Coin flip sounds good to me. If you honestly don't know how to solve a problem, inventing a discipline for the express purpose of having an authority to point to sounds like the worst possible idea. It makes it much harder to change course if you can't merely say "oh, we should try tails instead due to xyz" because now you've got another institution fighting to justify its own survival.
We need a reason to sound Certain. We should do away with the Fed, etc and systematise on the Oracle. That way when things go wrong we can still say it was the will of the Gods without needing to have an inquiry about it.
Though we would probably just have one about who offended the gods.
