what was asked for was a system of selecting public officials
There are a lot of political system where the power flows from the top down. Monarchies, dictatorships, etc.
Your example would be, I guess, a junta?
What I had in mind was more a hybrid between feudalism and the democratic process originally described. Democratic, bottom up above a certain level, top down below a certain level. But the idea was promoting a single person from a small group to a small group of similarly promoted people and so on ad infinitum, concentrating power by either process. I'm thinking of a system that could be implemented in practice.
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