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

[Markus Schulze]

Dear Paul Kislanko,

Kevin Venzke wrote (10 Jan 2009):

> [Situation #1]
>
> 26 A>B
> 25 B>A
> 49 C
>
> Mutual Majority elects {A,B}
>
> Now add 5 A bullet votes:
>
> [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,
> because after adding 5 votes it takes 53 votes to
> 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