Bare majority winners

[DEMOREP1 at aol.com]

More complexity--

Another way to look at the single winner problem is to note majority groups
versus minority groups.

With 3 choices and no truncated votes the head to head combinations are--

4 vs. 2 
3 vs. 3    

 2 on each side have the same first choice.

With 4 choices and no truncated votes the head to head combinations are--

18 vs. 6
17 vs. 7
16 vs. 8
15 vs. 9
14 vs. 10
13 vs. 11
12 vs. 12

6 on each side have the same first choice.  

With 5 choices and no truncated votes the head to head combinations are--

96 vs. 24
95 vs. 25
etc.     etc.
49 vs. 47
48 vs. 48

24 on each side have the same first choice.  

The other votes come from the voters who have some other first choice.

If there is a circular tie, then one of the combinations will produce a result
that is nearest to a bare majority.  

Example- 500 voters.  5 Choices.
One of the 13 vs. 11 combinations might be 260 to 240.  Assume all other
combinations have a pair winner getting more than 260 votes.

Should the winner that is nearest to a bare majority be the consensus majority
winner ?

A larger tie example

15  A>B>C>D>E>F
16  B>C>D>E>F>A
17  C>D>E>F>A>B
18  D>E>F>A>B>C
19  E>F>A>B>C>D
20  F>A>B>C>D>E
105

Assume each is acceptable to a majority of the voters using a YES/NO vote.

89 A/B  16
88 B/C  17
87 C/D  18
86 D/E  19
85 E/F   20
90 F/A  15

72 A/C  33
70 B/D  35
68 C/E  37
66 D/F  39
70 E/A  35
74 F/B  31

54 A/D 51
51 B/E  54
48 C/F  57

A>B>C>D>E>F>A

The winners nearest to a bare majority are--

54 A/D  51
54 E/B  51
but
70 E/A  35
Should E win ?