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In this paper, we introduce the first application of the belief propagation algorithm in the design and evaluation of trust and reputation management systems. We approach the reputation management problem as an inference problem and describe it as computing marginal likelihood distributions from complicated global functions of many variables. However, we observe that computing the marginal probability functions is computationally prohibitive for large-scale reputation systems. Therefore, we propose to utilize the belief propagation algorithm to efficiently (in linear complexity) compute these marginal probability distributions; resulting a fully iterative probabilistic and belief propagation-based approach (referred to as BP-ITRM). BP-ITRM models the reputation system on a factor graph. By using a factor graph, we obtain a qualitative representation of how the consumers (buyers) and service providers (sellers) are related on a graphical structure. Further, by using such a factor graph, the global functions factor into products of simpler local functions, each of which depends on a subset of the variables. Then, we compute the marginal probability distribution functions of the variables representing the reputation values (of the service providers) by message passing between nodes in the graph. We show that BP-ITRM is reliable in filtering out malicious/unreliable reports. We provide a detailed evaluation of BP-ITRM via analysis and computer simulations. We prove that BP-ITRM iteratively reduces the error in the reputation values of service providers due to the malicious raters with a high probability. Further, we observe that this probability drops suddenly if a particular fraction of malicious raters is exceeded, which introduces a threshold property to the scheme. Furthermore, comparison of BP-ITRM with some well-known and commonly used reputation management techniques (e.g., Averaging Scheme, Bayesian Approach, and Cluster Filtering) indicates the superiority of - he proposed scheme in terms of robustness against attacks (e.g., ballot stuffing, bad mouthing). Finally, BP-ITRM introduces a linear complexity in the number of service providers and consumers, far exceeding the efficiency of other schemes.