Without multiple repetition, risk aversion is, I would argue, an extremely sensible strategy for utility maximisation. Of course if one believes that one will be faced with a similar choice multiple times, then one can revert back to utility maximisation.
The big problem with risk aversion is that it violates translation invariance. If someone will give me $2 if a coin flip lands heads, I might go “well, I’m risk averse, so I want to avoid getting nothing, which means I would only pay like $.5 for this bet.” But if I’ve got even a couple dollars in my bank account, what does that do to the bet? Now it’s $100 vs. $102, and so where’s the risk to avert? I’ll pay $ .98!
The way to resolve this asymmetry with things like money or candy bars is to say “well, we value the first candy bar more than the 400th. I’d rather have a certainty of 1 candy bar than a 1 in 400 chance of 400”—that is, our “wanting” becomes a nonlinear function of the amount of stuff. But utility is, by its definition, a unit with such nonlinearities removed. If you only can really eat 3 candy bars, then your utility as a function of candy bars will reflect this perfectly—it will increase from one through 3 and then remain constant. Similarly, if you don’t really want $100,000 more than you want $20,000, utility can reflect this too, by increasing steeply at first and then leveling off. Utility is what you get after you’ve taken that stuff into account.
When nonlinearities are accounted for and solved away, there’s nothing that breaks translational symmetry—there’s no landmarks to be risk-averse relative to. It’s a bit difficult to grok, I know.
The big problem with risk aversion is that it violates translation invariance. If someone will give me $2 if a coin flip lands heads, I might go “well, I’m risk averse, so I want to avoid getting nothing, which means I would only pay like $.5 for this bet.” But if I’ve got even a couple dollars in my bank account, what does that do to the bet? Now it’s $100 vs. $102, and so where’s the risk to avert? I’ll pay $ .98!
The way to resolve this asymmetry with things like money or candy bars is to say “well, we value the first candy bar more than the 400th. I’d rather have a certainty of 1 candy bar than a 1 in 400 chance of 400”—that is, our “wanting” becomes a nonlinear function of the amount of stuff. But utility is, by its definition, a unit with such nonlinearities removed. If you only can really eat 3 candy bars, then your utility as a function of candy bars will reflect this perfectly—it will increase from one through 3 and then remain constant. Similarly, if you don’t really want $100,000 more than you want $20,000, utility can reflect this too, by increasing steeply at first and then leveling off. Utility is what you get after you’ve taken that stuff into account.
When nonlinearities are accounted for and solved away, there’s nothing that breaks translational symmetry—there’s no landmarks to be risk-averse relative to. It’s a bit difficult to grok, I know.