Kakistocracy

From Dictionary.com

government by the worst persons; a form of government in which the worst persons are in power. 

The city of Wasilla was a  Kakistocracy from 1996-99.

The state of Alaska was a Kakistocracy from 2006-2009.

And the United State would have been a Kakistocracy if McCain had been elected president and died while in office.