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.)
----
Election-Methods mailing list - see http://electorama.com/em for list info
