Arrow is not at all "procedural", the French know it well: the 1995 presidential election ended with a Chirac vs Le Pen (the patriarch) duel, even though Lionel Jospin was the favorite and would have beaten both if he had faced them off... A clear example of non-transitivity in elections.
That's my point, sorry if it wasn't clear. Non-transitivity is resolved procedurally. We can theorize about Arrow all we want; in the meantime we can write rules that actually do produce electoral results.
My point is that it wasn't resolved: Jospin was the favorite, but the French were forced to choose between two candidates the majority of them loathed. The rules were a failure.