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

So I agree. It's lucky I've never met a game theorist in the desert.

Less flippantly. The logic pretty much the same yes. But I don't see that as a problem for the point I'm making; which is that the perfect predictor isn't a thought experiment we should worry about.

Elsewhere on this comment thread I've discussed why I think those "rules" are not interesting. Basically, because they're impossible to implement.

According to what rules? And anyway I have preferences for all kinds of impossible things. For example, I prefer cooperating with copies of myself, even though I know it would never happen, since we'd both accept the dominance reasoning and defect.

So these alternative decision theories have relations of dependence going back in time? Are they sort of couterfactual dependences like "If I were to one-box, Omega would have put the million in the box"? That just sounds like the Evidentialist "news value" account. So it must be some other kind of relation of dependence going backwards in time that rules out the dominance reasoning. I guess I need "Other Decision Theories: A Less Wrong Primer".

See mine and orthonormal's comments on the PD on this post for my view of that.

The point I'm struggling to express is that I don't think we should worry about the thought experiment, because I have the feeling that Omega is somehow impossible. The suggestion is that Newcomb's problem makes a problem with CDT clearer. But I argue that Newcomb's problem makes the problem. The flaw is not with the decision theory, but with the concept of such a predictor. So you can't use CDT's "failure" in this circumstance as evidence that CDT is wrong.

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.

Would one-boxing ever be advantageous if Omega were reasoning like that? No. The point is Omega will always reason that two-boxing dominates once the contents are fixed. There seems to be something unstable about Omega's reasoning. I think this is related to why I feel Omega is impossible. (Though I'm not sure how the points interact exactly.)

Aha. So when agents' actions are probabilistically independent, only then does the dominance reasoning kick in?

So the causal decision theorist will say that the dominance reasoning is applicable whenever the agents' actions are causally independent. So do these other decision theories deny this? That is, do they claim that the dominance reasoning can be unsound even when my choice doesn't causally impact the choice of the other?

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

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?

Yes, but it would be strictly better (for me) to be the kind of agent who defects against near-copies of myself when they co-operate in one-shot games. It would be better to be the kind of agent who is predicted to one-box, but then two-box once the money has been put in the opaque box.

But the point is really that I don't see it as the job of an alternative decision theory to get "the right" answers to these sorts of questions.

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

No. What is preferable is to be the kind of person Omega will predict will one-box, and then actually two-box. As long as you "trick" Omega, you get strictly more money. But I guess your point is you can't trick Omega this way.

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.