Online rating systems are often used in numerous web or mobile applications, e.g., Amazon and TripAdvisor, to assess the ground-truth quality of products. Due to herding effects, the aggregation of historical ratings (or historical collective opinion) can significantly influence subsequent ratings, leading to misleading and erroneous assessments. We study how to manage product ratings via rating aggregation rules and shortlisted representative reviews, for the purpose of correcting the assessment error. We first develop a mathematical model to characterize important factors of herding effects in product ratings. We then identify sufficient conditions (via the stochastic approximation theory), under which the historical collective opinion converges to the ground-truth collective opinion of the whole user population. These conditions identify a class of rating aggregation rules and review selection mechanisms that can reveal the ground-truth product quality. We also quantify the speed of convergence (via the martingale theory), which reflects the efficiency of rating aggregation rules and review selection mechanisms. We prove that the herding effects slow down the speed of convergence while an accurate review selection mechanism can speed it up. We also study the speed of convergence numerically and reveal trade-offs in selecting rating aggregation rules and review selection mechanisms. To show the utility of our framework, we design a maximum likelihood algorithm to infer model parameters from ratings, and conduct experiments on rating datasets from Amazon and TripAdvisor. We show that proper recency aware rating aggregation rules can improve the speed of convergence in Amazon and TripAdvisor by 41% and 62% respectively.

翻译：在线评分系统广泛用于众多网络或移动应用（如亚马逊和TripAdvisor）中以评估产品的真实质量。由于羊群效应，历史评分（或历史集体意见）的聚合会显著影响后续评分，导致误导性和错误性评估。本研究探讨如何通过评分聚合规则与精选代表性评论来管理产品评分，以修正评估误差。我们首先建立数学模型来刻画产品评分中羊群效应的关键因素。随后通过随机近似理论确定充分条件，使得历史集体意见收敛于全体用户的真实集体意见。这些条件界定了一类能够揭示产品真实质量的评分聚合规则与评论筛选机制。我们进一步运用鞅理论量化收敛速度，以反映评分聚合规则与评论筛选机制的效率。研究证明羊群效应会减缓收敛速度，而精准的评论筛选机制能加速该过程。我们通过数值方法分析了收敛速度，并揭示了选择评分聚合规则与评论筛选机制时的权衡关系。为验证框架的实用性，我们设计了最大似然算法从评分数据中推断模型参数，并在亚马逊和TripAdvisor的评分数据集上进行实验。结果表明，采用适当的时效感知评分聚合规则可分别将亚马逊和TripAdvisor的收敛速度提升41%和62%。