Maybe the problem comes from my understanding of what the "alternative", "choice" or "act" in the VNM axioms is.
To me it's a single, atomic real-world choice you have to make: you're offered a clear choice between options, and you've to select one. Like you're offered a lottery ticket, and you can decide to buy it or not. Or to make my original example A = "in two months you'll be given a voucher to go to Ecuador", B = "in two months you'll be given a laptop" and C = "in two months you'll given a voucher to go to Iceland". And the independence axiom that, over those choices, if I chose B over C, then I must chose (0.5A, 0.5B) over (0.5A, 0.5C). In my original understanding, things like "preparation" or "what I would do with the money if I win the lottery" are things I'm free to evaluate to chose A, B or C, but aren't part of A, B or C.
The "world histories" view of benelliott seem to fix the problem at first glance, but to me it makes it even worse. If what you're choosing is not individual actions, but whole "world histories", then the independence axiom isn't false, but doesn't even make sense to me. Because the whole "world history" is necessarily different - the whole world history when offered to chose between B and C is in fact B' = "B and knowing you had to chose between B and C" vs C' = "C and knowing you had to chose between B and C", while when offered to chose between D=(0.5A, 0.5B) vs E=(0.5A, 0.5C) is in fact (0.5A² = "A and knowing you had to chose between D and E", 0.5B² = "B and knowing you had to chose between D and E") vs (0.5A², 0.5C² = "C and knowing you had to chose between D and E").
So, how do you define those (A, B, C) in the independence axiom (and the other axioms) so it doesn't fall to the first problem, without making them factor the whole state of the world, in which case you can't even formulate it?
I agree that things get complicated. In the worst case, you really do have to take the entire state of the world into consideration, including your own memory. For the sake of simple toy models, you can pretend that your memory is wiped after you make the choice so you don't remember making it.
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?