Would this work?
What if grouped people as chunks of 300 people based on geographical location. Then let them elect one person from that group, which will move on to next phase of 300 people who got elected from all different groups. And so on when we reach the final group of the last elected person would be highest office holder, then all other positions can be taken in the last group, and all other positions can be filled by group of people in previous groups. Would that make any difference from current form of democracy?