This! If you’re risk averse, then you want to avoid risk, and so in the real utility calculation upon which you base your decisions the risk-averse option gets a little extra positive term for being, well, risk-averse. And then the two options no longer have the same expected utility.
Unfortunately, under your new “fixed” utility function there will again be a point of indifference at some slightly different probability/payoff combination, where you, being risk-averse, have to go for the sure deal, so you will end up stuck in an infinite recursion trying to adjust your utility function further and further. I tried to explain this more clearly here.
I don’t think that follows. The risk-aversion utility attaches to the choice, not the outcome: I get extra utility for having made a choice with lower expected variance, not for one of the outcomes. If you then offer me a choice between choices, then sure, there will be more risk aversion, but I don’t think it’s viciously recursive.
Another way to interpret this situation is that the “utility function” being used to calculate the expected value is a fake utility function.
This! If you’re risk averse, then you want to avoid risk, and so in the real utility calculation upon which you base your decisions the risk-averse option gets a little extra positive term for being, well, risk-averse. And then the two options no longer have the same expected utility.
Unfortunately, under your new “fixed” utility function there will again be a point of indifference at some slightly different probability/payoff combination, where you, being risk-averse, have to go for the sure deal, so you will end up stuck in an infinite recursion trying to adjust your utility function further and further. I tried to explain this more clearly here.
I don’t think that follows. The risk-aversion utility attaches to the choice, not the outcome: I get extra utility for having made a choice with lower expected variance, not for one of the outcomes. If you then offer me a choice between choices, then sure, there will be more risk aversion, but I don’t think it’s viciously recursive.