If one defines rationality in some way that isn't about winning, your example shows that rationalists-in-such-a-sense might not win.
If one defines rationality as actually winning, your example shows that there are things that even Omega cannot do because they involve logical contradiction.
If one defines rationality as something like "expected winning given one's model of the universe" (for quibbles, see below), your example shows that you can't coherently carry around a model of the universe that includes a superbeing who deliberately acts so as to invalidate that model.
I find all three of these things rather unsurprising.
The traditional form of Newcomb's problem doesn't involve a superbeing deliberately acting so as to invalidate your model of the universe. That seems like a big enough difference from your version to invalidate inferences of the form "there's no such thing as acting rationally in grobstein's version of Newcomb's problem; therefore it doesn't make sense to use any version of Newcomb's problem in forming one's ideas about what constitutes acting rationally".
I think the third definition is pretty much what Eliezer is getting at when he declares that rationalists/rationality should win. Tightening it up a bit, I think we get something like this: rationality is a strategy S such that at each moment, acting as S tells you to act -- given (1) your beliefs about the universe at that point and (2) your intention of following S at all times -- maximizes your net utility (calculated in whatever way you prefer; that is mostly not a question of rationality). This isn't quite a definition, because there might turn out to be multiple such strategies, especially for people whose initial beliefs about the universe are sufficiently crazy. But if you add some condition to the effect that S and your initial beliefs shouldn't be too unlike what's generally considered (respectively) rational and right now, there might well be a unique solution to the equations. And it seems to me that what your example shows about this definition is simply that you can't consistently expect Omega to act in a way that falsifies your beliefs and/or invalidates your strategies for acting. Which is (to me) not surprising, and not a reason for defining rationality in this sort of way.
What is it, pray tell, that Omega cannot do?
Can he not scan your brain and determine what strategy you are following? That would be odd, because this is no stronger than the original Newcomb problem and does not seem to contain any logical impossibilities.
Can he not compute the strategy, S, with the property "that at each moment, acting as S tells you to act -- given (1) your beliefs about the universe at that point and (2) your intention of following S at all times -- maximizes your net utility [over all time]?" That would be very odd, since y...
Followup to: Newcomb's Problem and Regret of Rationality
"Rationalists should win," I said, and I may have to stop saying it, for it seems to convey something other than what I meant by it.
Where did the phrase come from originally? From considering such cases as Newcomb's Problem: The superbeing Omega sets forth before you two boxes, a transparent box A containing $1000 (or the equivalent in material wealth), and an opaque box B that contains either $1,000,000 or nothing. Omega tells you that It has already put $1M in box B if and only if It predicts that you will take only box B, leaving box A behind. Omega has played this game many times before, and has been right 99 times out of 100. Do you take both boxes, or only box B?
A common position - in fact, the mainstream/dominant position in modern philosophy and decision theory - is that the only reasonable course is to take both boxes; Omega has already made Its decision and gone, and so your action cannot affect the contents of the box in any way (they argue). Now, it so happens that certain types of unreasonable individuals are rewarded by Omega - who moves even before they make their decisions - but this in no way changes the conclusion that the only reasonable course is to take both boxes, since taking both boxes makes you $1000 richer regardless of the unchanging and unchangeable contents of box B.
And this is the sort of thinking that I intended to reject by saying, "Rationalists should win!"
Said Miyamoto Musashi: "The primary thing when you take a sword in your hands is your intention to cut the enemy, whatever the means. Whenever you parry, hit, spring, strike or touch the enemy's cutting sword, you must cut the enemy in the same movement. It is essential to attain this. If you think only of hitting, springing, striking or touching the enemy, you will not be able actually to cut him."
Said I: "If you fail to achieve a correct answer, it is futile to protest that you acted with propriety."
This is the distinction I had hoped to convey by saying, "Rationalists should win!"
There is a meme which says that a certain ritual of cognition is the paragon of reasonableness and so defines what the reasonable people do. But alas, the reasonable people often get their butts handed to them by the unreasonable ones, because the universe isn't always reasonable. Reason is just a way of doing things, not necessarily the most formidable; it is how professors talk to each other in debate halls, which sometimes works, and sometimes doesn't. If a hoard of barbarians attacks the debate hall, the truly prudent and flexible agent will abandon reasonableness.
No. If the "irrational" agent is outcompeting you on a systematic and predictable basis, then it is time to reconsider what you think is "rational".
For I do fear that a "rationalist" will clutch to themselves the ritual of cognition they have been taught, as loss after loss piles up, consoling themselves: "I have behaved virtuously, I have been so reasonable, it's just this awful unfair universe that doesn't give me what I deserve. The others are cheating by not doing it the rational way, that's how they got ahead of me."
It is this that I intended to guard against by saying: "Rationalists should win!" Not whine, win. If you keep on losing, perhaps you are doing something wrong. Do not console yourself about how you were so wonderfully rational in the course of losing. That is not how things are supposed to go. It is not the Art that fails, but you who fails to grasp the Art.
Likewise in the realm of epistemic rationality, if you find yourself thinking that the reasonable belief is X (because a majority of modern humans seem to believe X, or something that sounds similarly appealing) and yet the world itself is obviously Y.
But people do seem to be taking this in some other sense than I meant it - as though any person who declared themselves a rationalist would in that moment be invested with an invincible spirit that enabled them to obtain all things without effort and without overcoming disadvantages, or something, I don't know.
Maybe there is an alternative phrase to be found again in Musashi, who said: "The Way of the Ichi school is the spirit of winning, whatever the weapon and whatever its size."
"Rationality is the spirit of winning"? "Rationality is the Way of winning"? "Rationality is systematized winning"? If you have a better suggestion, post it in the comments.