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Name :   Danny Kleinman
Organization :   N/A
Post Date :   9/30/2005

General Comments
Comment :  (6c) Continued


All right, now that all the ballots have been matchpointed, let’s add the matchpoints of all three ballots:

CANDIDATE            MATCHPOINTS    
McReynolds                6.5
Nader                      10.5
Gore                        12.0  
Bradley                    13.0
McCain                    16.0
Bush                       13.0
Buchanan                  7.0
Browne                     6.0
   
Some political scientists have proposed that we stop here, and declare McCain the winner on the basis of his high matchpoint total.  However, to adopt that proposal would sometimes result in a violation of Criterion (6), the Condorcet Criterion.  In this essay, I won’t bother showing an example of how that could happen, but when I prove that the voting system whose presentation I am about to complete always satisfies the Condorcet Criterion, you will see that the proof doesn’t work if we stop here.
The next step is simply to eliminate the lowest-scoring candidate from the tallying process (in this case, Browne) and repeat our tally with one fewer candidate, so that the computer which does the tallying creates a revised set of ballots, and keeps repeating the process until only one candidate (the winner) remains:

CANDIDATE        RANK                MATCHPOINTS        
McReynolds         2nd                   5.0
Nader                  1st                   6.0
Gore                   3rd                   3.5
Bradley               3rd                   3.5
McCain                4th                   2.0
Bush                   5th                   1.0
Buchanan            6th                   0.0

CANDIDATE        RANK                MATCHPOINTS    
McReynolds                                 0.5
Nader                                         0.5
Gore                   99                    2.5
Bradley               99                    2.5
McCain                 2                     5.0
Bush                    1                     6.0
Buchanan             5                     4.0

CANDIDATE        RANK                MATCHPOINTS    
McReynolds         8                      0.0
Nader                 5                      2.0
Gore                   3                      4.0
Bradley               2                      5.0
McCain                1                      6.0
Bush                   4                      3.0
Buchanan            6                      1.0