The Behavioral Meaning of the Median

摘要

We generalize the notion of statistical preference to the theory of imprecise probabilities, by proposing an alternative notion of desirability of a gamble. As a natural consequence, we derive a general definition of median, providing it with a behavioral meaning. Furthermore, we show that, when we restrict to absolutely continuous probability distributions, a random variable is statistically preferred to another one if and only if the the median of their difference is positive.