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

Juho Laatu juho4880 at yahoo.co.uk
Sun Jan 11 02:45:18 PST 2009

```--- On Sun, 11/1/09, Paul Kislanko <kislanko at airmail.net> wrote:

> Arrrgggg. Explain, someone, anyone, how MM can change an (A
> B) to an (A B C)
> possible winner set by adding voters for A.

One way to say this is that since in the
first example there was a set of voters
(26 A>B, 25 B>A) that had a mutual majority
opinion on candidate set {A, B} the winner
must come from this set. In the second
example there is no such majority set of
voters that would prefer some set of
candidates, so the criterion says nothing.

There is thus no requirement not to allow
C to win. There is also no requirement to
allow C to win.

Note also that set {A, B, C} refers to all
candidates, i.e. {A, B, C, D, ... ,Z} (if
there are more candidates than the three
mentioned three).

There are methods that meet mutual majority
and are "not very good". A method that would
elect a random candidate from the set of all
candidates but limiting the choice using the
mutual majority criterion would be problematic
in in the way you mention. Bullet votes would
add C to the set of potential winners.

Typically methods that meet mutual majority
have however also other rules (or algorithm)
that would elect the "most sensible" candidate
from the sets {A, B} and {A, B, C}. Mutual
majority could be just one of the criteria
that the method meets.

The behaviour of the methods is also often
"smooth" in the sense that if there is almost
mutual majority then the method elects a
candidate that is (almost) in the mutual
majority candidate set. So, even if some
criterion may not apply in some set of votes
the criterion may still roughly point out the
direction where the winner will be found.

> 26 A>B
> 25 B>A
> 49 C
>
> Mutual Majority elects {A,B}
>
>
> 26 A>B
> 25 B>A
> 49 C
> 5 A
>
> Now Mutual Majority elects {A,B,C}.

Here words "Now Mutual Majority elects
{A,B,C}" are a bit confusing since mutual
majority doesn't set any requirements on
who should be elected (nor "elect" anyone).
There also seems to be a hidden assumption
that there are no other candidates than A,
B and C. Maybe it would be clearer to just
say that any candidate can be elected (A,
B, C or any other).

Juho

P.S. Also my direct mail to you was returned
back to me (and this happened also with
Kristofer Munsterhjelm some time ago).

> -----Original Message-----
> From: election-methods-bounces at lists.electorama.com
> [mailto:election-methods-bounces at lists.electorama.com] On
> Behalf Of
> Kristofer Munsterhjelm
> Sent: Sunday, January 11, 2009 2:23 AM
> To: election-methods at electorama.com
> Cc: 'Markus Schulze'
> Subject: Re: [EM] "Beatpath GMC" compliance a
> mistaken standard?
>
> Paul Kislanko wrote:
> > This still makes no sense to me, since C has no more a
> majority in case 2
> > than it had in case 1.
> >
> > If mutual majority selects (A B) in case 1 and (A B C)
> in case 2, it makes
> > no sense at all and should never be mentioned again.
>
> Mutual majority can still be useful. Let's make an
> analogy to Condorcet.
> The Condorcet criterion elects the CW if there is one. In
> other words,
> if there is a CW and that CW is candidate X, then the set
> from which
> Condorcet methods elect is { X }. If there is no CW, and
> the candidates
> for election are {A B C ... X }, then the set from which
> Condorcet
> methods elect is {A B C ... X }.
>
> Thus, Condorcet is useful when there is indeed a CW, but
> does nothing
> when there isn't.
>
> So it is with mutual majority as well. When there's a
> set that a
> majority ranks above all the others, then a method that
> passes mutual
> majority must elect from that set. When there is no such
> set, the method
> is free to pick any candidate yet still pass mutual
> majority.
>
> In that light, mutual majority seems very reasonable
> indeed: if there is
> a set so that a majority prefers that set to all others
> outside the set,
> then a candidate within that set should be elected.
> It's simply
> "majority" transported to sets.
>
> (And on another note, sorry for not mailing you this
> directly as well,
> Paul, but airmail.net seems to think my ISP is a dirty
> spammer.)
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