Here is where you can find out about the Mushroom Kingdom's government, curtesy of Speedy.
Basically, there are three provinces of office in the Mushroom Kingdom. Portabella, Tortellini, and Fungi Prime. The three provinces share power over the land. However, the Fungi Prime has more power than the other two provinces because the Fungi Prime houses the King and the Supreme Council. The Portabella and Tortellini both have presidents elected to lead them. The Portabella and Tortellina provinces may change laws, but they must first propose them to be approved by the Supreme Council. If approved by the council, the law is then proposed to the King, who will ultimately decide whether or not it will become a national law to be obeyed throughout the land. The presidents of the Portabella and Tortellini provinces are in control of certain nations within the kingdom, but the king has the power to remove the presidents from office if they have committed a betraying act or serious crime. The province of Portabella is now open for election because the previous president tried to get a law illegally passed to give himself more money, weapons, and power to lead a revolt against the Fungi Prime.