I can't remember if this is a short story or a novella. Definitely sci-fi written in 50s or 60s when fear of annihilation by nuclear bomb was at its height. The story - in the first person - is about a man chosen for his absolute coolness in obeying, doing what he is told regardless of the consequences for humanity. He ends up, I think, responsible for a whole load of people saved from the nuclear holocaust and living underground in tiers of importance. He has to push a button to decide what they get and don't get.
Any ideas, please? I would be so grateful!