I have to say that I don't think it makes sense for an individual to prefer A to B, B to C, and C to A. It's just logically contradictory. Individual preferences should be assumed to be transitive.
I've argued the same thing in the past, but ultimately the same argument can be made without appealing to a single person's intransitivity. For example:
Say there is an A>B>C faction, a B>C>A faction, and a C>A>B faction. No faction is a majority, or of exactly equal size to another faction.
Assume that the election method in question can come up with SOME result. (If the election can't come up with a result, it's not of much use.) Without loss of generality, assume A wins.
Now, imagine the same election without candidate B. A majority prefer C to A, and they are the only two candidates, so any rational election method will elect C.
Now add B back in. A wins. Therefore, IIA has been violated.
This is not a rigorous proof, since I did not provide a rigorous justification why C should win the pairwise contest (although it is obvious). But this example suffices to show, in my opinion, that no reasonable method will ever pass IIA.
-Adam
---- Election-methods mailing list - see http://electorama.com/em for list info
