Another thing: People who propose theoretical systems for governance seem to have a weird fondness of lotteries. I can't really understand it.
Yes, it may be "just" in a mathematical or statistical sense, but it's also maximally intransparent (it's literally impossible to predict who will be chosen, that's the entire idea), so people may view the outcomes as unfair or arbitrary.
It's also easy to manipulate: The people who operate the lottery would be in the best position to become the new power brokers.
Has there ever been any real-life political system that uses lotteries?