Goldfish (single-winner method)

[Blake Cretney]

--

On Thu, 27 Aug 1998 00:40:07   Norman Petry wrote:
>Blake,
>
>You wrote:
>
>>>My previous posting turns out to be incorrect as an implementation of
>original Tideman.  However, I still like it better than Goldfish 0.2, so I
>am calling this algorithm Goldfish 0.3.  I also like it better than Tideman,
>and it passes the GMC test from the
>
>You're right, it's definitely not Tideman.  In fact, it's much better than
>Tideman.  I think what you've discovered with Goldfish 0.3 is a very
>efficient algorithm for the Schulze method.
>
That's my hope.  Anyway, I thought I would provide an
example of Goldfish at work.  Here's how Goldfish 0.3
handles the Tideman bad example for GMC.

100 voters.

B>A 61
A>D 62
D>B 60
B>C 1
C>D 2
C>A 59

Here's how Goldfish handles this example
      A   B   C   D
   A  X           62 
   B  61  X   1     
   C  59      X   2 
   D      60      X 

I find the highest value among non-eliminated rows, that's the 62 
in A,D.  I star the D row to show it has been eliminated.  I update
the A row by copying any greater values from D.  I treat X's as
high values.

      A   B   C   D
   A  X   60      X  
   B  61  X   1     
   C  59      X   2 
*  D      60      X 

      A   B   C   D
   A  X   60      X  
   B  61  X   1       The new high value is 61
   C  59      X   2 
*  D      60      X 

      A   B   C   D
*  A  X   60      X  
   B  X   X   1   X   The high is 59.  Remember that starred
   C  59      X   2   rows can still be used for merges
*  D      60      X   they can still lose, they just can't win

      A   B   C   D
*  A  X   60      X  
   B  X   X   1   X    The 60 is higher than the 1, so C wins      
   C  X   60  X   X   
*  D      60      X 

      A   B   C   D
*  A  X   60      X
*  B  X   X   1   X
   C  X   60  X   X   
*  D      60      X 

I hope this will help anyone who is having trouble with the method.



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