Expected utility is perfectly rational as the number of "bets" you take goes to infinity.
That's not the way in which maximizing expected utility is perfectly rational.
The way it's perfectly rational is this. Suppose you have any decision making algorithm; if you like, it can have an internal variable called "utility" that lets it order and compare different outcomes based on how desirable they are. Then either:
the algorithm has some ugly behavior with respect to a finite collection of bets (for instance, there are three bets A, B, and C such that it prefers A to B, B to C, and C to A), or
the algorithm is equivalent to one which maximizes the expected value of some utility function: maybe the one that your internal variable was measuring, maybe not.
The first condition is not true, since it gives a consistent value to any probability distribution of utilities. The second condition is not true other since the median function is not merely a transform of the mean function.
I'm not sure what the "ugly" behavior you describe is, and I bet it rests on some assumption that's too strong. I already mentioned how inconsistent behavior can be fixed by allowing it to predetermine it's actions.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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