It seems one problem with using median is that the result depends on how coarsely you model the possible outcomes. E.g. suppose I am considering a bus trip: the bus may be on time, arrive early, or arrive late; and it may be late because it drove over a cliff killing all the passengers, or because it caught fire horribly maiming the passengers, or because it was stuck for hours in a snowstorm, or because it was briefly caught in traffic.
With expected utility it doesn’t matter how you group them: the expected value of the trip is the weighted sum of the expected value of being late/on-time/early. But the median of [late, on time, early] is different from the median of [cliff, fire, snowstorm, traffic, on time, early]
It seems one problem with using median is that the result depends on how coarsely you model the possible outcomes. E.g. suppose I am considering a bus trip: the bus may be on time, arrive early, or arrive late; and it may be late because it drove over a cliff killing all the passengers, or because it caught fire horribly maiming the passengers, or because it was stuck for hours in a snowstorm, or because it was briefly caught in traffic.
With expected utility it doesn’t matter how you group them: the expected value of the trip is the weighted sum of the expected value of being late/on-time/early. But the median of [late, on time, early] is different from the median of [cliff, fire, snowstorm, traffic, on time, early]