I'm not sure why I'm getting downmodded into oblivion here. I'll go out on a limb and assume that I was being incomprehensible, even though I'll be digging myself in deeper if that wasn't the reason...
In classical game theory (subgame-perfect equilibrium), if you eat my chocolate, it is not rational for me to tweak your nose in retaliation at cost to myself. But if I can first commit myself to tweaking your nose if you eat my chocolate, it is no longer rational for you to eat it. But, if you can even earlier commit to definitely eating my chocolate even if I commit to then tweaking your nose, it is (still in classical game theory) no longer rational for me to commit to tweaking your nose! The early committer gets the good stuff.
Eliezer's arguments have convinced me that a better decision theory would work like Vladimir says, acting as if you had made a commitment in all situations where you would like to make a commitment. But as far as I can see, both the nose-tweaker and the chocolate-eater can do that -- speaking in intuitive human terms, it comes down to who is more stubborn. So what does happen? Is there a symmetry breaker? Can it happen that you commit to eating my chocolate, I commit to tweaking your nose, and we end up in the worst possible world for both of us? (Well, I'm pretty confident that that's not what Eliezer's theory (not shown) would do.)
Borrowing from classical game theory, perhaps we say that one of the two commitment scenarios happens, but we can't say which (1. you eat my chocolate and I don't tweak your nose; 2. you don't eat my chocolate, which is a good thing because I would tweak your nose if you did). In the simple commitment game we're considering here, this amounts to considering all Nash equilibria instead of only subgame perfect equilibria (Nash = "no player can do better by changing their strategy" -- but I'm allowed to counterfactually tweak your nose at cost to myself if we don't actually reach that part of the game tree at equilibrium). But of course, if you accept Eliezer's arguments, Nash equilibrium is wrong in general, and in any case, it's not obvious to me if "either of the two scenarios can happen" is the right solution to this game.
To make the implicit motivation behind these two comments explicit: I'm worried that there's a danger of writing "the rightful owner will keep their chocolate" on the bottom line, noticing that a proper decision theory would allow them to retaliate, and saying "done!" without even considering whether the same logic allows the nefarious villain to spitefully commit to eating the chocolate anyhow. If the theory says that either of the two commitment outcomes may happen, ok, but I think it deserves mention. And if the theory says is something else, I want to know that too. :-)
You can't argue with a rock, so you can't stop a rock-solid commitment, even with your own rock-solid commitment. But you can solve the game given the commitments, with the outcome for each side. If this outcome is inferior to other possible commitments, then those other commitments should be used instead.
So, if the hero expects that his commitment to die will still result in villain making him die, this commitment is not a good idea and shouldn't be made (for example, maybe the villain just wants to play the game). The tricky part is that if the hero exp...
The word "rational" is overloaded with associations, so let me be clear: to me [here], more "rational" means better believing what is true, given one's limited info and analysis resources.
Rationality certainly can have instrumental advantages. There are plenty of situations where being more rational helps one achieve a wide range of goals. In those situtations, "winnners", i.e., those who better achieve their goals, should tend to be more rational. In such cases, we might even estimate someone's rationality by looking at his or her "residual" belief-mediated success, i.e., after explaining that success via other observable factors.
But note: we humans were designed in many ways not to be rational, because believing the truth often got in the way of achieving goals evolution had for us. So it is important for everyone who intends to seek truth to clearly understand: rationality has costs, not only in time and effort to achieve it, but also in conflicts with other common goals.
Yes, rationality might help you win that game or argument, get promoted, or win her heart. Or more rationality for you might hinder those outcomes. If what you really want is love, respect, beauty, inspiration, meaning, satisfaction, or success, as commonly understood, we just cannot assure you that rationality is your best approach toward those ends. In fact we often know it is not.
The truth may well be messy, ugly, or dispriting; knowing it make you less popular, loved, or successful. These are actually pretty likely outcomes in many identifiable situations. You may think you want to know the truth no matter what, but how sure can you really be of that? Maybe you just like the heroic image of someone who wants the truth no matter what; or maybe you only really want to know the truth if it is the bright shining glory you hope for.
Be warned; the truth just is what it is. If just knowing the truth is not reward enough, perhaps you'd be better off not knowing. Before you join us in this quixotic quest, ask yourself: do you really want to be generally rational, on all topics? Or might you be better off limiting your rationality to the usual practical topics where rationality is respected and welcomed?