It's a tempting thought. But I think it's hard to make the math work that way.
I have a lovely laptop here that I am going to give you. Suppose you assign some utility U to it. Now instead of giving you the laptop, I give you a lottery ticket or the like. With probability P I give you the laptop, and with probability 1 - P you get nothing. (The lottery drawing will happen immediately, so there's no time-preference aspect here.) What utility do you attach to the lottery ticket? The natural answer is P * U, and if you accept some reasonable assumptions about preferences, you are in fact forced to that answer. (This is the basic intuition behind the von Neumann-Morgenstern Expected Utility Theorem.)
Given that probabilities are real numbers, it's hard to avoid utilities being real numbers too.
it's hard to avoid utilities being real numbers too
If we are going into VNM utility, it is defined as the output of the utility function and the utility function is defined as returning real numbers.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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