Read/watch this interview [1] with Ada Palmer on her new book about the Renaissance. Florence did this for a time.

> You put names in a bag. You examine all of the merchant members of guilds. You choose which ones are fit to serve, meaning not ill and dying, not insane, not so deeply in debt that they could be manipulated by the people whom they owe money to. Their names go in a bag. You choose nine guys at random. They rule the city. They are put in a palace where they rule the city from that tower.

> They’re actually locked in the tower for the duration of their time in office because if they left the tower, they could be bribed or kidnapped. They rule the city for two or three months. At the end, they are thanked for their service and escorted out, and then a different nine guys share power for the next three months. It’s a power sharing that is designed to be tyrant-proof because you need consensus of nine randomly selected guys to decide to do anything.

[1] https://www.dwarkesh.com/p/ada-palmer

Perhaps you're joking, but Athenian democracy had a significant amount of randomness, with candidates being chosen randomly from the top vote winners. Terms were also only 1 year for most positions.

These, and other systems, helped prevent any one person from monopolizing power.

This is a good video on this: https://youtu.be/pIgMTsQXg3Q

How about both? A chamber of life peers and a chamber of temporary randomly selected representatives.