> Arrow's theorem concerns the situation where your election procedure needs to deliver (not just a single winner, but) a ranking of all the candidates. Well,

> Arrow's theorem concerns the situation where your election procedure needs to deliver (not just a single winner, but) a ranking of all the candidates. Well, any social welfare function that can pick a single winner can also be used to form a complete ordering, by repeating the process with the previous winner eliminated. So any social welfare function is a social ordering function.