10 candidate tie example more

[Bruce Anderson]

On May 13, 10:49pm, DEMOREP1 at aol.com wrote:
> Subject: 10 candidate tie example more
> Below is the array (matrix) of the A-J example.
> If the candidate in the top row beats (loses to) the candidate at the left
> (first column), there is a W (L) in the cell. For each W, there is the
> corresponding L. T= tie. X= diagonal
> 
> X A B C D E F G H I J
> A X L L T T T T T T T
> B W X L W T T T T T T
> C W W X L T T T T T T
> D T L W X T T T T T T
> E T T T T X L T T T T
> F T T T T W X L T T T
> G T T T T T W X L T T
> H T T T T T T W X T T
> I T T T T T T T T X L
> J T T T T T T T T W X
> 
> The general case is that a candidate survives if he/she does not lose to
> every other candidate.
> 
>-- End of excerpt from DEMOREP1 at aol.com

For whatever it's worth, there is an error in the array above.  G should beat E, 
not tie E.  So the correct array, as it defined above, for the aforementioned 
10-candidate example is:

> X A B C D E F G H I J
> A X L L T T T T T T T
> B W X L W T T T T T T
> C W W X L T T T T T T
> D T L W X T T T T T T
> E T T T T X L W T T T
> F T T T T W X L T T T
> G T T T T L W X L T T
> H T T T T T T W X T T
> I T T T T T T T T X L
> J T T T T T T T T W X

DEMOREP1 and I must have opposite-sided (or opposite-handed) brains.  DEMOREP1 
defines the array above so that there is a W in the row-column position if the 
column candidate beats the row candidate.  I like to define the arrays I work 
with such that there is a W in the row-column position if the row candidate 
beats the column candidate.  The choice is completely arbitrary, and is a matter 
of personal taste.  Defined my way, with -  on the diagonal, the corresponding 
array is:

- A B C D E F G H I J    W, L, T
A - W W T T T T T T T    2, 0, 7
B L - W L T T T T T T    1, 2, 6
C L L - W T T T T T T    1, 2, 6
D T W L - T T T T T T    1, 1, 7
E T T T T - W L T T T    1, 1, 7
F T T T T L - W T T T    1, 1, 7
G T T T T W L - W T T    2, 1, 6
H T T T T T T L - T T    0, 1, 8
I T T T T T T T T - W    1, 0, 8
J T T T T T T T T L -    0, 1, 8

Two similarly interesting (to me) examples, in my notation, are as follows:

6 candidates --

- A B C D E F    W, L, T
A - T W W W W    4, 0, 1
B T - T T T T    0, 0, 5
C L T - W W W    3, 1, 1
D L T L - L W    1, 3, 1
E L T L W - L    1, 3, 1
F L T L L W -    1, 3, 1

and:

6 candidates --

- A B C D E F    W, L, T
A - W W L W L    3, 2, 0
B L - L T W W    2, 2, 1
C L W - T L W    2, 2, 1
D W T T - T L    1, 1, 3
E L L W T - W    2, 2, 1
F W L L W L -    2, 3, 0

Bruce