Is bounded utility truly necessary to normalize it? So long as the utility function never actually returns infinity in practice, normalization will work.
Huh?
Suppose my utility function is unbounded and linear in kittens (for any finite number of kittens I am aware of, that number is the output of my utility function). How do you normalize this utility to [-1,1] (or any other interval) while preserving the property that I’m indifferent between 1 kitten and a 1/N chance of N kittens?
Is the number of possible kittens bounded? That’s the point I was missing earlier.
If the number of kittens is bounded by M, your maximum utility u_max is bounded by M times the constant utility of a kitten (M * u_kitten). Therefore u_kitten is bounded by 1/M.
In future, consider expressing these arguments in terms of ponies. Why make a point using hypothetical utility functions, when you can make the same point by talking about what we really value?
Huh?
Suppose my utility function is unbounded and linear in kittens (for any finite number of kittens I am aware of, that number is the output of my utility function). How do you normalize this utility to [-1,1] (or any other interval) while preserving the property that I’m indifferent between 1 kitten and a 1/N chance of N kittens?
Is the number of possible kittens bounded? That’s the point I was missing earlier.
If the number of kittens is bounded by M, your maximum utility u_max is bounded by M times the constant utility of a kitten (M * u_kitten). Therefore u_kitten is bounded by 1/M.
In future, consider expressing these arguments in terms of ponies. Why make a point using hypothetical utility functions, when you can make the same point by talking about what we really value?