Expected utility is convenient and makes for a nice mathematical theory.
It also makes a lot of assumptions. One assumes that the expectation does, in fact, exist. It need not. For example, in a game where two players toss a fair coin, we expect that in the long run the number of heads should equal the number of tails at some point. It turns out that the expected waiting time is infinite. Then there’s the classic St. Petersburg paradox.
There are examples of “fair” bets (i.e. expected gain is 0) that are nevertheless unfavorable (in the sense that you’re almost certain to sustain a net loss over time).
Expected utility is a model of reality that does a good job in many circumstances but has some key drawbacks where naive application will lead to unrealistic decisions. The map is not the territory, after all.
Expected utility is convenient and makes for a nice mathematical theory.
It also makes a lot of assumptions. One assumes that the expectation does, in fact, exist. It need not. For example, in a game where two players toss a fair coin, we expect that in the long run the number of heads should equal the number of tails at some point. It turns out that the expected waiting time is infinite. Then there’s the classic St. Petersburg paradox.
There are examples of “fair” bets (i.e. expected gain is 0) that are nevertheless unfavorable (in the sense that you’re almost certain to sustain a net loss over time).
Expected utility is a model of reality that does a good job in many circumstances but has some key drawbacks where naive application will lead to unrealistic decisions. The map is not the territory, after all.