I'm also a fan of Monte-Carlo sampling and would like to see it implemented more in choosing a government, but fully random people wouldn't have legitimacy to t

I'm also a fan of Monte-Carlo sampling and would like to see it implemented more in choosing a government, but fully random people wouldn't have legitimacy to their rule. Social order only works if people believe in it and I don't see how we can make people believe in fully random choice. That person could only have power if they fully control the army and why would the army let themselves be controlled rather than kill the random person and put someone else in charge, who will promise them the cushy life. You did mention giving the person training. The problem with that is this will result in a fully self-perpetuating system that finds ways to not give power to people who disagree with it. It still sounds better than the current system, so I'm all for it.