Already have that test
Anybody who can get through a modern presidential campaign needs to be under serious psychiatric observation, and probably face-tattooed "Do Not Follow" in case they escape the facility. The system seems to have failed last time - the current President seems almost sane.
I can only think of two systems that are better optimizations for selecting the worst available leader. Monarchy and revolution.
Neither of those is entirely foolproof. England had a really good king (Aelfred the Great) in the 900's. But he was the seventh son, so nobody expected him to be king. And Vaclev Havel - wtf? A poet and actual decent human being running a successful revolution? Seriously, wtf?
