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