Well, the effective altruists believe that ethical problems can be approached using a lot of the techniques outlined in "measuring intangibles in business". That is, through proper analysis and approaching it like a programming/engineering problem.
And according to Aumann's agreement theorem, if your priors are the same (such as preference utilitarianism) two people should agree.
That is to say, I think it can work like that, as long as everyone involved agrees on an ethical framework and decision theory. And that everyone probably should do that.
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?
I think getting total agreement on what ethical framework to use is really hard. For most hard problems, you need all the help you can get, and turning away anyone who doesn't exactly fit your framework is counterproductive. It might work in cases where the group of people you're working with are determined by a common interest or a common worldview.
And according to Aumann's agreement theorem, if your priors are the same (such as preference utilitarianism) two people should agree.
That is to say, I think it can work like that, as long as everyone involved agrees on an ethical framework and decision theory. And that everyone probably should do that.