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Reputation systems in mobile ad-hoc networks can be tricked by the spreading of false reputation ratings, be it false accusations or false praise. Simple solutions such as exclusively relying on one's own direct observations have drawbacks, as they do not make use of all the information available. We propose a fully distributed reputation system that can cope with false disseminated information. In our approach, everyone maintains a reputation rating and a trust rating about everyone else that they care about. From time to time first-hand reputation information is exchanged with others; using a modified Bayesian approach we designed and present in this paper, only second-hand reputation information that is not incompatible with the current reputation rating is accepted. Thus, reputation ratings are slightly modified by accepted information. Trust ratings are updated based on the compatibility of second-hand reputation information with prior reputation ratings. Data is entirely distributed: someone's reputation and trust is the collection of ratings maintained by others. We enable node redemption and prevent the sudden exploitation of good reputation built over time by introducing re-evaluation and reputation fading. We present the application of our generic reputation system to the context of neighborhood watch in mobile ad-hoc networks, specifically to the CONFIDANT protocol for the detection and isolation of nodes exhibiting routing or forwarding misbehavior. We evaluate the performance by simulation.