The original post focuses on the limiting edge case where the only information coming out of the doctor is a single bit: Treatment vs Healthy. I believe the sub

The original post focuses on the limiting edge case where the only information coming out of the doctor is a single bit: Treatment vs Healthy. I believe the subject can reasonably expect some explanation from the doctor, and then we are in the territory of Interactive Proofs and Arthur-Merlin Games. (https://en.wikipedia.org/wiki/Interactive_proof_system https://en.wikipedia.org/wiki/Interactive_proof_system) Actually I'm a bit surprised they were not mentioned in the original post, nor in any of the 127 comments so far. They are the computational complexity models of a situation when a (computationally) all-powerful but unreliable agent has to convince another, (computationally) limited agent. If there's a second greedy doctor, or a greedy detective, we have Multi-prover Interactive Proofs.