Your citations here are talking about trying to model human behavior based on trying to fit concave functions of networth-to-utility to realistic numbers. The bit you quoted here was from a passage wherein I was ceding this precise point.
I was explaining that I had previously thought you to be making a broader theoretical point, about any sort of risk premia—not just those that actually model real human behavior. Your quoting of that passage lead me to believe that was the case, but your response here leads me to wonder whether there is still confusion.
If you try to reuse this utility curve for any other bet or bet with more than two outcomes, you’ll start seeing the same person accepting infinite, near-zero, or even negative risk premia.
Do you mean this to apply to any theoretical utility-to-dollars function, even those that do not well model people?
If so, can you please give an example of infinite or negative risk premia for an agent (an AI, say) whose dollars-to-utility function is U(x) = x / log(x + 10).
This utility function has near zero risk aversion at relevant range.
Assuming our AI has wealth level of $10000, it will happily take a 50:50 bet of gaining $100.10 vs losing $100.00.
Yes, it is weak risk aversion—but is it not still risk aversion, as I had initially meant (and initially thought you to mean)?
It also gets to infinities if there’s a risk of dollar worth below -$10.
Yes, of course. I’d considered this irrelevant for reasons I can’t quite recall, but it is trivially fixed; is there a problem with U(x) = x/log(x+10)?
You are being frustrating.
Your citations here are talking about trying to model human behavior based on trying to fit concave functions of networth-to-utility to realistic numbers. The bit you quoted here was from a passage wherein I was ceding this precise point.
I was explaining that I had previously thought you to be making a broader theoretical point, about any sort of risk premia—not just those that actually model real human behavior. Your quoting of that passage lead me to believe that was the case, but your response here leads me to wonder whether there is still confusion.
Do you mean this to apply to any theoretical utility-to-dollars function, even those that do not well model people?
If so, can you please give an example of infinite or negative risk premia for an agent (an AI, say) whose dollars-to-utility function is U(x) = x / log(x + 10).
This utility function has near zero risk aversion at relevant range.
Assuming our AI has wealth level of $10000, it will happily take a 50:50 bet of gaining $100.10 vs losing $100.00.
It also gets to infinities if there’s a risk of dollar worth below -$10.
Yes, it is weak risk aversion—but is it not still risk aversion, as I had initially meant (and initially thought you to mean)?
Yes, of course. I’d considered this irrelevant for reasons I can’t quite recall, but it is trivially fixed; is there a problem with U(x) = x/log(x+10)?