Some misbehavior detection and reputation systems in mobile ad-hoc networks rely on the dissemination of information of observed behavior, which makes them vulnerable to false accusations. This vulnerability could be removed by forbidding the dissemination of information on observed behavior in the first place, but, as we show here, this has more drawbacks than a solution that allows dissemination and copes with false accusations. We propose a method for reducing the impact of false accusations. In our approach, nodes collect first-hand information about the behavior of other nodes by direct observation. In addition, nodes maintain a rating about every other node that they care about, in the form of a continuous variable per node. From time to time nodes exchange their first-hand information with others, but, using the Bayesian approach we designed and present in this paper, only second-hand information that is not incompatible with the current rating is accepted. Ratings are slightly modified by accepted information. The reputation of a given node is the collection of ratings maintained by others about this node. By means of simulation we evaluated the robustness of our approach against several types of adversaries that spread false information, and its efficiency at detecting malicious nodes. The simulation results indicate that our system largely reduces the impact of false accusations, while still benefiting from the accelerated detection of malicious nodes provided by second-hand information. We also found that when information dissemination is not used, the time until malicious nodes are detected can be unacceptable.