In hindsight, I phrased that poorly, and you're right, discussing it that way would probably be unproductive.
First, let me specify that when I say "histories" here I mean past histories from the point of view of the agent (which sounds weird, but a lot of the other comments use it to refer to future histories as well). With that in mind, how about this: the actions of the set of agents who care about histories are indistinguishable from the actions of some subset of the agents who do not care about histories. In (something closer to) English, there's a way to describe your caring about histories in terms of only caring about the present and future without changing any decisions you might make.
I find the above "obvious" (which I usually take as a sign that I should be careful). The reason I believe it is that all information you have about histories is contained within your present self. There is no access to the past - everything you know about it is contained either in the present or future, so your decisions must necessarily be conditional only on the present and future.
Would you agree with that? And if so, would you agree that discussing an agent who cares about the histories leading up the present state is not worth doing, since there is no case in which her decisions would differ from some agent who does not? (I suppose one fairly reasonable objection is time travel, but I'm more interested in the case where it's impossible, and I'm not entirely sure whether it would change the core of the argument anyway.)
There is no access to the past - everything you know about it is contained either in the present or future
That's fair, but it just seems to show that I can be fooled. If I'm fooled and the trick is forever beyond my capacity to detect, my actions will be the same as if I had actually accomplished whatever I was trying for. But that doesn't mean I got what I really wanted.
Followup to : Is risk aversion really irrational?
After reading the decision theory FAQ and re-reading The Allais Paradox I realized I still don't accept the VNM axioms, especially the independence one, and I started thinking about what my true rejection could be. And then I realized I already somewhat explained it here, in my Is risk aversion really irrational? article, but it didn't make it obvious in the article how it relates to VNM - it wasn't obvious to me at that time.
Here is the core idea: information has value. Uncertainty therefore has a cost. And that cost is not linear to uncertainty.
Let's take a first example: A is being offered a trip to Ecuador, B is being offered a great new laptop and C is being offered a trip to Iceland. My own preference is: A > B > C. I love Ecuador - it's a fantastic country. But I prefer a laptop over a trip to Iceland, because I'm not fond of cold weather (well, actually Iceland is pretty cool too, but let's assume for the sake of the article that A > B > C is my preference).
But now, I'm offered D = (50% chance of A, 50% chance of B) or E = (50% chance of A, 50% chance of C). The VNM independence principle says I should prefer D > E. But doing so, it forgets the cost of information/uncertainty. By choosing E, I'm sure I'll be offered a trip - I don't know where, but I know I'll be offered a trip, not a laptop. By choosing D, I'm no idea on the nature of the present. I've much less information on my future - and that lack of information has a cost. If I know I'll be offered a trip, I can already ask for days off at work, I can go buy a backpack, I can start doing the paperwork to get my passport. And if I know I won't be offered a laptop, I may decide to buy one, maybe not as great as one I would have been offered, but I can still buy one. But if I chose D, I've much less information about my future, and I can't optimize it as much.
The same goes for the Allais paradox: having certitude of receiving a significant amount of money ($24 000) has a value, which is present in choice 1A, but not in all others (1B, 2A, 2B).
And I don't see why a "rational agent" should neglect the value of this information, as the VNM axioms imply. Any thought about that?