[EM] Voting paradoxes article

[DEMOREP1 at aol.com]

On Fri, 17 Sep 1999, Markus Schulze wrote:

> Example 1:
> 
> There are 120 voters and 4 candidates for 2 seats.
> 8 voters vote A > C > B > D.
> 8 voters vote A > C > D > B.
> 8 voters vote B > C > A > D.
> 8 voters vote B > C > D > A.
> 8 voters vote C > A > B > D.
> 8 voters vote C > A > D > B.
> 8 voters vote D > A > B > C.
> 8 voters vote D > A > C > B.
> 7 voters vote A > D > B > C.
> 7 voters vote A > D > C > B.
> 7 voters vote B > D > A > C.
> 7 voters vote B > D > C > A.
> 7 voters vote C > B > A > D.
> 7 voters vote C > B > D > A.
> 7 voters vote D > B > A > C.
> 7 voters vote D > B > C > A.
---
D--

The general head to head case is 

TW1-TW2-etc. versus  TL  with TOL1-TOL2-etc.

TW = Test Winner(s), TL = Test loser, TOL = Test other loser(s)

The 2nd, etc. votes for each 1st choice TOL go to the TW or TL whichever 
happens first (in the legislative body case).  

In the executive/judicial office case with N to be elected, the highest N 
votes from the TOL go to the TW or TL.

After doing all of the combinations of 2 vs. 1 with 1 TOL in the example 
(assuming the legislative body case), no choice wins in all of its 
combinations when it is a test winner.

Wins as a TW
A 4
B 4
C 4
D 3

15 of possible 24

Wins as TL

A 3
B 2
C 2
D 2

9 of possible 12

The simple (manufactured) head to head math is --

62 A/B 58
60 A/C 60
61 A/D 59
59 B/C 61
60 B/D 60
62 C/D 58

A > B
C > D
A = C
B = D
A > D
C > B

That is, a box with A at top left, B at top right, C at bottom left and D at 
bottom right with the diagonals -  a rather unlikely result in a real world 
election.

Should A and C win ?