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 suppresses all symmetric information at once. The Gaussian perturbation model is used here not because human decisions are exactly Gaussian, but because observed judgment errors often result from the accumulation of many small effects. In such a context, the central limit principle provides a natural heuristic justification for Gaussian noise. This makes it possible to derive explicit estimators and probability assessments while keeping the model interpretable for decision problems.

翻译：成对比较广泛用于决策分析、偏好建模和评估问题。在许多实际情境中，观测到的比较矩阵并不满足互易性。这种非互易性通常被视为需要立即纠正的缺陷。本文采用不同的视角：部分非互易性可能反映评估尺度的真实变异，而另一部分则源于随机扰动。我们引入一个加性模型，其中未知的潜在比较矩阵是一致的但不必互易。互易分量承载全局排序信息，而对移分量描述可能的尺度变异。围绕该结构化矩阵，我们添加随机扰动，并展示如何估计噪声水平、评估尺度变异是否仍处于适度范围，以及为成对比较的严格排序意义下的可容许排序区域分配概率。我们还将此方法与直接投影到互易矩阵（该方法会瞬间抑制所有对称信息）进行比较。在此使用高斯扰动模型并非因为人类决策精确服从高斯分布，而是因为观测到的判断误差往往源于大量微小效应的累积。在此背景下，中心极限定理为高斯噪声提供了自然的启发式依据。这使得在保持模型可解释性以供决策问题使用的同时，能够推导出显式估计量和概率评估。