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.
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. ;)