You say that as if the only possible options are “utility proportional to wealth, and trying to maximize expected utility” and “utility proportional to log wealth, and trying to maximize expected utility” but of course there are many many options besides those.
One possibly-relevant example: Some people argue that we should use bounded utility functions, on one or more of the following grounds:
Human brains are finite and simply can’t represent an unbounded range of utilities. So if “utility” means anything your brain is actually capable of evaluating, it has an upper bound.
It’s possible (and not all that difficult) to construct paradoxical situations in which the existence of unbounded utilities is an essential feature (e.g., because the expectations you’re trying to construct end up diverging) and bounded utility functions aren’t vulnerable to those problems.
If your utility function is bounded and its upper bound isn’t outrageously large then 3^^^3-type Pascal muggings won’t work on you.
(Note: There are reasons not to want a bounded utility function, too. I am not claiming that we should use them.)
You say that as if the only possible options are “utility proportional to wealth, and trying to maximize expected utility” and “utility proportional to log wealth, and trying to maximize expected utility” but of course there are many many options besides those.
One possibly-relevant example: Some people argue that we should use bounded utility functions, on one or more of the following grounds:
Human brains are finite and simply can’t represent an unbounded range of utilities. So if “utility” means anything your brain is actually capable of evaluating, it has an upper bound.
It’s possible (and not all that difficult) to construct paradoxical situations in which the existence of unbounded utilities is an essential feature (e.g., because the expectations you’re trying to construct end up diverging) and bounded utility functions aren’t vulnerable to those problems.
If your utility function is bounded and its upper bound isn’t outrageously large then 3^^^3-type Pascal muggings won’t work on you.
(Note: There are reasons not to want a bounded utility function, too. I am not claiming that we should use them.)