[2604.04588] Noisy Nonreciprocal Pairwise Comparisons: Scale Variation, Noise Calibration, and Admissible Ranking Regions

Statistics > Machine Learning arXiv:2604.04588 (stat) [Submitted on 6 Apr 2026] Title:Noisy Nonreciprocal Pairwise Comparisons: Scale Variation, Noise Calibration, and Admissible Ranking Regions Authors:Jean-Pierre Magnot View a PDF of the paper titled Noisy Nonreciprocal Pairwise Comparisons: Scale Variation, Noise Calibration, and Admissible Ranking Regions, by Jean-Pierre Magnot View PDF HTML (experimental) Abstract:Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect to be corrected immediately. In this article, we adopt a different point of view: part of the nonreciprocity may reflect a genuine variation in the evaluation scale, while another part is due to random perturbations. We introduce an additive model in which the unknown underlying comparison matrix is consistent but not necessarily reciprocal. The reciprocal component carries the global ranking information, whereas the symmetric component describes possible scale variation. Around this structured matrix, we add a random perturbation and show how to estimate the noise level, assess whether the scale variation remains moderate, and assign probabilities to admissible ranking regions in the sense of strict ranking by pairwise comparisons. We also compare this approach with the brutal projection onto reciprocal matrices, which sup...