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.
Venice's system also involved random selection, though in a very convoluted way.
There were multiple repeated iterations where they selected a random group of eligible people and then that group voted to select a group who would then have a random selection taken who would then elect another group and so on.
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.
Not joking, although maybe not terribly serious either. I could envision a random (filtered) selection of citizens being given a veto power over legislation, as another check against abuse.
Not quite the same thing, but in Ireland, it's become more common for Citizens Assemblies, which are randomly selected (this is disputed by some) citizens appointed to help word referenda on constitutional amendments and otherwise gauge public feeling on certain issues.
The assembly then passes it's recommendation to the Parliament who are free to ignore it if they don't like it.
Some people who actively seek positions of power are terribly unqualified or have other discommending properties, as well. This does not seem too great an impediment to their success.