[EM] Looking for a little voting insight...
Markus Schulze
markus.schulze at alumni.tu-berlin.de
Mon May 1 02:14:18 PDT 2006
Dear Matthew Welland,
you wrote (30 April 2006):
> Rubyvote has pure condorcet and cloneproof schwartz
> sequential available.
At Wikipedia, "pure Condorcet" is called "Minimax
Condorcet":
http://en.wikipedia.org/wiki/Minimax_Condorcet
At Wikipedia, "cloneproof Schwartz sequential dropping"
is called "Schulze method":
http://en.wikipedia.org/wiki/Schulze_method
******************************************
You wrote (30 April 2006):
> I want to keep things simple.
> Does it matter which method I choose?
Yes, it does matter. Minimax and Schulze are different
methods.
Example:
3 A > B > D > C
5 A > D > B > C
1 A > D > C > B
2 B > A > D > C
2 B > D > C > A
4 C > A > B > D
6 C > B > A > D
2 D > B > C > A
5 D > C > A > B
Suppose d[X,Y] is the number of voters who strictly
prefer candidate X to candidate Y. Then we get:
d[A,B]=18
d[A,C]=11
d[A,D]=21
d[B,A]=12
d[B,C]=14
d[B,D]=17
d[C,A]=19
d[C,B]=16
d[C,D]=10
d[D,A]=9
d[D,B]=13
d[D,C]=20
Minimax chooses candidate B.
The strongest paths are:
A-18-B
A-21-D-20-C
A-21-D
B-17-D-20-C-19-A
B-17-D-20-C
B-17-D
C-19-A
C-19-A-18-B
C-19-A-21-D
D-20-C-19-A
D-20-C-19-A-18-B
D-20-C
Schulze chooses candidate A.
Markus Schulze
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