Spectral Ranking Inferences Based on General Multiway Comparisons

Ranking Inferences for General Multiway Comparisons Ranking inference underpins critical decision-making across diverse domains including e.g. university ranking, journal ranking, academic paper review, voting, online recommendation and tournament competition. Beyond generating point estimates of ranks, these applications also demand confidence intervals for ranks through robust uncertainty quantification, in order to ensure reliable and informed decisions. However, existing approaches predominantly rely on classical models such as Bradley-Terry-Luce and Plackett-Luce, which assume homogeneous comparison structures and prove inadequate for complex real-world scenarios. This paper presents a unified spectral ranking methodology for heterogeneous multiway comparisons, which simultaneously achieves statistical efficiency under minimal structural assumptions and computational scalability. The authors establish comprehensive ranking inference tools, grounded in the asymptotic normality theory and bootstrapping techniques, facilitating top-K selection, rank confidence interval construction, and hypothesis testing for cross-population or cross-period ranking consistency.