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

[Marcos C. Ribeiro]

Thank you for your answer and information, Forest. It makes me feel I have company and more confident on my thoughts.  :)

To be more precise, my thought is that the IIA criterion could be worded as 'the election winner must win every other candidate in a pairwise dispute'. In other words, the IIA criterion requires a Condorcet winner. This means that IIA is a false criterion, because the absence of a Condorcet winner can not be considered a problem with any election method, it only reflects ambiguities in the electors preferences. Valid is the Cordorcet criterion, much more conscious: IF there is a Condorcet winner, a good election method must declare it the winner. This is OK.

THE CONCLUSIONS ARE:
-> If IAA is a false criterion, it doesn't make sense to verify if any method fulfils it. We must be very secure with the principles from which we start. To verify false criterions is to go in a wrong line of thought. Simple so. 
-> If the Arrow's theorem depends on the IAA criterion, it is a false "theorem", no matter how famous it is. (To go ahead, I think we must ignore authority arguments and to have a discussion between equals.)  

You established a difference that I judge important, the difference between 'fundamental level' and 'in terms of ballots'. It seems to me that:
-> First, all criteria shall always be formulated and evaluated in the fundamental level, in terms of the logic of democracy. 
-> IF, and only IF, a criterion is considered valid at the fundamental level, it then must be translated 'in terms of ballots', what already enters in the field of its practical application and verification. 
Do you agree with this ? Do you want to clarify the difference between 'fundamental level' and 'ballots level' ?

I have affinity for the Independence of Clones criterion, but I haven't evaluated it carefully yet. I think it would be better named by 'Independence of DEFEATED Clones Criterion', or 'Independence of Irrelevant Clones', and I word it as: 'the winner should remain the same with the elimination of defeated clones'. This drives us to think that a Condorcet cycle tends to happen only between clones, but I'm not sure about this. What do you think about ? I have affinity for the Independence of Clones because the presence of similar candidates should not aid nor prejudice them. 

Best regards.

Marcos.


-----Mensagem Original----- 
De: "Forest Simmons" <fsimmons at pcc.edu>
Para: "Marcos C. Ribeiro" <marcoscanrib at ig.com.br>
Cc: <election-methods-electorama.com at electorama.com>
Enviada em: Segunda-feira, 29 de Março de 2004 19:26
Assunto: Re: [EM] Does the 'Independence of Irrelevant Alternatives Criterion' Imply a Condorcet Winner ?

> Yes, Arrow did use the IIA criterion, and yes, most folks here agree that
> it is the criterion that is too strict, and therefore should be relaxed in
> one way or another.  For example, the winner should come from the Smith
> set, and (at very least) the method should have "clone independence."
> 
> Any time there is a "Condorcet cycle" of the type A beats B beats C beats
> A, no matter who the winner is, eliminating the candidate that the winner
> beats, turns the winner into a loser.
> 
> Some folks believe that this is a defect of Condorcet methods.  But
> Condorcet cycles are a fact of life, whether or not my favorite method
> detects them.
> 
> So at some fundamental level no method really, truly satisfies the IIAC.
> However, some methods like Approval satisfy it technically when it is
> expressed in terms of ballots.
> 
> Suppose in the above example that A is the Approval winner and that B
> withdraws from the contest.  Then the approval ballots will still say that
> A beats C even though, if the voters had a chance to vote for A or C with
> B out of the contest, they would choose C.
> 
> How is this possible?  Ballots that approved only B would approve nobody
> after B's withdrawal, while ballots that disapproved both A and C before
> the withdrawal of B, would disapprove nobody after the withdrawal.
> 
> In other words, the ballots would not be realistic reflections of the
> voter wishes for a two way contest between A and C.
> 
> You probably already figured this out, but perhaps it is worth putting in
> writing one more time for new lurkers.
> 
> Forest
> 


> On Mon, 29 Mar 2004, Marcos C. Ribeiro wrote:
> 
> > Hi Democracy Friends.
> >
> > As long as I know, the 'Independence of Irrelevant Alternatives Criterion' may be explained as: If an election is held and a winner is declared, this winning candidate should remain the winner in any recalculation of votes as a result of one or more of the losing candidates dropping out.
> >
> > To me, this criteria implies that any election should have a Condorcet winner, because we might drop out all of the defeated candidates, except 1 of them, and this would establish a pairwise dispute between the winner and only one of the defeated candidates, any one of them.
> >
> > However, the absence of a Condorcet winner can not be considered a problem with an election method, but, instead, it only reflects ambiguities in the electors' preferences. If what I wrote is correct, this means that the 'Independence of Irrelevant Alternatives' is not a valid criteria to evaluate any voting method.
> >
> > I'm afraid I am not understanding correctly the 'Independence of Irrelevant Alternatives Criterion' , so I ask you to correct me if this is happening.
> >
> > I also ask confirmation if Arrow used this criteria to prove his famous impossibility theorem.
> >
> > Thank you.
> >
> > Marcos C. Ribeiro
> > Belo Horizonte - Minas Gerais - Brasil.
> >
>