Agreement between observers, a physical principle?

Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. The seminal Agreement Theorem by Aumann (Annals of Statistics, 1976) states that two (classical) agents cannot agree to disagree. We examine the extension of this theorem to no-signalling settings. In particular, we establish an Agreement Theorem for quantum agents. We also construct examples of (post-quantum) no-signalling boxes where agents can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.