Tiebreakers

[DEMOREP1 at aol.com]

Regarding the 2 examples of Markus Schulze from Subj:   Re: Near Clone Sets,
Date:  Wed, Jun 10, 1998 8:05 AM EDT---

Part A.   One tiebreaker has successive worst defeats causing losses.

100 voters

A/C  70/30
A/D  55/45

B/A   80/20
B/C   50/50

C/B   50/50
C/D   85/15  D loses

D/B  65/35

Check remaining   B>A>C=B
----
A/C  70/30

B/A   80/20  A loses
B/C   50/50

C/B   50/50
-----
B/C   50/50
                       B and C tied
C/B   50/50
--------------
106 voters

  A/C  70/36
  A/D   55/51

  B/A   86/20   A loses
  B/C   56/50

  C/D   85/21

  D/B   71/35

Check remaining  B>C>D>B
--------------
  B/C   56/50

  C/D   85/21  D loses

  D/B   71/35

--------
  B/C   56/50  B wins.  D complains.

Part B.  Another tiebreaker is having the choice with the fewest first choice
votes losing (based on the idea that such fewest number of voters is less
likely to be correct).

100 voters

  35 voters vote B > A > C > D.
  30 voters vote C > D > B > A.
  20 voters vote A > C > D > B.
  15 voters vote D > B > A > C.  D loses
--
  35 voters vote B > A > C
  30 voters vote C > B > A.
  20 voters vote A > C > B.
  15 voters vote B > A > C.

  A:B=20:80
  A:C=70:30
  B:C=50:50

B>A>C=B
A loses  (20 first choice votes)

  35 voters vote B > C
  30 voters vote C > B 
  20 voters vote C > B.
  15 voters vote B > C.

B/C  50/50  Tie
------
106 voters
  35 voters vote B > A > C > D.
  30 voters vote C > D > B > A.
  20 voters vote A > C > D > B.  A loses
  15 voters vote D > B > A > C.
   6 voters vote D > B > C > A.
--
  35 voters vote B > C > D.
  30 voters vote C > D > B 
  20 voters vote C > D > B.  
  15 voters vote D > B > C.
    6 voters vote D > B > C 

  B:C=56:50
  B:D=35:71
  C:D=85:21

Check remaining  B>C>D>B
D loses  (21 first choice votes)
B Wins.  D complains.

Part C.  Another tiebreaker is summing the earliest choices to get a majority
(first plus second choice votes, first plus second plus third choice votes (if
necessary), etc.).  [variation of the Bucklin and a limited variation of the
simple Approval voting method]

100 voters
  35 voters vote B > A > C > D.
  30 voters vote C > D > B > A.
  20 voters vote A > C > D > B.
  15 voters vote D > B > A > C.

first plus second choices-
A 55, B 50, C 50, D 45    A wins
---
106 voters

  35 voters vote B > A > C > D.
  30 voters vote C > D > B > A.
  20 voters vote A > C > D > B.
  15 voters vote D > B > A > C.
    6 voters vote D > B > C > A.

first plus second choices-
A 55, B 56, C 50, D 51     B Wins

Part D.  
Summary   
Tiebreaker         100 voters     106 voters

worst defeat        B,C tied           B wins

1st choices           B,C tied           B wins

sum choices          A wins            B wins

Any other tie breakers (derived just by looking at the raw results in line
form or in a N x N matrix) ???

Part E.  As I have mentioned many times, I suggest that a YES/NO vote be done
first regarding the acceptability of each choice for executive and judicial
offices (since number voting only shows relative rankings).   Only choices
getting a majority YES vote would go head to head (thus reducing the
probability of circular ties).