# 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
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
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,
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.

```