Other forms: kakistocracies
A government run by the least qualified people can be called a kakistocracy.
The term kakistocracy first appeared in the 17th century, coined from the Greek kakistos, "worst," and -cracy, "rule by," which is used in words like aristocracy and democracy. It's often used to disparage governments that are seen as inept, corrupt, or both. If a president appointed her close friends and relatives to fill all the most important cabinet jobs, despite their lack of experience, it would be an example of kakistocracy.