I think you are not allowed to refer explicitly to utility in the options.

I was going to answer that I can easily reword my example to not explicitly mention any utility values, but when I tried to that it very quickly led to something where it is obvious that u(A) = u(C). I guess my rewording was basically going through the steps of the proof of VNM theorem.

I am still not sure I am convinced by your objection, as I don’t think there’s anything self-referential in my example, but that did give me some pause.

I get what you are saying. You have convinced me that the following two statements are contradictory:

Axiom of Independence: preferring A to B implies preferring ApC to BpC for any p and C.

The variance and higher moments of utility matter, not just the expected value.

My confusion is that it intuitively it seems both must be true for a rational agent but I guess my intuition is just wrong.

Thanks for your comments, they were very illuminating.