I knew there was a word for it:

kakistocracy

SYLLABICATION: kak·is·toc·ra·cy

PRONUNCIATION: kk-stkr-s, käk-

NOUN: Inflected forms: pl. kak·is·toc·ra·cies

Government by the least qualified or most unprincipled citizens.

ETYMOLOGY: Greek kakistos, worst, superlative of kakos, bad; see caco– + –cracy.