Careful, this might sound intuitive but be deathly wrong

Care to elaborate on your concerns? We're obviously speaking theoretically here at a high level of abstraction

My concern is that it might be possible to watch each other while keeping authority. You say it's not possible as if there was some kind of proof.

If everyone can watch everyone with equal transparency, that would seem to imply a distributed system with information symmetry, which is antithetical to centralized authority. If there was a central authority/super admin in such a system, how would you keep them from covertly creating information asymmetry?