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Don't Have a Utility Function?
An answer you don't want to give is that unless someone is perfectly rational, they don't have a utility function at all. For example, maybe if I ask you about a bunch of coin flips between dollar amounts, maybe that's something you have pretty good access to and can tell me about. And then I can figure out your utility function from that. Then I can then use your utility function when I advise you how to play poker or how to invest in the stock market. Those are much more complicated decisions that you don't have any intuitive preferences about.