The Asymmetry of Trust

Trust is asymmetric in many ways. For example, to trust is not to be trusted. Also it takes many examples of demonstrated reliability to develop trust, but only one instance of unreliability to break it. There's another more subtle form of asymmetry though.

Suppose that someone takes your lunch at work. If you approach a person you trust and you ask "Did you take my lunch", you have an expectation that the person will tell the truth. Whether they say yes or no, you believe their answer (although "yes" might piss you off or make you trust them less). On the other hand, if you approach someone you don't trust, while you might have an expectation that they will lie to you, you would probably accept a "yes" answer as truthful. In other words, while you have a low expectation of a "yes" answer in both cases, you are about as likely to believe this answer from either a trusted or untrusted party, whereas a "no" answer would only seem trustworthy from the trusted party.

I'm not sure if this is already a well-understood phenomenon in decision theory or game theory. It would probably be expressible in terms of prior and posterior probabilities in a Bayesian sense. The prior probability favors a true answer for the trusted party and a false answer for the untrusted party (there's a probability p of a "true" answer and a probability 1-p of a "false" answer). Given a "yes" answer the posterior probability changes in favor of true for the untrusted party, but not for the trusted party.