The belief signaling trilemma (or signaling trilemma for simplicity) points out that (a) people assign reputation based on claims; (b) people want to maintain their reputation; therefore, (c) people warp their claims. This presents a trilemma:
We could agree to stop assigning reputation based on beliefs, but this would deprive us of an extremely valuable tool for evaluating others, besides being impossible to enforce.
We could agree to always report honest beliefs, but this could be very costly for cooperators and again impossible to enforce.
We could embrace dishonest reporting of beliefs, but this can severely warp the discourse.