[EM] Net Wins Tiebreaker, Supp. 11

[DEMOREP1 at aol.com]

I return to the 3 clone circular tie example in Supp. 5 but adding the raw 
votes--

      X     Y1    Y2    Y3     Z     HTot    Net
X     --    40    40    40    65      185    -30
Y1    60    --   100   100    25      285    170
Y2    60     0   --    100    25      185    -30
Y3    60     0     0    --    25       85   -230
Z     35    75    75    75    --      260    120

VTot 215   115   215   315   140     1000      0

Note;  1000 wins/losses = 100 voters x (4+3+2+1)

The highest raw number in a column indicates the most cloning.  i,e. Y3

Eliminating Y3 produces   

      X     Y1    Y2     Z     HTot     Net
X     --    40    40    65      145     -10
Y1    60    --   100    25      185      70
Y2    60     0   --     25       85    -130  
Z     35    75    75    --      185      70

VTot 155   115   215   115      600       0


Note:  600 wins/losses = 100 voters x (3+2+1)

Eliminating Y2 produces

      X     Y1     Z     HTot      Net
X     --    40    65      105       10
Y1    60    --    25       85      -30
Z     35    75    --      110       20

VTot  95   115    90      300        0


Note: 300 wins/losses = 100 voters x (2+1)

Eliminating Y1 produces

      X        Z     HTot      Net
X     --      65       65       30
Z     35      --       35      -30

VTot  35      65      100        0


X wins.

I am not sure if Condorcet meant the above elimination procedure in case of 
circular ties (due to his somewhat cryptic language). If yes, then it can be 
called the Max Losses (or ??? Condorcet) tiebreaker.

Using the raw numbers in a matrix should be a little simpler for test 
purposes using a larger matrix and a computer program.