To refine the question:
Goal: a society/government capable of lasting centuries. This takes place somewhere within a technological time period (1000BCE to 1000CE). No gunpowder or explosives. I'm imagining warring states in China or Greek city-states.
General idea: people not from the government consistently have the power to fight the government. I'd say perhaps every one or two centuries one has the power to overthrow it.
Personal ideas: ONE: protege/apprenticeship, leaders passing down power as they age to a promising, powerful and younger follower? TWO: democracies? (possible, because a small army could overthrow a tyrant in a revolution, especially if the secret police is weaker than a newly born strong kid)
Refinements that can be ignored, written to clarify what I want:
People get powers at birth, strength can vary from "normal human" to "small army, 1 thousand humans can probably beat the strongest person".
Powers from birth are COMPLETELY random (in terms of strength), perhaps not random in terms of nature (speed, strength, magic, etc.)
Power-balancing exists. Country A won't randomly get a thousand super-strong people and dominate the world. If it has a thousand super-strong people, the rest of the people will have very weak (or no) powers. If a super powerful leader dies, a super powerful kid gets born, or instead five regular powerful kids, or a thousand slightly strong kids. The effect is geographic, so if a war is waged almost at the heart of a country, that country will have the strength of both old armies combined from its new generation (dead people's powers "reincarnated" near that area).
Good luck at making my nonsense work, and thank you if you succeed!