Online rating systems are an indispensable building block for many web applications, yet they are pervasively affected by data biases that distort our understanding of user preferences. A key source of this bias is the “Spiral of Silence” (SoS) phenomenon, where users who perceive their opinions to be in the minority tend to withhold them, leading to non-random missing data. While initial research has begun to explore this issue, existing SoS models for recommender systems fail to capture real-world complexities, such as rating recency, user heterogeneity (e.g., “hardcore” users immune to social pressure), and asymmetric responses to conforming versus dissenting opinions. Furthermore, these models often lack formal theoretical guarantees. To fill this gap, we introduce Bi-MCP, a modular probabilistic framework to quantify and mitigate SoS effects. Bi-MCP models a bifurcated user population (hardcore vs. conformist) and their bidirectional (asymmetric) response to the perceived opinion climate. The framework is (i) Expressive, capturing novel factors missed by prior work; (ii) Modular, allowing its components to be extended or replaced to support future research; and (iii) Theoretically grounded, with a formal proof of convergence for its Generalized Expectation-Maximization (GEM) inference algorithm. Experimental results on four large-scale public datasets demonstrate that our model significantly improves recommendation accuracy over state-of-the-art baselines, showcasing the practical benefit of explicitly modeling these nuanced SoS effects.

Online rating system serves as an indispensable building block for many web applications. Previous studies showed that due to assimilate-contrast effects, historical ratings could significantly distort users' ratings, leading to low accuracy of product quality estimation and recommendation. To understand assimilate-contrast effects, an “accurate” model is still missing as previous models do not capture important factors like rating recency, selection bias, etc. Furthermore, an analytical framework to characterize product estimation accuracy under assimilate-contrast effects is also missing. This paper aims to fill in this gap. We propose a probabilistic model to quantify the aforementioned important factors on assimilate-contrast effects. We apply stochastic approximation theory to show that when the rating bias satisfies mild contraction conditions, the aggregate rating converges under aggregate opinion heterogeneity. We also apply non-stationary Markov chain theory to show that when the strength of assimilate-contrast satisfies mild stable conditions, the aggregate rating converges under rating recency. We also derive an equation to characterize the converged aggregate ratings. These conditions reveal important insights on how the aforementioned factors influence the convergence and guide the online rating system operator to design appropriate rating aggregation rules and rating displaying strategies. We apply it to rating prediction tasks and product recommendation tasks. Experiment results on four public datasets show that our model can improve the rating prediction and recommendation accuracy over previous models significantly, under various metrics like RMSE, NDCG, etc. We also demonstrate the flexibility of our model by showing that it can be applied to enhance other rating behavior models.

Online rating system serves as an indispensable building block for many web applications such as Amazon, TripAdvior and Yelp. It enables production quality estimation via aggregate ratings (a.k.a. wisdom of the crowd) as well as product recommendation via inferring user preference from ratings, etc. Previous studies showed that due to assimilate-contrast effects, historical ratings can significantly distort user's ratings, leading to low accuracy of product quality estimation and recommendation. To understand assimilate-contrast effects, an "accurate'' model is still missing as previous models do not capture important factors like rating recency, selection bias, etc. Furthermore, an analytical framework to characterize product estimation accuracy under assimilate-contrast effects is also missing. This paper aims to fill in this gap. We propose a mathematical model to quantify the aforementioned important factors on assimilate-contrast effects. Our model attains a good balance between model complexity and model accuracy, such that it is neat enough for us to develop an analytical framework to study assimilate-contrast effects. Based on our model, we derive sufficient conditions, under which the product estimation and collective opinion converges to the "ground-truth''. These conditions reveal important insights on how the aforementioned factors influence the convergence and guide the online rating system operator to design appropriate rating aggregation rules and rating displaying strategies. To demonstrate the versatility of our model, we apply to rating prediction tasks and product recommendation tasks. Experiment results on four public datasets show that our model can improve the rating prediction and and recommendation accuracy over previous models significantly.

Online product rating systems have become an indispensable component for numerous web services such as Amazon, eBay, Google Play Store, and TripAdvisor. One functionality of such systems is to uncover the product quality via product ratings (or reviews) contributed by consumers. However, a well-known psychological phenomenon called “ message-based persuasion ” lead to “ biased ” product ratings in a cascading manner (we call this the persuasion cascade ). This article investigates: (1) How does the persuasion cascade influence the product quality estimation accuracy? (2) Given a real-world product rating dataset, how to infer the persuasion cascade and analyze it to draw practical insights? We first develop a mathematical model to capture key factors of a persuasion cascade. We formulate a high-order Markov chain to characterize the opinion dynamics of a persuasion cascade and prove the convergence of opinions. We further bound the product quality estimation error for a class of rating aggregation rules including the averaging scoring rule, via the matrix perturbation theory and the Chernoff bound. We also design a maximum likelihood algorithm to infer parameters of the persuasion cascade. We conduct experiments on both synthetic data and real-world data from Amazon and TripAdvisor. Experiment results show that our inference algorithm has a high accuracy. Furthermore, persuasion cascades notably exist, but the average scoring rule has a small product quality estimation error under practical scenarios.

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.