Ideocracy is government according to the principles of a particular ideology, or a society run that way — ideo- (idea) plus -cracy (rule), first documented in 1813. It sits one letter from idiocracy, and A.Word.A.Day notes the gap really can be that narrow. Its usage example: Mikhail Epstein in Moscow, building playful alternatives to “Soviet ideocracy” (The Chronicle of Higher Education, 2002).