I am writing a paper on a dystopia and how the leader came to be. I need a term to describe how he wasn't elected into power but he just assumed the role of instigator and no one questioned him.
I don't think there's a standard single-word term, but Google Books claims about 3,220 results for...
(There are a few hundred more for self-appointed ruler, for example.)
I don't think self-appointed necessarily and inherently carries negative connotations, but it's possible not everyone shares that view. So you might also consider...
de facto - something generally accepted or agreed to without any formal decision in its favor:
“They never elected him; he became their leader de facto.” - dictionary.reference.com
“He is our de facto leader”
To describe a head of state (or another constituency) who wasn't elected but assumed office through sheer determination, charisma, trickery, demagoguery, assassination or war, I would say he muscled his way to the top.
A providential leader may fit.
Essentially the "providential leader" is an influent patriot that has the opportunity to do something for the country and that takes into account the concerns expressed by the people in charge and around to bring a better contribution to its country.
"he naturally emerged as a leader"
- His personality traits - actions and attitudes - were such that he naturally emerged as a leader.
"he was a born-leader"
All others were no match for him. He was a born-leader and rose to that post naturally, facing no opposition.
There is a concept benevolent despotism (also called enlightened despotism) that suggests absolute power, but with a heart.
Associated with this term is a saying I have heard, but whose source I cannot find:
The best form of government is benevolent despotism -- so long as I get to pick the despot.