[EM] How close can we get to the IIAC

[fsimmons at pcc.edu]

----- Original Message -----
From: Kristofer Munsterhjelm 
Date: Friday, April 16, 2010 10:14 am
Subject: Re: [EM] How close can we get to the IIAC
To: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> fsimmons at pcc.edu wrote:
> 
> > Schulze's CSSD (Beatpath) method does not satisfy the IIAC, 
> but it does satisfy
> > all of Arrow's other criteria, that is to say all of the 
> reasonable ones plus
> > some others like Clone Independence, Independence from Pareto 
> Dominated> Alternatives, etc. We cannot hold the IIAC against 
> Schulze, because no
> > reasonable method satisfies the IIAC. 
> 
> A nitpick: Schulze doesn't satisfy Independence from Pareto-
> dominated 
> Alternatives. Steve Eppley gives an example on his site:
> 
> 1: A>D>E>C>B
> 5: A>D>E>B>C
> 3: A>B>D>E>C
> 2: B>A>D>E>C
> 2: B>D>E>C>A
> 6: C>B>A>D>E
> 4: C>A>B>D>E
> 5: D>E>C>A>B
> 2: D>B>E>C>A
> 
> D Pareto-dominates E. If E is removed, Schulze elects A, but if 
> not, 
> Schulze elects B.

Thanks for the correction.


> > A couple of years ago someone proposed that if adding a 
> candidate changed the
> > winner, the new winner should be either the new candidate or 
> someone that beats
> > the new candidate pairwise.
> 
> I think Woodall has stated a weak version of IIA, as well. Ah 
> yes, here 
> it is:
> 
> Weak-IIA. If x is elected, and one adds a new candidate y ahead 
> of x on 
> some of the ballots on which x was first preference (and nowhere 
> else), 
> then either x or y should be elected.

Here's a method I proposed a while back that is monotone, clone free, always elects a candidate from 
the uncovered set, and is independent from candidates that beat the winner, i.e. if a candidate that 
pairwise beats the winner is removed, the winner still wins:

1. List the candidates in order of decreasing approval.

2.  If the approval winner A is uncovered, then A wins.

3.  Otherwise, let C1 be the first candidate is the list that covers A.  If C1 is uncovered, then C1 wins.

4.  Else let C2 be the first candidate in the list that covers C1.  If C2 is uncovered, then C2 wins.

etc.

There are variations on this method that preserve all of the mentioned properties, including methods that 
do not require approval information, but I think it is nicer to take into account approval information.  If this 
is done via an approval cutoff on ranked ballots, the approval cutoff, AC, itself can be considered a 
candidate with 50% approval.  No candidate with less than 50% approval can cover the AC, and the AC 
beats pairwise every candidate with less than 50% approval, so no candidate at all can cover the AC 
unless it pairwise beats all of the candidates with less than 50% approval.

What do we do if AC wins the election?   If we want a deterministic answer, I suggest that we elect the 
candidate C that has the least pairwise opposition from the AC.