A computationally intensive ranking system for paired comparison data

Abstract

In this paper, we introduce a new ranking system where the data are preferences resulting from paired comparisons. When direct preferences are missing or unclear, then preferences are determined through indirect comparisons. Given that a ranking of n subjects implies (2n) paired preferences, the resultant computational problem is the determination of an optimal ranking where the agreement between the implied preferences via the ranking and the data preferences is maximized. Comparisons are carried out via simulation studies where the proposed rankings outperform Bradley–Terry in a particular predictive comparison. Keywords: Nonparametric methods, NCAA basketball, Ranking, Simulated annealing, Statistical computing