Iterative ranking aggregation using quality improvement of subgroup ranking

Abstract

Ranking aggregation concerns the combination of rankings to obtain a consensus ranking that best represents all the input rankings according to a specific criterion. However, finding the optimal aggregated ranking, i.e., the one with the highest quality, is usually NP-hard. To reduce the computational cost, many heuristic aggregation methods have been proposed. They cannot ensure the optimality and the qualities of aggregated rankings obtained actually can be further improved. To find a better aggregated ranking, a novel iterative ranking aggregation method (IRAM) is proposed in this paper using the quality improvement of the subgroup ranking. IRAM starts from an aggregated ranking generated by a traditional heuristic ranking aggregation method. In each iteration step, IRAM attempts to improve the ranking’s quality of a subgroup of items. If the ranking’s quality of a subgroup of items is improved, the full aggregated ranking’s quality is consequently improved. Moreover, a window iterative ranking aggregation method (W-IRAM) is designed, which is simpler than the IRAM. We prove that IRAM and W-IRAM bring better (or at least the same) aggregation qualities compared with the traditional heuristic ranking aggregation methods. Simulation results show that our iterative ranking aggregation approaches perform well.