Question

What kind of government did plato advocate?

Answer 1

The head of state would be a Philosopher King, in effect an autocrat who made all the decisions themselves. 
However, these decisions would be based entirely on reason and logic, not on self interest. The Philosopher King would be chosen on the basis of being the wisest and most logical person for the position. 
Of course Plato saw himself as the ideal choice for the role.