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

[Ken Johnson]

> Date: Mon, 29 Mar 2004 14:26:20 -0800 (PST)
> From: Forest Simmons <fsimmons at pcc.edu>
> ...
> 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. 

I think the most technically accurate, plain-English statement of 
Arrow's IIAC is the following: "The group preference relationship 
between two candidates, as determined by the voting method, depends only 
on the voters' relative rankings of those two candidates. It does not 
depend on their ranking of any third candidate." There's been a lot of 
confusion about IIAC because many people mistakenly interpret it to mean 
that the two-candidate ranking would not change if the election were 
held without the third candidate (possibly causing voters to 
strategically change their ranking of the first two). Maybe there's a 
more technically correct term for the latter concept, but it shouldn't 
be called IIAC because that confuses it with Arrow's criterion.
In a strict technical sense, IIAC only applies to ranked methods, but it 
can be obviously generalized to rating methods (Approval, CR) by 
substituting "ratings" for "relative rankings" in the above definition. 
With this generalization,  Approval and CR  really, truly satisfy IIAC. 
Arrow may have demonstrated brilliant mathematics, but he only created 
confusion and misunderstanding by limiting the scope of his definitions 
and theorem to ranked methods.

> 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.
>
> ...
>
> Forest

I think the ballots could arguably be more realistic, in the sense that 
the ballots may more accurately reflect voters' sincere ratings. It's 
not unnatural for a voter to sincerely approve all the candidates - or 
none - on a ballot, it just doesn't make sense strategically to vote 
that way. Removing candidate C may make it less likely that voters will 
vote sincerely.

Ken Johnson