Trying to identify a scifi short story, possibly from the golden age, where all citizens carry sidearm weapons. Everyone is super-polite because it is legal and accepted to challenge another citizen to a duel to the death at any perceived slight or unresolvable dispute. Anyone not carrying a sidearm (e.g. children, the elderly, infirm, pacifists etc.) not therefore being able to defend themselves have to defer utterly to true citizens. Any ideas?
It's a novel rather than a short story, but that sounds exactly like Beyond this Horizon by Robert Heinlein.
The novel depicts a world where genetic selection for increased health, longevity, and intelligence has become so widespread that the unmodified 'control naturals' are a carefully managed and protected minority. Dueling and the carrying of arms is a socially accepted way of maintaining civility in public; a man can wear distinctive clothing to show his unwillingness to duel, but this results in a lower social status.
This novel is also the source of the quote "An armed society is a polite society"
L. Neil Smith has a book called "The Probability Broach". In it, a parallel Earth that's a libertarian utopia works the way you describe.