You’re treating utility like a fact, and actual outcomes as irrelevant, they conclusing risk preference is an artifact. But as you admitted, risk aversion over monetary outcomes exist, and it’s the transformation to utility that removes it. Similarly, we’d expect risk aversion over non-monetary goods—having children and years of life are actual outcomes, and risk preference is secondary to those. So your example proves too much.
And yes, you can construct situations where “preferences” that are normally risk-averse become risk-loving when you change what concrete outcome you’re discussing because you put in place arbitrary rules. So I can similarly make almost anyone risk-loving in money by saying that they die if they have too little money, and they need to double their current money to survive—but that’s an artifact of the scenario, and says very little about risk preferences in less constrained scenarios.
As long as you have a utility function u(), on an outcome x (preferebly monotonous), but non-linear you get some kind of “risk aversion”.
But a clear narrative on the u() non linearity is necessary for any risk aversion argument.
For example, I have some intuition that the same total human population spread over time is better than concentrated on a given period. Something like “time is interesting, better be represented across it”.
This generates a kind of “risk aversion”. The opposite intuition (the more human lives are overlapped, the more interesting), would lead to other.
There are many risk aversions, and they are very different; “risk aversion” is exactly as “non linearity”. How much useful can be said about “non-linearity”?
I agree with your point that risk aversion is “just” pointing out a non-linearity, but there is an incredible amount you can say about non-linearity. And you can say the same thing about how any concept, when reduced to “just X” seems trivial, but they are still often useful.
Could be useful, but I would say that the more explicit is the u() and the x, the easier is to assess the validity of the argument. Thank you for the nice (and clarifiying) discussion!
You’re treating utility like a fact, and actual outcomes as irrelevant, they conclusing risk preference is an artifact. But as you admitted, risk aversion over monetary outcomes exist, and it’s the transformation to utility that removes it. Similarly, we’d expect risk aversion over non-monetary goods—having children and years of life are actual outcomes, and risk preference is secondary to those. So your example proves too much.
And yes, you can construct situations where “preferences” that are normally risk-averse become risk-loving when you change what concrete outcome you’re discussing because you put in place arbitrary rules. So I can similarly make almost anyone risk-loving in money by saying that they die if they have too little money, and they need to double their current money to survive—but that’s an artifact of the scenario, and says very little about risk preferences in less constrained scenarios.
As long as you have a utility function u(), on an outcome x (preferebly monotonous), but non-linear you get some kind of “risk aversion”.
But a clear narrative on the u() non linearity is necessary for any risk aversion argument.
For example, I have some intuition that the same total human population spread over time is better than concentrated on a given period. Something like “time is interesting, better be represented across it”.
This generates a kind of “risk aversion”. The opposite intuition (the more human lives are overlapped, the more interesting), would lead to other.
There are many risk aversions, and they are very different; “risk aversion” is exactly as “non linearity”. How much useful can be said about “non-linearity”?
I agree with your point that risk aversion is “just” pointing out a non-linearity, but there is an incredible amount you can say about non-linearity. And you can say the same thing about how any concept, when reduced to “just X” seems trivial, but they are still often useful.
Could be useful, but I would say that the more explicit is the u() and the x, the easier is to assess the validity of the argument. Thank you for the nice (and clarifiying) discussion!