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

General Comments
Comment :  (6b) Continued  

What is that system?
You already know the heart of it: matchpoints.  Suppose that each candidate I’ve mapped on the political spectrum were to play (with a partner of the same name) in an 8-table pair game.  I shall show one possible travelling scoresheet for Board 1:

CONTESTANT      SCORE               MATCHPOINTS    
McReynolds         +110                 6.0
Nader                 +140                 7.0
Gore                   +100                 4.5
Bradley               +100                 4.5
McCain                 +50                 3.0
Bush                     -50                 2.0
Buchanan             -110                 0.5
Browne                -110                 0.5

Now I shall show how one voter, call him Voter 1, a Nader supporter, might mark his ballot if permitted to rank the candidates fully rather than just “vote for one”:

CANDIDATE        RANK                BORDA POINTS    
McReynolds         2nd                   6.0
Nader                 1st                    7.0
Gore                   3rd                   4.5
Bradley               3rd                   4.5
McCain                4th                   3.0
Bush                   5th                   2.0
Buchanan            6th                   0.5
Browne               6th                   0.5

The ranking of the candidates by Voter 1 is exactly the same as the rankings of the contestants on Board 1.  The Borda Points of the candidates are the same as the matchpoints of the bridge players.  From now on, I’ll simply right “matchpoints” instead of “Board Points” (the name by which mathematicians and political scientists call them).   Of course, just as there is more than one board in a duplicate bridge game, there is more than one ballot in a Presidential election.  Voter 2, a Bush supporter, might mark his ballot as follows:

CANDIDATE        RANK                MATCHPOINTS    
McReynolds                                 0.5
Nader                                         0.5
Gore                  99                     2.5
Bradley              99                     2.5
McCain                2                      6.0
Bush                   1                      7.0
Buchanan            5                      4.5
Browne               5                      4.5

Notice that I’ve dropped off the “st,” “nd,” “rd” and “th”  that indicate order, leaving only the numbers.  Notice also that it is not necessary to rank candidates with consecutive numbers; indeed, to require voters to do so would result in discarding large numbers of ballots as invalid.  Notice, finally, that candidates for whom no rank has been marked are treated as tied for last in the voter’s order of preference.  In this example, Voter 2 has left Nader and McReynolds unmarked because he finds them both abhorrent.   That’s all right: we don’t want to require a voter to vote “for” a candidate, which he may think he’d be doing even by ranking that candidate last.  
Though an election for President would use millions of ballots, for purposes of illustration I’ll show only one more, for Voter 3, an independent “centrist” voter:



CANDIDATE        RANK                MATCHPOINTS    
McReynolds         8                       0.0
Nader                 5                       3.0
Gore                   3                       5.0
Bradley               2                       6.0
McCain               1                        7.0
Bush                  4                        4.0
Buchanan           6                        2.0
Browne              7                        1.0