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

[Marcos C. Ribeiro]

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.
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