YES matrix

[DEMOREP1 at aol.com]

A manufactured tie example--

22   A > B > C > D > E
21   B > C > D > E > A
20   C > D > E > A > B
19   D > E > A > B > C
18   E > A > B > C > D

79 A/B 21
59 A/C 41
40 A/D 60
22 A/E 78
80 B/C 20
61 B/D 39
43 B/E 57
81 C/D 19
63 C/E 37
82 D/E 18
A>B>C>D>E>A

Assuming that the the first 4 choices on each ballot are YES, the sum of the
YES votes would be
     4        3          2
A   79      59       40
B   80      61        43
C   81      63        41
D   82      60        39
E   78      57        37
One subtiebreaker would be have the lowest majority lose when all choices get
majorities or minorities. Namely, E loses with 57.

Rechecking the head to head math--
79 A/B 21
59 A/C 41
40 A/D 60
80 B/C 20
61 B/D 39
81 C/D 19
A>B>C>D>A
Rechecking the YES matrix--
     4        3          2
A   79      59       40
B   80      61        43
C   81      63        41
D   82      60        39

A loses with 59.
Rechecking the head to head math--
80 B/C 20
61 B/D 39
81 C/D 19
B>C>D
B wins.  Note B's combination of 1st, 2nd and 3rd place votes in the top
matrix.

In a real election the matrix would likely be much more mixed-  a possible 120
(5x4x3x2) lines for 5 choices- and obviously not all choices would be getting
YES votes in the first 4 places.  In other words, I estimate that there would
be very few circular ties.