[EM] Net Wins Tiebreaker, Supp. 1

DEMOREP1 at aol.com DEMOREP1 at aol.com
Thu May 27 03:50:01 PDT 1999


I sent this earlier but it apparently got lost in email land.  See Supp. 2 
after looking at this.
-----------------
If the negatives are added then there would be

Table of NET wins (left column over top row)
      A          B        C          D         E       Total
A      X       58       18      -20      -56         0
B    -58      X         60       22       -14       10
C    -18     -60       X        62         26       10
D      20     -22     -62       X          64         0
E      56      14       -26     -64          X      -20
Tot  0       -10      -10        0          20        0                       
                   

Note the reversed totals (especially if an example is put in reverse order).

Net 60 B > C

Summing the positive and negative net wins is the analogy to "games behind" 
in various sporting events.

Thus, an election may be viewed as multiple games between the choices.
Wins/Losses on 1 ballot
1      A>B    
3      A>B>C
6      A>B>C>D
10    A>B>C>D>E

The general formula ----  ((C x C) - C)/2  where C is the number of choices.
The minus C is the diagonal in a C x C checkboard square (5 x 5 example at 
top).

Dropping a choice will continue to result in having sign reversed totals.

Example- Choice A in the original posting does not run (B, C, D, E still have 
at least 1 net win) ---

Horizontal totals
B  68
C  28
D -20
E -76

Vertical totals are the same but with reversed signs.

Thus, majority YES, head to head (Condorcet), Net Wins (positive and 
negative) (if tie), head to head (if tie in the positive totals).



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