Signals by Brian Skyrms is a great book in this area. It shows how signalling can evolve in even quite simple set-ups.

Here's a related point: Omega will never put the money in the box. Smith act like a one-boxer. Omega predicts that Smith will one-box. So the million is put in the opaque box. Now Omega reasons as follows: "Wait though. Even if Smith is a one-boxer, now that I've fixed what will be in the boxes, Smith is better off two-boxing. Smith is smart enough to realise that two-boxing is dominant, once I can't causally affect the contents of the boxes." So Omega doesn't put the money in the box.

By that logic, you can never win in Kavka's toxin/Parfit's hitchhiker scenario.

According to what rules?

I think he meant according to the rules of the thought experiments. In Newcomb's problem, Omega predicts what you do. Whatever you choose to do, that's what Omega predicted you would choose to do. You cannot to choose to do something that Omega wouldn't predict - it's impossible. There is no such thing as "the kind of agent who is predicted to one-box, but then two-box once the money has been put in the opaque box".

The larger point makes sense. Those two things you prefer are impossible according to the rules, though.

That's one valid way of looking at the distinction.

CDT allows the causal link from its current move in chess to its opponent's next move, so it doesn't view the two as independent.

In Newcomb's Problem, traditional CDT doesn't allow a causal link from its decision now to Omega's action before, so it applies the independence assumption to conclude that two-boxing is the dominant strategy. Ditto with playing PD against its clone.

(Come to think of it, it's basically a Markov chain formalism.)

Which brings me back to whether Omega is feasible. I just don't share the intuition that Omega is capable of the sort of predictive capacity required of it.

Well, I guess my response to that would be that it's a thought experiment. Omega's really just an extreme - hypothetical - case of a powerful predictor, that makes problems in CDT more easily seen by amplifying them. If we were to talk about the prisoner's dilemma, we could easily have roughly the same underlying discussion.

Again, the dominance reasoning seems impeccable to me. In fact, I'm tempted to say that I would want any future advanced decision theory to satisfy some form of this dominance principle: it's crazy to ever choice an act that is guaranteed to be worse.

It's not always cooperating- that would be dumb. The claim is that there can be improvements on what a CDT algorithm can achieve: TDT or UDT still defects against an opponent that always defects or always cooperates, but achieves (C,C) in some situations where CDT gets (D,D). The dominance reasoning is only impeccable if agents' decisions really are independent, just like certain theorems in probability only hold when the random variables are independent. (And yes, this is a precisely analogous meaning of "independent".)

Given the discussion, strictly speaking the pill reduces Ghandi's reluctance to murder by 1 percentage point. Not 1%.

I generally share your reservations.

But as I understand it, proponents of alternative DTs are talking about a conditional PD where you know you face an opponent executing a particular DT. The fancy-DT-users all defect on PD when the prior of their PD-partner being on CDT or similar is high enough, right?

Wouldn't you like to be the type of agent who cooperates with near-copies of yourself? Wouldn't you like to be the type of agent who one-boxes? The trick is to satisfy this desire without using a bunch of stupid special-case rules, and show that it doesn't lead to poor decisions elsewhere.

Here's an example of a related kind of "reflexivity makes prediction meaningless". Let's say Omega bets you $100 that she can predict what you will eat for breakfast. Once you accept this bet, you now try to think of something that you would never otherwise think to eat for breakfast, in order to win the bet. The fact that your actions and the prediction of your actions have been connected in this way by the bet makes your actions unpredictable.

Your actions have been determined in part by the bet that Omega has made with you - I do not see how that is supposed to make them unpredictable any more than adding any other variable would do so. Remember: You only appear to have free will from within the algorithm, you may decide to think of something you'd never otherwise think about but Omega is advanced enough to model you down to the most basic level - it can predict your more complex behaviours based upon the combination of far simpler rules. You cannot necessarily just decide to think of something random which would be required in order to be unpredictable.

Similarly, the whole question of whether you should choose to two box or one box is a bit iffy. Strictly speaking there's no SHOULD about it. You will one box or you will two box. The question phrased as a should question - as a choice - is meaningless unless you're treating choice as a high-level abstraction of lower level rules; and if you do that, then the difficult disappears - just as you don't ask a rock whether it should or shouldn't crush someone when it falls down a hill.

Meaningfully, we might ask whether it is preferable to be the type of person who two boxes or the type of person who one boxes. As it turns out it seems to be more preferable to one-box and make stinking great piles of dosh. And as it turns out I'm the sort of person who, holding a desire for filthy lucre, will do so.

It's really difficult to side step your intuitions - your illusion that you actually get a free choice here. And I think the phrasing of the problem and its answers themselves have a lot to do with that. I think if you think that people get a choice - and the mechanisms of Omega's prediction hinge upon you being strongly determined - then the question just ceases to make sense. And you've got to jettison one of the two; either Omega's prediction ability or your ability to make a choice in the sense conventionally meant.