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

Paul Kislanko kislanko at airmail.net
Sat Jan 10 13:08:15 PST 2009

```How can mutual majority say "nothing?" Only if no combination has a
majority. But A is in the A>B, B>A, and new A's, so A is on 56 ballots,
which is a majority of ballots (and no one else is)

If a majority of voters (with the new voters, and where did they come from
anyway) the only candidate with a majority win is A. Using
"Mutual majority says: When a majority of the voters
strictly prefers every candidate of a given set of
candidates to every candidate outside this set of
candidates, then the winner must be chosen from this
set of candidates."

we get after adding five voters from theoretical space, only A meets this
criterion.

-----Original Message-----
From: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Markus
Schulze
Sent: Saturday, January 10, 2009 2:45 PM
To: election-methods at electorama.com
Subject: Re: [EM] "Beatpath GMC" compliance a mistaken standard?

Dear Paul Kislanko,

Kevin Venzke wrote (10 Jan 2009):

> [Situation #1]
>
> 26 A>B
> 25 B>A
> 49 C
>
> Mutual Majority elects {A,B}
>
>
> [Situation #2]
>
> 26 A>B
> 25 B>A
> 49 C
> 5 A
>
> Now Mutual Majority elects {A,B,C}.

You wrote (10 Jan 2009):

> I guess I don't understand "mutual majority", then,
> have a majority, and only A has a majority. B is
> 51/105 and C is 45/105.
>
> Five bullet-votes for A appear to change (A,B) to (A).

Mutual majority says: When a majority of the voters
strictly prefers every candidate of a given set of
candidates to every candidate outside this set of
candidates, then the winner must be chosen from this
set of candidates.

column1 = set of candidates

column2 = number of voters who strictly prefer every
candidate in column1 to every candidate outside column1

************

For situation #1, we get:

column1 / column2
A / 26
B / 25
C / 49
AB / 51
AC / 0
BC / 0

So mutual majority says that the winner must be
chosen from {A,B}.

************

For situation #2, we get:

column1 / column2
A / 31
B / 25
C / 49
AB / 51
AC / 0
BC / 0

So mutual majority says nothing.

Markus Schulze

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