[EM] Net Wins Tiebreaker

DEMOREP1 at aol.com DEMOREP1 at aol.com
Wed May 26 03:32:00 PDT 1999


One of my standard circular ties--

Assume that each choice is acceptable to a majority on a YES/NO vote.

22 ABCDE
21 BCDEA
20 CDEAB
19 DEABC
18 EABCD
100
                      NET
79 AB 21        58 A
59 AC 41        18 A
40 AD 60        20 D
22 AE 78        56 E
80 BC 20        60 B
61 BD 39        22 B
43 BE 57        14 E
81 CD 19        62 C
63 CE 37        26 C
82 DE  18       64 D

No head to head winner (i.e. each choice has at least one victory and one 
defeat).

Table of NET wins (left column over top row)
      A     B      C     D      E     Total
A    X     58    18    0      0      76
B    0      X     60    22    0       82
C    0      0     X      62   26      88  max
D   20     0     0       X     64     84
E   56    14    0       0      X      70
                                            400

Note the C diagonal in the example.

Note that a second choice cannot hurt a first choice in a given vote since 
the first choice defeats the second choice.

Thus- Majority YES, head to head (Condorcet) and Net Wins tiebreaker (a 
variant of Borda).
Thus, were Borda and Condorcet both partially correct ???



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