Example with contrary half preference votes

[Lucien Saumur]

In an article, dfb at bbs.cruzio.com (Mike Ossipoff) writes:

>Say we were using Condorcet's method, with the added provision,
>recently proposed, that if a ballot ranks X & Y equally, below
>everything else in the Smith set, then that ballot is counted
>as casting half a vote for X over Y, & half a vote for Y over
>X.
>
>Sincere rankings:
>
>46%: Dole, Clinton, Nader
>20%: Clinton
>34%: Nader, Clinton, Dole
>
>Dole voters truncate:
>
>46%: Dole
>20%: Clinton
>34%: Nader, Clinton
>
>With the compulsory contrary half preferences provision,
>Dole wins. Without it, Clinton wins. Clinton is the Condorcet
>winner, & Dole is the only candidate over whom a majority
>has ranked someone else.

     I am trying to understand the "lease-beaten" concept and I do
not understand why Clinton would win rather than Dole, with or
without half preferences.

     I have designed the following matrices to explain what I
understand. Please explain where I have gone wrong.

     [Theses matrices should be viewed using the "Courrier" font and
may contain transcription and other errors.]

     The following matrix explains how I would tally the "sincere
rankings". Clinton wins.

           AGAINST:
          |DOLE |CLINT|NADER|
          |-----|-----|-----|
FOR       |XXXXX| 46  | 46  |
DOLE      |XXXXX|  0  | 10  |
          |XXXXX|  0  |  0  |
          |XXXXX|____ |____ |
          |XXXXX| 46  | 56  |
          |XXXXX|(-8) |(+12)|
          |-----|-----|-----|
FOR       |  0  |XXXXX| 46  |
CLINTON   | 20  |XXXXX| 20  |
          | 34  |XXXXX|  0  |
          |____ |XXXXX|____ |
          | 54  |XXXXX| 66  |
          |(+8) |XXXXX|(+32)|
          |-----|-----|-----|
FOR       |  0  |  0  |XXXXX|
NADER     | 10  |  0  |XXXXX|
          | 34  | 34  |XXXXX|
          |____ |____ |XXXXX|
          | 44  | 34  |XXXXX|
          |(-12)|(-32)|XXXXX|
          |-----|-----|-----|


     The following matrix explains how I think that you are tallying
the "sincere rankings". Clinton also wins.

           AGAINST:
          |DOLE |CLINT|NADER|
          |-----|-----|-----|
FOR       |XXXXX| 46  | 46  |
DOLE      |XXXXX|  0  |  -  |
          |XXXXX|  0  |  0  |
          |XXXXX|____ |____ |
          |XXXXX| 46  | 46  |
          |XXXXX|(-8) |(+12)|
          |-----|-----|-----|
FOR       |  0  |XXXXX| 46  |
CLINTON   | 20  |XXXXX| 20  |
          | 34  |XXXXX|  0  |
          |____ |XXXXX|____ |
          | 54  |XXXXX| 66  |
          |(+8) |XXXXX|(+32)|
          |-----|-----|-----|
FOR       |  0  |  0  |XXXXX|
NADER     |  -  |  0  |XXXXX|
          | 34  | 34  |XXXXX|
          |____ |____ |XXXXX|
          | 34  | 34  |XXXXX|
          |(-12)|(-32)|XXXXX|
          |-----|-----|-----|


     The following matrix explains how I would tally the truncated
vote which produces a circular tie. Dole is "least beaten" by 8
votes.

           AGAINST:
          |DOLE |CLINT|NADER|
          |-----|-----|-----|
FOR       |XXXXX| 46  | 46  |
DOLE      |XXXXX|  0  | 10  |
          |XXXXX|  0  |  0  |
          |XXXXX|____ |____ |
          |XXXXX| 46  | 56  |
          |XXXXX|(-8) |(+12)|
          |-----|-----|-----|
FOR       |  0  |XXXXX| 23  |
CLINTON   | 20  |XXXXX| 20  |
          | 34  |XXXXX|  0  |
          |____ |XXXXX|____ |
          | 54  |XXXXX| 43  |
          |(+8) |XXXXX|(-14)|
          |-----|-----|-----|
FOR       |  0  | 23  |XXXXX|
NADER     | 10  |  0  |XXXXX|
          | 34  | 34  |XXXXX|
          |____ |____ |XXXXX|
          | 44  | 57  |XXXXX|
          |(-12)|(+14)|XXXXX|
          |-----|-----|-----|


     The following matrix explains how I think that you would tally
the truncated vote which produces a circular tie. Dole is also "least
beaten" by 8 votes.

           AGAINST:
          |DOLE |CLINT|NADER|
          |-----|-----|-----|
FOR       |XXXXX| 46  | 46  |
DOLE      |XXXXX|  0  |  -  |
          |XXXXX|  0  |  0  |
          |XXXXX|____ |____ |
          |XXXXX| 46  | 46  |
          |XXXXX|(-8) |(+12)|
          |-----|-----|-----|
FOR       |  0  |XXXXX|  -  |
CLINTON   | 20  |XXXXX| 20  |
          | 34  |XXXXX|  0  |
          |____ |XXXXX|____ |
          | 54  |XXXXX| 20  |
          |(+8) |XXXXX|(-14)|
          |-----|-----|-----|
FOR       |  0  |  -  |XXXXX|
NADER     |  -  |  0  |XXXXX|
          | 34  | 34  |XXXXX|
          |____ |____ |XXXXX|
          | 34  | 34  |XXXXX|
          |(-12)|(+14)|XXXXX|
          |-----|-----|-----|

__________________________________________
     aa447 at FreeNet.Carleton.CA
     http://www.igs.net/~lsaumur/