I argue that the thought experiment is ambiguous, and that for a certain definition of utility (vNM utility), it is trivial and doesn’t solve any problems. For this definition of utility I argue that your example doesn’t work. You do not appear to have engaged with this argument, despite repeated requests to point out either where it goes wrong, or where it is unclear. If it goes wrong, I want to know why, but this conversation isn’t really helping.
For other definitions of utility, I do not, and have never claimed that the thought experiment is trivial. In fact, I think it is very interesting.
I argue that the thought experiment is ambiguous, and that for a certain definition of utility (vNM utility), it is trivial and doesn’t solve any problems. For this definition of utility I argue that your example doesn’t work.
If by “your example” you refer to the setup described in this comment, I don’t understand what you are saying here. I don’t use any “definition of utility”, it’s just a parameter of the tool.
It’s also an entity in the problem set-up. When Omega says “I’ll double your utility”, what is she offering to double? Without defining this, the problem isn’t well-specified.
I argue that the thought experiment is ambiguous, and that for a certain definition of utility (vNM utility), it is trivial and doesn’t solve any problems. For this definition of utility I argue that your example doesn’t work. You do not appear to have engaged with this argument, despite repeated requests to point out either where it goes wrong, or where it is unclear. If it goes wrong, I want to know why, but this conversation isn’t really helping.
For other definitions of utility, I do not, and have never claimed that the thought experiment is trivial. In fact, I think it is very interesting.
If by “your example” you refer to the setup described in this comment, I don’t understand what you are saying here. I don’t use any “definition of utility”, it’s just a parameter of the tool.
It’s also an entity in the problem set-up. When Omega says “I’ll double your utility”, what is she offering to double? Without defining this, the problem isn’t well-specified.
Certainly, you need to resolve any underspecification. There are ways to do this usefully (or not).
Agreed. My point is simply that one particular (tempting) way of resolving the underspecification is non-useful. ;)