@article {COUSO2015127,
title = {The behavioral meaning of the median},
journal = {Information Sciences},
volume = {294},
year = {2015},
note = {Innovative Applications of Artificial Neural Networks in Engineering},
pages = {127 - 138},
abstract = {We extend the notion of statistical preference to the general framework of imprecise probabilities, by proposing a new notion of desirability of gambles called {\textquotedblleft}sign-desirability{\textquotedblright}, different from the usual desirability notion in Walley{\textquoteright}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.},
keywords = {Desirable gamble, Imprecise Probability, Median, Statistical preference, Stochastic ordering},
issn = {0020-0255},
doi = {https://doi.org/10.1016/j.ins.2014.08.049},
url = {http://www.sciencedirect.com/science/article/pii/S0020025514008548},
author = {In{\'e}s Couso and Seraf{\'\i}n Moral and Luciano S{\'a}nchez}
}