Phrenocracy

Craniometer.

Phrenocracy is government by phrenology (nonfiction).

• 

  Head of state.

Origin

The word "phrenocracy" was coined by Karl Jones in November 2013:

Phrenology would work just fine, if we lived in a Phrenocracy.

Source: http://bbs.boingboing.net/t/tsa-blows-a-billion-bucks-on-unscientific-behavioral-detection-program-reinvents-phrenology/14210/14

Nonfiction cross-reference

Phrenology (nonfiction)