[EM] "Beatpath GMC" compliance a mistaken standard?

[Juho Laatu]

--- On Sun, 11/1/09, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:

> Juho Laatu wrote:
> > --- On Sun, 11/1/09, Kristofer Munsterhjelm
> <km-elmet at broadpark.no> wrote:
> > 
> >> Let's consider the first election first, with
> >> truncation extended to full preference:
> >> 
> >> 26: A > B > C
> >> 25: B > A > C
> >> 49: C > A = B
> > 
> >> 	A B C: 100 prefer {A B C} to the empty set
> > 
> > This case is interesting (not that it
> > would have any impact on the ongoing
> > mutual majority discussion but just
> > for theoretical interest).
> > 
> > The number of candidates was not exactly
> > stated in the example. If there are e.g.
> > four candidates then the votes would be:
> > 
> > 26: A > B > C = D
> > 25: B > A > C = D
> > 49: C > A = B = D
> > 
> > Set {A, B, C} has in this case no support.
> > 
> > Let's assume that there are also other
> > citizens (=potential candidates who
> > are however not candidates) than the
> > named candidates. The opinions of the
> > first 26 voters could be as follows.
> > 
> > 26: X1 > A > B > X2 > C = D = X3 > X4
> > 
> > The point here is that the voters have
> > not said that they would prefer A, B, C
> > and D to the other citizens / potential
> > candidates (X1, X2,...).
> > 
> > It is ok to say that if there are no
> > "mutual majorities" the winner can be
> > elected from the whole set of candidates
> > {A, B, C} or {A, B, C, D} or whatever set.
> > One can not say that the voters would
> > prefer the all the candidates (or those
> > that are named on the ballots) to other
> > citizens. What is the meaning of saying
> > that they prefer these candidates to an
> > empty set?
> 
> There is no real meaning - it's just an artifact of
> taking the process to its conclusion. The only thing it
> means is that all voters who voted, voted for the candidates
> they voted for, which is a tautology.
> 
> Smaller unanimity sets can only exist if there's a
> candidate or a candidate set that everybody ranks last.
> 
> Also note that changing a vote from A > B to X1 > A
> > B can dissolve what would otherwise be a majority for
> {A B}. Mutual majority isn't complete - it only says
> that in certain cases (majority support for a set), certain
> things should happen (the method should elect from the set).
> In that respect, it's kind of like independence of
> clones. You can make a method that technically passes mutual
> majority yet wouldn't be any good, just like you can
> prefix a method with "remove clones" yet it would
> be a bad method if a single voter didn't vote clones in
> strict clone order.

Yes. I wish we had a more stable definitions and terms
for discussing about criteria and how they are applied
(e.g. just to meet the criterion or also its spirit
when working outside of the defined scope of the
criterion).

Since all criteria can not be met I'd also like to have
terminology for "almost meeting" some criteria, and
"following the spirit" in most cases although not fully
and formally meeting the criterion.

(One example. Minmax(margins) doesn't meet independence
of clones nor mutual majority, but it is very close to
meeting both. It elects the candidate with weakest
opposition instead (= their strength over the defenders
when compared pairwise to any of the other candidates),
and wile following this "good" principle is forced to
violate "the other good principles".)

All methods violate some criteria. Typically we need a
good balance of the violations and appropriate level of
violation of each criterion.

Juho