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.
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 ?
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