I am not aware of any systematic attempt to study these things. My own opinion is formed from a somewhat casual reading of Matt Ridley's Rational Optimist, Jared Diamond's Guns Germs and Steel and Collapse, and probably a few other books that don't leap to mind. These books have plenty of citation of studies if you are interested.

I think you would be hard pressed to find any existing "significant" country that does not engender a strong belief in patriotism among its populace, which does not lionize especially those who have given their lives in wars on behalf of the country. If you can think of any significant counter examples among the 50 richest or 50 most populous countries, please let me know. I am essentially hypothesizing that the scarcity of genteel foreigner-loving pacifist countries among the richest and most populous is not a mere coincidence.

Learning about useful models helps people escape anthropomorphizing human society or the economy or government. The latter is particularly salient. I think most people slip up occasionally in assuming that say something like the United States government can be successfully modelled as a single agent to explain most of its "actions".

As an interesting (to me, at least) aside, Gene Sharp's research on nonviolent resistance indicates that successful nonviolent resistance invariably involves taking to heart this little idea -- that governments are not single agents but systems of many agents pursuing their own ends -- and exploiting it to the max.

Actually, mere possibilities can make a difference... if you have effects that propagate backwards in time.

It still has to happen. It might happen in the future instead of the past, but it still has to happen.

Jaynes died in 1998. How did he never hear of MWI? I'd heard of MWI in 1998, and I was just a kid.

EDIT: Google Books turns up the following snippet in The Many Worlds of Hugh Everett III:

All possibilities 'actually realized,' with corresp. observer states.15 In May 1957, Everett wrote a critical letter to ET Jaynes, a physicist at Stanford University who was pioneering the use of von Neumann-Shannontype information...

I have been unable to find any copies online, Amazon wants $30 for any copy, and neither my local library nor university nor county catalog hold it. Man!

EDITEDIT: Google Books gives more access to The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980, which gives an entire chapter 18 to 'Correspondence: Everett and Jaynes (1957)': http://books.google.com/books?id=dowpli7i6TgC&pg=PA261&dq=jaynes+everett&hl=en&sa=X&ei=N9CdT9PSIcLOgAf-3vTxDg&ved=0CDYQ6AEwAQ#v=onepage&q&f=false

I'm not sure what they are discussing, and many-worlds doesn't seem to come up (at least under that name) and most of the chapter is inaccessible, but it's clear from the chapter summary Jaynes doesn't think much of Everett's position.

a simple expected-utility maximization gives you the right answer, assuming you know that the other player will make the same move that you do.

A simple expected utility maximization does. A CDT decision doesn't. Formally specifying a maximization algorithm that behaves like CDT is, from what I understand, less simple than making it follow UDT.

OK, ignore those examples for a second, and ignore the word "advanced."

The OP is drawing a distinction between CDT, which he claims fails in situations where competing agents can predict one another's behavior to varying degrees, and other decision theories, which don't fail. If he's wrong in that claim, then articulating why would be helpful.

If, instead, he's right in that claim, then I don't see what's useless about theories that don't fail in that situation. At least, it certainly seems to me that competing agents predicting one another's behavior is something that happens all the time in the real world. Does it not seem that way to you?

Of course, in these two problems we know which causal links to draw. They were written to be simple enough. The trick is to have a general theory that draws the right links here without drawing wrong links in other problems, and which is formalizable so that it can answer problems more complicated than common sense can handle.

Among human beings, the relevant distinction is between decisions made before or after the other agent becomes aware of your decision- and you can certainly come up with examples where mutual ignorance happens.

Finally, situations with iterated moves can be decided differently by different decision theories as well: consider Newcomb's Problem where the big box is transparent as well! A CDT will always find the big box empty, and two-box; a UDT/ADT will always find the big box full, and one-box. (TDT might two-box in that case, actually.)

They're no more artificial than the rest of Game Theory- no human being has ever known their exact payoffs for consequences in terms of utility, either. Like I said, there may be a good deal of advanced-decision-theory-structure in the way people subconsciously decide to trust one another given partial information, and that's something that CDT analysis would treat as irrational even when beneficial.

One bit of relevance is that "rational" has been wrongly conflated with strategies akin to defecting in the Prisoner's Dilemma, or being unable to geniunely promise anything with high enough stakes, and advanced decision theories are the key to seeing that the rational ideal doesn't fail like that.

If your goal is to figure out what to have for breakfast, not much relevance at all.
If your goal is to program an automated decision-making system to figure out what breakfast supplies to make available to the population of the West Coast of the U.S., perhaps quite a lot.
If your goal is to program an automated decision-making system to figure out how to optimize all available resources for the maximum benefit of humanity, perhaps even more.

There are lots of groups represented on LW, with different perceived needs. Some are primarily interested in self-help threads, others primarily interested in academic decision-theory threads, and many others. Easiest is to ignore threads that don't interest you.

Are you sure that you need an advanced decision theory two handle the one-box/two-box problem, or the PD-with-mental-clone problem? You write that

a CDT agent assumes that X's decision is independent from the simultaneous decisions of the Ys- that is, X could decide one way or another and everyone else's decisions would stay the same.

Well, that's a common situation analyzed in game theory, but it's not essential to CDT. Consider playing a game of chess: your choice clearly affects the choice of your opponent. Or consider the decision of whether to punch a 6'5", 250 lb. muscle-man who has just insulted you -- your choice again has a strong influence on his choice of action. CDT is adequate for analyzing both of these situations.

It is true that in my two examples the other agent's choice is made after X's choice, rather than being simultaneous with his. But of what relevance is the stipulation of simultaneity? It's only relevance is that it leads one to assume that the other decisions are independent of X's decision! That is, the root of the difficulty is simply that you're analyzing the problem using an assumption that you know to be false!

It seems to me that you can analyze the one-box/two-box problem or the PD-with-a-mental-clone problem perfectly well using CDT; you just have to use the right causal graph. The causal graph needs an arc from your decision to Omega's prediction for the first problem, and an arc from your decision to the clone's decision in the second problem. Then you do the usual maximization of expected utility.