Methodologies and Algorithms for Group-Rankings Decision

Abstract

The problem of group ranking, also known as rank aggregation, has been studied in contexts varying from sports, to multicriteria decision making, to machine learning, to ranking Web pages, and to behavioral issues. The dynamics of the group aggregation of individual decisions has been a subject of central importance in decision theory. We present here a new paradigm using an optimization framework that addresses major shortcomings that exist in current models of group ranking. Moreover, the framework provides a specific performance measure for the quality of the aggregate ranking as per its deviations from the individual decision-makers’ rankings. The new model for the group-ranking problem presented here is based on rankings provided with intensity—that is, the degree of preference is quantified. The model allows for flexibility in decision protocols and can take into consideration imprecise beliefs, less than full confidence in some of the rankings, and differentiating between the expertise of the reviewers. Our approach relaxes frequently made assumptions of: certain beliefs in pairwise rankings; homogeneity implying equal expertise of all decision makers with respect to all evaluations; and full list requirement according to which each decision maker evaluates and ranks all objects. The option of preserving the ranks in certain subsets is also addressed in the model here. Significantly, our model is a natural extension and generalization of existing models, yet it is solvable in polynomial time. The group-rankings models are linked to network flow techniques.