The behavioral meaning of the median

TitleThe behavioral meaning of the median
Publication TypeJournal Article
Year of Publication2015
AuthorsCouso, Inés, Moral Serafín, and Sánchez Luciano
JournalInformation Sciences
Pagination127 - 138
KeywordsDesirable gamble, Imprecise Probability, Median, Statistical preference, Stochastic ordering

We extend the notion of statistical preference to the general framework of imprecise probabilities, by proposing a new notion of desirability of gambles called “sign-desirability”, different from the usual desirability notion in Walley’s framework. We axiomatically characterize coherent families of sign-desirable gambles. We furthermore prove that the pair of lower and upper previsions of a gamble, according to this new desirability notion, coincides with the pair of bounds (infimum and supremum) of the set of medians associated to a coherent family of linear previsions. Thus, a general notion of median is naturally derived, and provided with a behavioral meaning. As a consequence of these results, the connection between statistical preference in classical Probability Theory, and the sign of the median of the difference of two random variables is laid bare.


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