The vNM axioms specify that your utilities should be linear in probability. That’s it.
I don’t think this is right. You are perhaps thinking of the continuity axiom here? But the completeness axiom is not about this (indeed, one cannot even construct a unique utility function to represent incomplete preferences, so there is nothing which may be linear or non-linear in probability).
I don’t think this is right. You are perhaps thinking of the continuity axiom here? But the completeness axiom is not about this (indeed, one cannot even construct a unique utility function to represent incomplete preferences, so there is nothing which may be linear or non-linear in probability).
Oops, you’re of course right. I’ll change my comment.