Preference-sorting structures extending scores and ordered categories: an axiomatic distance approach in group decision making

In various popular group decision making problems, e.g., proposal funding review, decision makers are required to provide both score values and sorting labels for alternatives. In this study, this kind of preference structure is formally defined as preference-sorting structure, which is a hybrid preference representation system extending the cardinal preference (score) model by combining multiple ordered categories in the process of preference modeling. In some cases, due to time and capacity limitations, the alternatives evaluated by a decision maker may constitute only a subset of the total alternatives. Several appealing axioms are introduced to characterize an “ideal” distance functions for preference-sorting structures in both complete and incomplete scenarios, respectively. Each set of axioms imply the existence of a unique distance function for complete and incomplete scenarios where the distance function for incomplete preference-sorting structures generalizes that for complete structures. Furthermore, based on the unique distance function for incomplete preference-sorting structures, an axiomatic distance approach with desirable properties is developed to aggregate individual incomplete preference-sorting structures. Through theoretical proof and simulation analysis, it is demonstrated that the group preference-sorting structure derived from the axiomatic distance approach exhibits a strong correlation with both the median score and median sorting.