Before revision:  Median comparisons using parametric models such as the ordered probit and logit can be readily carried out using familiar statistical softwares like STATA. We also show a previously assumed impractical task of estimating a semiparametric median ordered-response model is also possible by using a novel constrained mixed integer optimization technique.
After revision:  The median ranking can also be performed semiparametrically and we provide a new constrained mixed integer optimization technique.