I’m standing at a 4-way intersection. I want to go the best restaurant at the intersection. To the west is a three-star restaurant, to the north is a two-star restaurant, and to the northwest, requiring two street-crossings, is a four-star restaurant. All of the streets are equally safe to cross except for the one in between the western restaurant and the northern one, which is more dangerous. So going west, then north is strictly dominated by going north, then west. Going north and eating there is strictly dominated by going west and eating there. This means that if I cross one street, and then change my mind about where I want to eat based on the fact that I didn’t die, I’ve been dutch-booked by reality.
That might need a few more elements before it actually restricts you to VNM-rationality.
What would be such adversarial assumptions in your street-crossing example?
I’m standing at a 4-way intersection. I want to go the best restaurant at the intersection. To the west is a three-star restaurant, to the north is a two-star restaurant, and to the northwest, requiring two street-crossings, is a four-star restaurant. All of the streets are equally safe to cross except for the one in between the western restaurant and the northern one, which is more dangerous. So going west, then north is strictly dominated by going north, then west. Going north and eating there is strictly dominated by going west and eating there. This means that if I cross one street, and then change my mind about where I want to eat based on the fact that I didn’t die, I’ve been dutch-booked by reality.
That might need a few more elements before it actually restricts you to VNM-rationality.
Where is reality’s corresponding utility gain?
The bad news is there is none. The good news is that this means, under linear transformation, that there is such a thing as a free lunch!