the question for the two-boxer will be whether the decision causally influences the result of this brain scan. If yes, then, the two-boxer will one-box (weird sentence). If no, the two-boxer will two-box.

How would it not causally influence the brain scan? Are you saying two-boxers can make decisions without using their brains? ;-)

In any event, you didn't answer the question I asked, which was at what point in time does the two-boxer label the decision "irrational". Is it still "irrational" in their estimation to two-box, in the case where Omega decides after they do?

Notice that in both cases, the decision arises from information already available: the state of the chooser's brain. So even in the original Newcomb's problem, there is a causal connection between the chooser's brain state and the boxes' contents. That's why I and other people are asking what role time plays: if you are using the correct causal model, where your current brain state has causal influence over your future decision, then the only distinction two-boxers can base their "irrational" label on is time, not causality.

The alternative is to argue that it is somehow possible to make a decision without using your brain, i.e., without past causes having any influence on your decision. You could maybe do that by flipping a coin, but then, is that really a "decision", let alone "rational"?

If a two-boxer argues that their decision cannot cause a past event, they have the causal model wrong. The correct model is one of a past brain state influencing both Omega's decision and your own future decision.

For me, the simulation argument made it obvious that one-boxing is the rational choice, because it makes clear that your decision is algorithmic. "Then I'll just decide differently!" is, you see, still a fixed algorithm. There is no such thing as submitting one program to Omega and then running a different one, because you are the same program in both cases -- and it's that program that is causal over both Omega's behavior and the "choice you would make in that situation". Separating the decision from the deciding algorithm is incoherent.

As someone else mentioned, the only way the two-boxer's statements make any sense is if you can separate a decision from the algorithm used to arrive at that decision. But nobody has presented any concrete theory by which one can arrive at a decision without using some algorithm, and whatever algorithm that is, is your "agent type". It doesn't make any sense to say that you can be the type of agent who decides one way, but when it actually comes to deciding, you'll decide another way.

How does your hypothetical two-boxer respond to simulation or copy arguments? If you have no way of knowing whether you're the simulated version of you, or the real version of you, which decision is rational then?

To put it another way, a two-boxer is arguing that they ought to two-box while simultaneously not being the sort of person who would two-box -- an obvious contradiction. The two-boxer is either arguing for this contradiction, or arguing about the definitions of words by saying "yes, but that's not what 'rational' means".

Indeed, most two-boxers I've seen around here seem to alternate between those two positions, falling back to the other whenever one is successfully challenged.

the two-boxer says that you should precommit to later making an irrational decision

I think the piece that this hypothetical two-boxer is missing is that they are acting as though the problem is cheating, or alternatively, that the premises can be cheated. That is, that you are able to make a decision that wasn't predictable beforehand. If your decision is predictable, two boxing is irrational, even considered as a single decision.

Try this analogy: instead of predicting your decision in advance, Omega simply scans your brain to determine what to put in the boxes, at the very moment you make the decision.

Does your hypothetical two-boxer still argue that one-boxing in this scenario is "irrational"?

If so, I cannot make sense of their answer. But if not, then the burden falls on the two boxer to explain how this scenario is any different from a prediction made a fraction of a millisecond sooner. How far before or after the point of decision does the decision become "rational" or "irrational" in their mind? (I use quotes here because I cannot think of any coherent definition of those terms that's still consistent with the hypothetical usage.)

[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.

The LW approach has focused on finding agent types that win on decision problems. Lots of the work has been in trying to formalize TDT/UDT, providing sketches of computer programs that implement these informal ideas. Having read a fair amount of the philosophy literature (including some of the recent stuff by Egan, Hare/Hedden and others), I think that this agent/program approach has been extremely fruitful. It has not only given compelling solutions to a large number of problems in the literature (Newcomb's, trivial coordination problems like Stag Hunt that CDT fails on, PD playing against a selfish copy of yourself) but it also has elucidated the deep philosophical issues that the Newcomb Problem dramatizes (concerning pre-commitment, free will / determinism and uncertainty about purely apriori/logical question). The focus on agents as programs has brought to light the intricate connection between decision making, computability and logic (esp. Godelian issues) --- something merely touched on in the philosophy literature.

