There’s a word that describes a system in which there is a leader, and that leader is seen as incapable of making mistakes, and all behaviors and actions taken by that leader are justified or elaborately explained away by followers as part of the philosophy, no matter how ridiculous or unlikely (in other words, followers’ devotion is so high that they will go to any lengths to reaffirm the belief system). Some people have used this work to describe Objectivist worship of Ayn Rand, but I cannot for the life of me remember what this word is. Any help?
Does cult of personality come close?
It’s close, but the word I’m thinking of sounds more formal, like “oligarchy” or “monopoly.”
Idolatry.
No, that’s not it either. It’s not a very common word, and my recollection is that it’s not a word that most people would know if they read it.
Benign Dictatorship?
Infallibility?
I finally thought of the word-- except I was confused and misdefined the word in the thread title. The word I was thinking of hagiography-- which doesn’t refer to the system, but the syncophantic writings relating to the leader. Thanks for the help, everyone, and sorry for misdefining.
Time for a neologism, then. From now on, we can refer to government run by those considered to be a saint as a “hagiocracy”.
Nicely done. Too bad such a government would be so rare that we’ll never get a chance to actually use the word.
I believe that would apply to The Vatican. 
I think such a word would be useful outside actual governments of countries. I can see describing a team at a former job with such a word. It is arguable that Dr. House and company form what this word would describe.
I looked up “hagiocracy” (Webster) and it strictly means a government by a priesthood. How are the chances of ever using that word in that way? 
I’m stumped at an alternative, though. What works of fiction feature a group whose leader is deemed infallible? We could construct an -ism out of it.
Republican
Fundamentalism.
religion
Closed?