[EM] Tideman and GMC

[DEMOREP1 at aol.com]

Mr. Markus Schulze wrote-

Example:

    26 voters vote C > A > B > D.
    20 voters vote B > D > A > C.
    18 voters vote A > D > C > B.
    14 voters vote C > B > A > D.
    08 voters vote B > D > C > A.
    07 voters vote D > A > C > B.
    07 voters vote B > D > A = C.
  [100]
----
D-

51 AB 49
45 AC 48  (note the 7 A=C votes)
58 AD 42
35 BC 65
75 BD 25
40 CD 60

A>B>D>C>A

I repeat my earlier observations--

A choice either does or does not get majority approval (of ALL of the voters- 
as shown by a simple YES or NO vote).

IF each choice in the example has such YES majorities (i.e. 51 or more YES 
votes), then---

D is the highest clone (of B)

51 AB 49
45 AC 48
35 BC 65

B is the now the highest clone (of C)

45 AC 48

C beats A

The above comes from the 3 choice circular tie with an added clone.

N1 A > N2 B
N3 B > N4 C
N5 C > N6 A

Assume A>B>C>A (i.e. N1 > N2, N3 > N4 and N5 > N6).

Add D to be a 100 percent clone of B.

  N1 A > N2 B  > N2 D
  N3 B > N3 D  > N4 C
  N5 C > N6 A
100 B > 0 D

A>B>D>C>A

ALL comparisons thus have clone aspects-- greatest absolute majorities (100 
to 0), medium absolute majorities (such as 60 to 40), bare absolute 
majorities (51 to 49), ties (50 to 50) or plurality majorities (such as 47 to 
41, 12 don't care).

Margins math (votes for X over Y minus votes for Y over X) comes into play 
depending on whether or not absolute majorities are involved, such as 
51 to 49  margin 2 or
49 to 1   margin 48 (50 don't care)