The minimal rank correlation, subject to order restrictions, with application to the weighted linear choice model (Q1085562)

The weighted linear choice model is one of the most popular models in the social sciences. In this model the utility of a choice object is represented as a weighted sum of attribute-level desirabilities, where the weights are attribute importances. In many empirical contexts the choice objects are such that individuals are highly correlated in terms of their desirability ordering of levels within attribute (e.g., price levels, durability levels, etc.) but may differ appreciably in terms of their evaluations of each attribute's importance. In this paper we address the problem of how dissimilar two individuals may be, in a rank correlation sense, given that they agree completely on the desirability ordering of levels within attributes, but may disagree considerably regarding the importance they attach to the attributes themselves. The problem has interesting implications regarding the potential value of clustering individuals' utility functions for market segmentation or other such purposes.