Thanks for your comment! I think the following is a closer analogy to what I say in the paper:
Suppose apples are better than oranges, which are in turn better than bananas. And suppose your choices are:
An apple and m bananas for sure.
An apple with probability 1−p and an orange with probability p, along with m oranges for sure.
Then even if you believe:
One apple is better than any amount of oranges
It still seems as if, for some large m and small p, 2 is better than 1. 2 slightly increases the risk you miss out on an apple, but it compensates you for that increased risk by giving you many oranges rather than many bananas.
On your side question, I don’t assume completeness! But maybe if I did, then you could recover the VNM theorem. I’d have to give it more thought.
Thanks for your comment! I think the following is a closer analogy to what I say in the paper:
On your side question, I don’t assume completeness! But maybe if I did, then you could recover the VNM theorem. I’d have to give it more thought.