[SilasX]

Yeah, but that takes the punch out of the theorem. It's saying, "hey, sometimes you have really screwy preferences, too bad."

Realistically, that kind of situation doesn't break a voting system. We can say "we don't care about that case -- just pick a random winner then", but it's no longer deterministic.

Is there a stronger version of the theorem that says there's no sane procedure even ignoring those cases?

[gweinberg]

No, of course not. It's really easy to come up with a system that always comes up with "good" results if you rule out "screwy" voter preferences, with a sufficiently restrictive value of "screwy".

[SilasX]

"Screwy" in this context means the sort of intransitive situations referred to in the parent of my last comment.

[reagency]

That is all the punch he theorem has. Arrows theorem shows that aggregate preferences have ties even when individuals don't, and strategic voting can tip the results in those cases.