Learning monotone preferences using a majority rule sorting model

We consider the problem of learning a function assigning objects into ordered categories. The objects are described by a vector of attribute values and the assignment function is monotone w.r.t. the attribute values (monotone sorting problem). Our approach is based on a model used in multicriteria decision analysis (MCDA), called MR-Sort. This model determines the assigned class on the basis of a majority rule and an artificial object that is a typical lower profile of the category. MR-Sort is a simplified variant of the ELECTRE TRI method. We describe an algorithm designed for learning such a model on the basis of assignment examples. We compare its performance with choquistic regression, a method recently proposed in the preference learning community, and with UTADIS, another MCDA method leaning on an additive value function (utility) model. Our experimentation shows that MR-Sort competes with the other two methods, and leads to a model that is interpretable.