First, believing that "extremely irrational" people can compete with other rational and irrational individuals or groups and climb a hierarchy of power to the t

First, believing that "extremely irrational" people can compete with other rational and irrational individuals or groups and climb a hierarchy of power to the top and control it (for decades sometimes) it's something self evidently irrational in my opinion. And second, I doubt the OP really knows what "Putin believes". Putin projects a lot of images for a lot of different people and that's part of a very rational strategy (most probably conceived by some advisor specialized on russian voter psychology). The OP is stuck on one of these projections because it's fed to him frequently by a very rational mass media which simply understands that the average joe needs/loves to believe he is smarter than the "obviously delusional dictator" of a country with 143 million people.