# Reverse Bucklin tiebreaker

DEMOREP1 at aol.com DEMOREP1 at aol.com
Fri Jun 12 22:33:06 PDT 1998

```  Upon further thought of Bucklin and majority and minority groups--

Attention Mike O.-- note the majority against and lesser of evils !!!!

Reverse Bucklin is another tiebreaker if there is no Condorcet winner.
If a choice has a majority against it (in the last choice or last 2 choices
(if necessary) or last 3 choices (if necessary), etc.), then it loses.

This comes about due to the possibility of having a divided majority and/ or a
divided minority.

Example--
A, B, C= divided majority;   D,E = divided minority

100 voters
17 A > B > C > (D or E)
17 B > C > A > (D or E)
17 C > A > B > (D or E)
25 D > E  > (A or B or C)
24 E > D  > (A or B or C)

Assume no candidate has a majority against in the last choice (5th place).
D and E would both have a majority against in the last 2 choices (4th and 5th
places) and thus lose.   The votes for A, B or C on the 49 D and E first
choice ballots would then move up.   Presumably the D and E voters would pick
the lesser of the majority evils (in their minds) as an original 3rd choice
which then becomes a 1st choice.

Reverse Bucklin applied to some earlier examples---

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.
100
no majority against in last choice, last 2 choices
A 45
B 50
C 50
D 55  D loses.
200

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

last choice
A  30
B  20
C  50
100

last 2 choices
A  80  loses
B  50    no majority winner ??
C  70  loses
200
--
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.
106

last choice
A  36
B  20
C  15
D  35
106
last 2 choices
A  45
B   50
C   56  loses
D  55   loses
216

35 voters vote B > A
30 voters vote  B > A.
20 voters vote A > B.
15 voters vote B > A
6 voters vote  B > A.
last choice
A 86  loses.
B  20  wins.
106
---
37 voters vote C > A > B > D.
20 voters vote B > D > A > C.
18 voters vote A > D > C > B.
15 voters vote B > D > C > A.
07 voters vote D > A > C > B.
03 voters vote C > B > A > D.
100
last 2 choices
A  38
B  62  loses
C  60  loses
D  40
200

37 voters vote A > D.
20 voters vote D > A
18 voters vote A > D
15 voters vote D > A.
07 voters vote D > A
03 voters vote A > D.
100
last choice
A  42  wins
D  58  loses
100
-----
37 voters vote C > A > B > D.
20 voters vote B > D > A > C.
18 voters vote A > D > C > B.
21 voters vote B > D > C > A.
07 voters vote D > A > C > B.
03 voters vote C > B > A > D.
106
last 2 choices
A  44
B  62 loses
C  66 loses
D  40
212

37 voters vote A > D
20 voters vote D > A
18 voters vote A > D
21 voters vote D > A
07 voters vote D > A
03 voters vote A > D
106
last choice
A 48   wins
D  58  loses
106

Bottom line-
YES/NO vote on each choice
Majority YES choices go head to head
Reverse Bucklin as tiebreaker.

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