These successes provide a sufficient reason to push the agent-centered approach (even if there were no compelling foundational argument that the 'decision' centered approach was incoherent). Similarly, I think there is no overwhelming foundational argument for Bayesian probability theory but philosophers should study it because of its fruitfulness in illuminating many particular issues in the philosophy of science and the foundations of statistics (not to mention its success in practical machine learning and statistics).

This response may not be very satisfying but I can only recommend the UDT posts (http://wiki.lesswrong.com/wiki/Updateless_decision_theory) and the recent MIRI paper http://intelligence.org/files/RobustCooperation.pdf.)

Rough arguments against the decision-centered approach:

Point 1

Suppose I win the lottery after playing 10 times. My decision of which numbers to pick on the last lottery was the cause of winning money. (Whereas previous decisions over numbers produced only disutility). But it's not clear there's anything interesting about this distinction. If I lost money on average, the important lesson is the failing of my agent-type (i.e. the way my decision algorithm makes decisions on lottery problems).

And yet in many practical cases that humans face, it is very useful to look back at which decisions led to high utility. If we compare different algorithms playing casino games, or compare following the advice of a poker expert vs. a newbie, we'll get useful information by looking at the utility caused by each decision. But this investigation of decisions that cause high utility is completely explainable from the agent-centered approach. When simulation and logical correlations between agents are not part of the problem, the optimal agent will make decisions that cause the most utility. UDT/TDT and variants all (afaik) act like CDT in these simple decision problems. If we came upon a Newcomb problem without being told the setup (and without any familiarity with these decision theory puzzles), we would see that the CDTer's decisions were causing utility and the EDTer's decisions were not causing any utility. The EDTer would look like lunatic with bizarrely good luck. Here we are following a local causal criterion in comparing actions. While usually fine, we would clearly be missing out on an important part of the story in the Newcomb problem.

Point 2

In AI, we want to build decision making agents that win. In life, we want to improve our decision making so that we win. Thinking about the utility caused by individual decisions may be a useful subgoal in coming up with winning agents, but it seems hard to see it as the central issue. The Newcomb problem (and the counterfactual mugging and Parfit's Hitchhiker) make clear that a local Markovian criterion (e.g. choose the action that will cause the highest utility, ignoring all previous actions/commitments) is inadequate for winning.

Point 3

The UDT one-boxer's agent type does not cause utility in the NP. However it does logically determine the utility. (More specifically, we could examine the one-boxing program as a formal system and try to isolate which rules/axioms lead to its one boxing in this type of problem). Similarly, if two people were using different sets of axioms (where one set is inconsistent), we might point to one of the axioms and say that its inclusion is what determines the inconsistency of the system. This is a mere sketch, but it might be possible to develop a local criterion by which "responsibility" for utility gains can be assigned to particular aspects of an agent.

It's clear that we can learn about good agent types by examining particular decisions. We don't have to always work with a fully specified program. (And we don't have the code of any AI that can solve decision problems the way humans can). So the more local approach may have some value.

The question is, how much of this utility can be attributed to the agent's decision rather than type.

That's the wrong question, because it presupposes that the agent's decision and type are separable.

In that case: the two-boxer isn't just wrong, they're double-wrong. You can't just come up with some related-but-different function ("caused gain") to maximize. The problem is about maximizing the money you receive, not "caused gain".

For example, I've seen some two-boxers justify two-boxing as a moral thing. They're willing to pay 999000$ for the benefit of throwing being predicted in the predictors face, somehow. Fundamentally, they're making the same mistake: fighting the hypothetical by saying the payoffs are different than what was stated in the problem.

The question is, how much of this utility can be attributed to the agent's decision rather than type.

To many two-boxers, this isn't the question. At least some two-boxing proponents in the philosophical literature seem to distinguish between winning decisions and rational decisions, the contention being that winning decisions can be contingent on something stupid about the universe. For example, you could live in a universe that specifically rewards agents who use a particular decision theory, and that says nothing about the rationality of that decision theory.

I still don't follow. The causal effect of two-boxing is getting 1000$ instead of 1000000$. That's bad. How are you interpreting it, so that it's good? Because they're following a rule of thumb that's right under different circumstances?

[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.

But the very point is that you can't submit one piece of code and run another. You have to run what you submitted. That, again, is the issue that decisions don't fall from the sky uncaused. The reason why CDT can't get Newcomb's right is that due to its use of surgery on the action node, it cannot conceive of its own choice as predetermined. You are precommitted already just in virtue of what kind of agent/program you are.