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

[James Green-Armytage]

Adam Tarr quoted from me:
>>         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.

then Adam Tarr wrote:
>
>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

I reply:
	I'm really confused here, Adam. Are you sure that you are understanding
my distinction between individual and collective preferences? Individual
preferences should be transitive. Collective preferences are unfortunately
not guaranteed to be transitive. I just can't figure out any way in which
your e-mail is a reply to mine. You don't seem to be disagreeing with me,
yet you seem to think that you are; I don't know why. I never said that a
method should be expected to pass IIA, or that collective preferences
should be transitive.

James