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gjm comments on Iterated Gambles and Expected Utility Theory - Less Wrong
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In fact it's pretty well established that typical levels of risk aversion cannot be explained by any halfway-credible utility function. A paper by Matthew Rabin shows, e.g., that if you decline a bet where you lose $100 or gain $110 with equal probability (which many people would) and this is merely because of the concavity of your utility function, then subject to rather modest assumptions you must also decline a bet where you lose $1000 or gain all the money in the world with equal probability.
Yep, I've been mentioning that on LW over and over again, but people seem reluctant to accept that.
There was some discussion of that paper and its ideas on LW in 2012. Vaniver suggests that the results may be more a matter of eliciting people's preferences in a lazy way that doesn't get at their real, hopefully better thought out, preferences. (But I fear people's actual behaviour matches that lazy preference-elicitation pretty well.) There are some other interesting comments there, too.
Some of those conclusions are not as absurd as Rabin appears to believe; I think he's typical-minding. Most people will pick a 100% chance of $500 over a 15% chance of $1M.
Prior or posterior to the evidence provided by the other person's willingness to offer the bet? ;-)
Such as assuming that that person would also decline the bet even if they had 10 times as much money to start with? That doesn't sound like a particularly modest assumption.