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thomblake comments on VNM expected utility theory: uses, abuses, and interpretation - Less Wrong
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Perhaps I'm missing something, but it seems to me this doesn't cover risk-aversion properly.
Suppose for me, utility($100) = 1, and utility($1000) = 100, and utility($0) = 0. Then, utility($100) < 10%utility($1000) + 90%utility($0); (1 < 10). Now suppose I am extremely risk-averse; I prefer to never wager any money I actually have and will practically always take a certain $100 over any uncertain $1000. It does not seem this configuration is impossible in an agent, but is not supported by your model of risk-aversion.
Does this merely mean that this type of risk-aversion is considered irrational and therefore not covered in the VNM model?
Yes. If you are risk-averse (or loss-averse) in terms of marginal changes in your money, then you're not optimizing any consistent function of your total amount of money.