Peer-to-peer (P2P) networks have received great attention for sharing and searching information in large user communities. The open and anonymous nature of P2P networks is one of its main strengths, but it also opens doors to manipulation of the information and of the quality ratings. In our previous work (J. X. Parreira, D. Donato, S. Michel and G. Weikum in VLDB 2006) we presented the JXP algorithm for distributed computing PageRank scores for information units (Web pages, sites, peers, social groups, etc.) within a link- or endorsement-based graph structure. The algorithm builds on local authority computations and bilateral peer meetings with exchanges of small data structures that are relevant for gradually learning about global properties and eventually converging towards global authority rankings. In the current paper we address the important issue of cheating peers that attempt to distort the global authority values, by providing manipulated data during the peer meetings. Our approach to this problem enhances JXP with statistical techniques for detecting suspicious behavior. Our method, coined Trust JXP, is again completely decentralized, and we demonstrate its viability and robustness in experiments with real Web data.