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somervta comments on Yet more "stupid" questions - Less Wrong Discussion
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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.
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.
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.