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gjm comments on Open thread, Apr. 18 - Apr. 24, 2016 - Less Wrong
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Yes, you are right. However even a log utility function does not let you escape a Pascal mugging (you just need bigger numbers).
Risk aversion (in reality) does not boil down to a concave utility function. So the OP's claim that a well-defined utility function will fully determine the optimal risk-reward tradeoff is still false.
See, e.g., this paper: there are theorems saying e.g. that if your utility function is concave enough to make you turn down a bet where you win $110 or lose $100 with equal probability, it must also be concave enough to make you turn down a bet where you win a trillion dollars or lose $1k with equal probability.
...at any wealth level, which should be surprising. If Bill Gates thinks that gamble is an expected utility loss, we predict he'll be opposed to basically any gamble, but why would we believe the premise that Bill Gates thinks that gamble is an expected utility loss?
The "concave utility function" theory of risk aversion predicts that, all else being equal, richer people will be less risk-averse about any given sum of money. And I would in fact expect Bill Gates to accept positive-dollar-expectation bets of size ~$100 without a moment's thought.