That's not what Aumann's agreement theorem says. First of all, it only applies to statistical reasoning about distributions of probabilities. It does not, for

That's not what Aumann's agreement theorem says. First of all, it only applies to statistical reasoning about distributions of probabilities. It does not, for example, apply to "what should one do in this situation?". Preference utilitarianism is not a prior. A prior might be "there is a 5% chance that all cats are dogs". Next, it only applies to Bayesian agents, a subspecies of unicorn. Next, it only applies when all agents have perfect "common knowledge" of each others' posteriors, where "common knowledge" refers to a theoretical infinite transitive closure of meta-knowledge. I think it should be clear that a situation where two agents have common knowledge of each others posteriors is almost as rare as a state where two agents are both reasoning using nothing but Bayesian inference. And lastly, as with your confusion about priors, the agreement that results is not agreement about what to do, or what ought to be done, but is merely an agreement of posteriors. Do you find it rational to apply mathematical theorems about very specific impossible circumstances to unrelated domains, and do you find that the word "theorem" allows to manipulate the unwary?