Tiebreakers
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Wed Jun 10 19:18:34 PDT 1998
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).
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