[EM] Does the 'Independence of Irrelevant Alternatives Criterion' Imply a

[Adam Tarr]

>         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