularly the part about timeless physics, you will find that time is most likely not even an explicit dimension. The past is more likely to be known, but it's not fundamentally different from the future.

The probability of box A having money in it is significantly higher given that you one box then the probability given that you do not. What more do you need to know?

Does Omega one-box against Omega?

Here is another way to think about this problem.

Imagine if instead of Omega you were on a futuristic game show. As you go onto the show, you enter a future-science brain scanner that scans your brain. After scanning, the game show hosts secretly put the money into the various boxes behind stage.

You now get up on stage and choose whether to one or two box.

Keep in mind that before you got up on the show, 100 other contestants played the game that day. All of the two-boxers ended up with less money than the one-boxers. As an avid watcher of the show, you clearly remember that in every previous broadcast (one a day for ten years) the one-boxers did better than the two-boxers.

Can you honestly tell me that the superior move here is two-boxing? Where does the evidence point? If one strategy clearly and consistently produces inferior results compared to another strategy, that should be all we need to discard it as inferior.

Didn't we have a thread about this really recently?

Anyhow, to crib from the previous thread - an important point is reflective equilibrium. I shouldn't be able to predict that I'll do badly - if I know that, and the problem is "fair" in that it's a decision-determined, I can just make the other decision. Or if I'm doing things a particular way, and I know that another way of doing things would be better, and the problem is "fair" in that I can choose how to do things, I can just do things the better way. To sit and stew and lose anyhow is just cray talk.

A totally different and very good example problem where this shows up was covered by Wei Dai here.

Okay, those with a two-boxing agent type don't win but the two-boxer isn't talking about agent types. They're talking about decisions. So they are interested in what aspects of the agent's winning can be attributed to their decision and they say that we can attribute the agent's winning to their decision if this is caused by their decision. This strikes me as quite a reasonable way to apportion the credit for various parts of the winning.

Do I understand it correctly that you're trying to evaluate the merits of a decision (to two-box) in isolation of the decision procedure that produced it? Because that's simply incoherent if the payoffs of the decision depend on your decision procedure.

To put it succinctly, Omega knows me far better than I know myself. I'm not going to second guess him/her.

The case of CDT vs Newcomb-like problems to me has a lot of similarity with the different approaches to probability theory.
In CDT you are considering only one type of information, i.e. causal dependency, to construct decision trees. This is akin to define probability as the frequency of some process, so that probability relations become causal ones. Other approaches like TDT construct decisions using causal and logical dependency, as the induction logic approach to probability does.
The Newcomb is not designed to be "unfair" to CDT, it is designed to show the limits of causal approach, exactly like calculating past sampling distribution from future extractions is a problem solvable only from the second approach (see the third chapter of Jaynes' book).

That said, we can argue about what rationality should really be: just the correct execution of whatever type of agency a system has? Or the general principle that an agent should be able to reason about whatever situation is at hand and correctly deal with it, using all the available information?
My sympathy goes to the second approach, not just because it seems to be more intuitively appealing, but also because it will be a fundamental necessity of a future AI.

Okay, those with a two-boxing agent type don't win but the two-boxer isn't talking about agent types. They're talking about decisions.

The problem doesn't care whether you are the type of agent who talks about agent types or the type of agent who talks about decisions. The problem only cares about which actions you choose.

Consider the following two mechanisms for a Newcomb-like problem.

A. T-Omega offers you the one or two box choice. You know that T-Omega used a time machine to see if you picked one or two boxes, and used that information to place/not place the million dollars.

B. C-Omega offers you the one or two box choice. You know that C-Omega is con man, that pretends great predictive powers on each planet he visits. Usually he fails, but on Earth he gets lucky. C-Omega uses a coin flip to place/not place the million dollars.

I claim the correct choice is to one box T-Omega, and two box C-Omega.

Can someone explain how it is in the “original” problem?
That is, what mechanism does the “real” Omega use for making his decision?

[Two boxers] are interested in what aspects of the agent's winning can be attributed to their decision and they say that we can attribute the agent's winning to their decision if this is caused by their decision. This strikes me as quite a reasonable way to apportion the credit for various parts of the winning.

What do you mean by "the agent's winning can be attributed to their decision"? The agent isn't winning! Calling losing winning strikes me as a very unreasonable way to apportion credit for winning.

It would be helpful to me if you defined how you're attributing winning to decisions. Maybe taboo the words winning and decision. At the moment I really can't get my head around what you're trying to say.

The one problem I had with Yudkowsky's TDT paper (which I didn't read very attentively, mind you, so correct me if I'm wrong) was the part where he staged a dramatic encounter where a one-boxer was pleading with a wistful two-boxing agent who wished he was a one-boxer to change his algorithm to choose just one box. It occurred to me that even if the two-boxer listened to her, then his algorithm would have been altered by totally external factors. For the superintelligence setting up the problem to have predicted his change of mind, he would have had to simulate not a single agent, but the whole two agent system in order to predict this particular scenario correctly. Future settings might be different.

PS. One-boxers tend to make errors like this quite often, actually, illegitimately reducing the whole problem to one algorithm run by a single agent. (Actually a lot of decision theorists do that IMO. I've just been introduced to the world of decision theory by one-boxers.)