  Reputation systems seek to infer which members of a community can be trusted
based on ratings they issue about each other. We construct a Bayesian inference
model and simulate approximate estimates using belief propagation (BP). The
model is then mapped onto computing equilibrium properties of a spin glass in a
random field and analyzed by employing the replica symmetric cavity approach.
Having the fraction of trustful nodes and environment noise level as control
parameters, we evaluate the theoretical performance in terms of estimation
error and the robustness of the BP approximation in different scenarios.
Regions of degraded performance are then explained by the convergence
properties of the BP algorithm and by the emergence of a glassy phase.
