# Example with contrary half preference votes

Lucien Saumur aa447 at freenet.carleton.ca
Thu Jul 11 10:59:11 PDT 1996

```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:
>
>20%: Clinton
>
>Dole voters truncate:
>
>46%: Dole
>20%: 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:
|-----|-----|-----|
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:
|-----|-----|-----|
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

AGAINST:
|-----|-----|-----|
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

AGAINST:
|-----|-----|-----|
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/

```