“Risk Aversion,” as a technical term, means that the utility function is concave with respect to its inpu [...]
Oh, ok. I mean the affect where people make their utility functions “risk averse” to avoid bad possibilities, or just go
ahead and avoid bad possibilities, and I have seen people on LW take “risk aversion” (whatever that means to them)
as terminal.
You don’t “make” your utility function anything; it is what it is. “Risk aversion” just means that the most obvious scale for measuring your utility isn’t proportional to your true utility scale. For example, one’s utility for money is generally not proportional to the amount of money, and is approximately proportional only if the amount is not large compared to your current wealth.
For larger quantities of money it’s not even close to proportional. In particular, I—and most people, for that matter—do not value $2 billion twice as much as $1 billion. The positive impact on my life of gaining $1 billion dollars at my current level of wealth is vastly greater than the additional positive impact of going from $1 billion to $2 billion. Hence if I were offered a choice between a guaranteed $1 billion dollars vs. a 90% chance of gaining $2 billion dollars, I would choose the sure thing—the expected utility of the second option is greater than 90% but less than 91% of the expected utility of the first option for me.
Likewise, suppose that my net worth is $100,000. An extra $100,000 would be great, but losing $100,000 would be disastrous; it would wipe me out. So my gain in utility from gaining $100,000 is considerably less than my loss of utility from losing $100,000… and it makes sense for me to do things like insure my home.
Both of these examples show me to be risk averse. It is not a strategy I have chosen; it is simply a statement of my personal utility function.
I know your position is dominant around here, but I intended to tackle it anyway. If you care about doing good, once you’ve handled your personal expenses, additional marginal dollars have fixed marginal utility (until you’re dealing with enough money to seriously impact the global market for marginal utility).
Money utility is linear between the amounts where you’re worrying about personal expenses, and the amounts where you’re impacting the global market for marginal utility. That’s most of the range.
This may be true, and so we might expect someone who was very wealthy to lose their risk-aversion for deicisions where they were sure there was no risk of losses cutting into what they need for personal use. Sounds pretty reasonable for a risk-averse agent to me.
You don’t “make” your utility function anything; it is what it is. “Risk aversion” just means that the most obvious scale for measuring your utility isn’t proportional to your true utility scale. For example, one’s utility for money is generally not proportional to the amount of money, and is approximately proportional only if the amount is not large compared to your current wealth.
For larger quantities of money it’s not even close to proportional. In particular, I—and most people, for that matter—do not value $2 billion twice as much as $1 billion. The positive impact on my life of gaining $1 billion dollars at my current level of wealth is vastly greater than the additional positive impact of going from $1 billion to $2 billion. Hence if I were offered a choice between a guaranteed $1 billion dollars vs. a 90% chance of gaining $2 billion dollars, I would choose the sure thing—the expected utility of the second option is greater than 90% but less than 91% of the expected utility of the first option for me.
Likewise, suppose that my net worth is $100,000. An extra $100,000 would be great, but losing $100,000 would be disastrous; it would wipe me out. So my gain in utility from gaining $100,000 is considerably less than my loss of utility from losing $100,000… and it makes sense for me to do things like insure my home.
Both of these examples show me to be risk averse. It is not a strategy I have chosen; it is simply a statement of my personal utility function.
I know your position is dominant around here, but I intended to tackle it anyway. If you care about doing good, once you’ve handled your personal expenses, additional marginal dollars have fixed marginal utility (until you’re dealing with enough money to seriously impact the global market for marginal utility).
Money utility is linear between the amounts where you’re worrying about personal expenses, and the amounts where you’re impacting the global market for marginal utility. That’s most of the range.
This may be true, and so we might expect someone who was very wealthy to lose their risk-aversion for deicisions where they were sure there was no risk of losses cutting into what they need for personal use. Sounds pretty reasonable for a risk-averse agent to me.
The flaw in this theory is that it assumes the extra money actually gets donated.
humph. if we are not assuming the money gets used, I’m not sure how we can apply any particular utility to it at all.
We can assume the money gets used on oneself, which is much more likely to happen in the stated scenario.