[EM] IIDA: IIA and SODA delegation

[Kristofer Munsterhjelm]

On 03/29/2012 09:41 PM, Ted Stern wrote:
> It is my impression that the only situations in which IIAC fails is
> when there is no majority.
>
> Would it be possible to get around IIAC by adding a two-candidate
> runoff?

I don't think so. In a subset of all possible two-round elections, the 
voters are perfectly consistent in the second round. That is, all the 
people who prefer A to B votes A above B if A and B are the second round 
candidates, and so for any and all pairs of candidates.

For these "perfectly consistent" scenarios, you can define a virtual 
one-round method that determines the winner and second-place finisher 
according to the original method, then determines how the voters would 
have voted in the second round according to the pairwise preferences 
submitted in the first round.

This virtual one-round method is an one-round method like any other. If 
it passes IIAC, then it serves as a one-round method that passes IIAC. 
So if a ranked two-round method passes IIAC, then there also exists a 
ranked one-round method that passes IIAC -- and if a rated two-round 
method passes IIAC, then there also exists a rated one-round method that 
passes IIAC. Runoffs by themselves don't grant IIAC where it otherwise 
wouldn't exist, because the runoff method has to be irrelevant of 
independent candidates in every single situation.

(Runoffs have other things going for them. They make strategy harder to 
pull off because strategists have to focus on two candidates, not just 
one; and the second round is always honest.)