Because doing so will lead to worse outcomes on average. Over a long series of events, someone who just follows the math will do better than someone who is risk-averse wrt to ‘utility’. Of course, often our utility functions are risk-averse wrt to real-world things, because of non-linear valuation—e.g, your first $100,000 is more valuable than your second, and your first million is not 10x as valuable as your first $100,000.
Because doing so will lead to worse outcomes on average.
In specific instances, avoiding the negative outcome might be beneficial, but only for that instance. If you’re constantly settling for less-than-optimal outcomes because they’re less risky, it’ll average out to less-than-optimal utility.
The terminology “non-linear valuation” seemed to me to imply some exponential valuation, or logarithmic or something; I think “subjective valuation” or “subjective utility” might be better here.
Yes, non-linear valuation means that your subjective value for X does not increase linearly with linear increases in X. It might increase logarithmically, or exponentially, or polynomially (with degree > 1), or whatever.
Is there any reason we don’t include a risk aversion factor in expected utility calculations?
If there is an established way of considering risk aversion, where can I find posts/papers/articles/books regarding this?
Because doing so will lead to worse outcomes on average. Over a long series of events, someone who just follows the math will do better than someone who is risk-averse wrt to ‘utility’. Of course, often our utility functions are risk-averse wrt to real-world things, because of non-linear valuation—e.g, your first $100,000 is more valuable than your second, and your first million is not 10x as valuable as your first $100,000.
Thanks. Just going to clarify my thoughts below.
In specific instances, avoiding the negative outcome might be beneficial, but only for that instance. If you’re constantly settling for less-than-optimal outcomes because they’re less risky, it’ll average out to less-than-optimal utility.
The terminology “non-linear valuation” seemed to me to imply some exponential valuation, or logarithmic or something; I think “subjective valuation” or “subjective utility” might be better here.
You just incorporate that straight into the utility function.
You have $100 to your name. Start with 100 utility.
Hey! Betcha $50 this coin comes up heads!
$150 and therefore 110 utility if you win.
$50 and therefore 60 utility if you lose.
So you don’t take the bet. It’s a fair bet dollar wise, but an unfair bet utility wise.
Yes, non-linear valuation means that your subjective value for X does not increase linearly with linear increases in X. It might increase logarithmically, or exponentially, or polynomially (with degree > 1), or whatever.