Kakistocracy
Government by the least qualified or worst persons.

The word derives directly from the Greek κάκιστος worst + -κρατία rule, but ultimately from the Indo-European root kakka-/kaka– (to defecate), which apparently also gave us poppycock, cacophony, cacology and cacography; as well as the Francophone caca. The earliest documented use was in 1829.
H/T: A.Word.A.Day