[EM] Does the 'Independence of Irrelevant Alternatives Criterion' Imply a
Adam Tarr
atarr at purdue.edu
Thu Apr 1 21:24:02 PST 2004
> 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
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