# Bare majority winners

DEMOREP1 at aol.com DEMOREP1 at aol.com
Tue Jun 23 20:25:56 PDT 1998

```More complexity--

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

4 vs. 2
3 vs. 3

2 on each side have the same first choice.

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.

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 ?

```