[EM] Irrelevant Ballots criterion

[Chris Benham]

Participants,
I've  come up with a criterion I like, in part inspired by  the  "Blank 
Ballot Criterion".  As that criterion is currently worded in the Electowiki:

> The addition of one or more blank ballots cannot change the winner. 

I don't think is very useful because any method can easily dodge it 
simply by including a rule that "blank ballots" aren't counted.

I propose the "Independence from Irrelevant Ballots" criterion:

"If  candidate X  pairwise loses to all other candidates and is ranked 
no higher than equal bottom on all ballots except those that plump for X,
then if  ballots that plump for X  are deleted the winner must not change."

I  think this covers Russ's intention in the way he proposed the Blank 
Ballot Criterion:

> No method that depends on "majority defeats" can pass this criterion 
> if it defines a majority it terms of the total number of voters.

So Irrelevant Ballots can somewhat embarrass  CDTT,IRV:
49: A
24: B
27: C>B
03: D
(103 ballots)
The CDTT  is {ABC} and  CDTT,IRV elects  A, but if we delete the 
"irrelevant" 3D ballots then A drops out of the CDTT
and the new CDTT,IRV winner is C.

Woodall's  Descending Acquiescing Coalitions (DAC) method doesn't use 
any "majority" concept, but in this excellent example from M.Harman (aka 
Auros) it stumbles on
Irrelevant Ballots:
03: D
14: A
34: A>B
36: C>B
13: C

ABCD 100
ABC   97 (eliminate D)
 BCD  52 (eliminate A)
AB D  51 (eliminate C, B wins)

DAC elects B, but if we delete the "irrelevant" 3D ballots then C wins.

A perhaps-more-elegant, stronger version that applies to methods that rank a candidate last could be called
"Strong Independence from Irrelevant Ballots" (BTW, I am happy for these to be abbreviated by dropping the "Independence from" bit).

"Deleting ballots that plump for the candidate ranked last must not change the winner".

But so far I think the main "weak" version is more useful. (BTW, "plump" in this context means "bullet-vote")

Chris Benham