this doesn’t imply we should maximize expected total utility, since it doesn’t rule out risk-aversion
What do you mean by this? Isn’t risk aversion just a fact about the utility function? You can maximize expected utility no matter how the utility function is shaped.
Ah, we use utility in two ways, the social welfare function whose expected value you maximize, and the welfares of individuals on which your social welfare function depends. You can be a risk-averse utilitarian, for example, with a social welfare function like f(∑iui), where the ui are the individual utilities/welfares and f:R→R is nondecreasing and concave.
An example function f, or an example where someone actually recommended or used a particular function f?
I don’t know of any of the latter, but using an increasing and bounded f has come up in some discussions about infinite ethics (although it couldn’t be concave towards −∞). I discuss bounded utility functions here.
An example function is 1−e−x. See this link for a graph. It’s strictly increasing and strictly concave everywhere, and bounded above, but not below.
Tangent:
What do you mean by this? Isn’t risk aversion just a fact about the utility function? You can maximize expected utility no matter how the utility function is shaped.
Ah, we use utility in two ways, the social welfare function whose expected value you maximize, and the welfares of individuals on which your social welfare function depends. You can be a risk-averse utilitarian, for example, with a social welfare function like f(∑iui), where the ui are the individual utilities/welfares and f:R→R is nondecreasing and concave.
Hm, I’ve never seen the use of $f$ like that. Can you point to an example?
An example function f, or an example where someone actually recommended or used a particular function f?
I don’t know of any of the latter, but using an increasing and bounded f has come up in some discussions about infinite ethics (although it couldn’t be concave towards −∞). I discuss bounded utility functions here.
An example function is 1−e−x. See this link for a graph. It’s strictly increasing and strictly concave everywhere, and bounded above, but not below.
Yes, I meant an example of someone using f in this way. It doesn’t seem to be standard in welfare economics.