51/48 example
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Wed Nov 13 15:31:33 PST 1996
A divided majority and divided minority example--
99 voters
51 voters in the ABC group
48 voters in the XYZ group
Votes to the left of the slash (/) are approval votes and votes to the right
of the slash are disapproval votes.
17 ABC/XYZ
17 BCA/YZX
15 CAB/ZXY
2 CAB/ZYX
16 XYZ/ABC
16 YZX/BCA
15 ZXY/CAB
1 ZXY/CBA
Approval votes- A,B and C each get 51 votes. X,Y and Z each get 48 votes.
Disapproval votes- A,B and C each get 48 votes. X, Y and Z each get 51 votes.
--
Head to Head Pairings- A or B or C beats X or Y or Z, 51 to 48.
A B B C C A
17 ABC/XYZ 17 17 17
17 BCA/YZX 17 17 17
15 CAB/ZXY 15 15 15
2 CAB/ZYX 2 2 2
16 XYZ/ABC 16 16 16
16 YZX/BCA 16 16 16
15 ZXY/CAB 15 15 15
1 ZXY/CBA 1 1 1
Tots 65 34 66 33 66 33
--
X Y Y Z Z X
17 ABC/XYZ 17 17 17
17 BCA/YZX 17 17 17
15 CAB/ZXY 15 15 15
2 CAB/ZYX 2 2 2
16 XYZ/ABC 16 16 16
16 YZX/BCA 16 16 16
15 ZXY/CAB 15 15 15
1 ZXY/CBA 1 1 1
Tots 64 35 66 33 66 33
With plain Condorcet, Y (with majority disapproval) wins with a mere 64 votes
against him/her in his/her worst defeat.
Should B (with majority approval) win with a mere 65 votes against him/her in
his/her worst defeat ?
Obviously the example is extreme (a majority group circular tie and a
minority group circular tie) but not impossible. Note that if the XYZ
variants are dropped, then A, B and C each have 33 first choice votes.
In a large election, the question is how many candidates will be getting
majority approval- (a) zero- a vacancy; (b) if 1, then he/she wins; (c) if 2,
then the head to head winner wins; (d) if 3 or more, then the head to head
winner wins, if any; (e) if a head to head tie with 3 or more, then which tie
breaker should be used- fewest votes against in worst defeat, lowest number
of first choices, lowest number of combined choices (1st +2nd, 1st +2nd +3rd,
etc.), lowest approval, highest disapproval, something else?
If (e) happens, then should all of the losers lose at the same time or one or
more at a time in a subcycle?
What will be understandable by the mythical "average" voter (and the media
and especially by a majority of the Justices of the U.S. Supreme Court)?
In a small election, there is obviously a much higher possibility of ties.
How many voters are necessary for a "large" election ? Answer- the method
used should not matter regardless of how few or many voters there are.
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