Popularised in Plato's Republic. Perhaps better called "philocracy"1: rule by philosophers.

This sounds like a joke to those who believe that philosophy accomplishes nothing, but some consider it a romantic ideal of government. It doesn't sound so bad to be governed by people obsessed with ethics and the human condition. Marcus Aurelius is usually considered the closest reality has ever come (although he didn't write much philosophy he studied it extensively).

In the Republic, Socrates discovers that it doesn't work to make kings philosophers but doesn't get a chance to try making a philosopher a king. I'm not sure how much philosophy I want my Members of Parliament to know, but I'd think all my Philosophy Professors would make very entertaining Prime Ministers.

A somewhat related system is rule by scientists, perhaps the two should merged to form a rule by the learned.

1: Although perhaps the sophia should be emphasised more than the philos.