Markus Schulze wrote--
Example 1a:
35 voters vote D > A > B > C.
32 voters vote C > A > B > D.
20 voters vote B > C > A > D.
13 voters vote D > B > C > A.
Demorep1-
100 voters- majority 51
D is the last choice of a majority of the voters and is a Condorcet loser
(i.e. loses automatically).
35 voters vote A > B > C.
32 voters vote C > A > B
20 voters vote B > C > A
13 voters vote B > C > A.
A/B 67/33
A/C 35/65
B/C 68/32
A>B>C>A circular tie
Reverse Bucklin CH = Choice
3CH 3+2 CH
A 33 65
B 32 67
C 35 68
A, B and C all have majorities against. C loses with worst defeat (note-- the
worst beaten candidate with Reverse Bucklin is also the candidate with the
lowest number of first choice votes)
A/B 67/33, A wins
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Markus Schulze wrote more--
35 voters vote D > A > B > C.
32 voters vote C > A > B > D.
20 voters vote B > C > A > D.
13 voters vote D > B > C > A.
06 voters vote A > D > C > B.
Demorep1-
106 voters- majority 54
No majority against D as last choice (52) so D continues.
A/B 73/33
A/C 41/65
A/D 58/48
B/C 68/38
B/D 52/54
C/D 52/54
A>B>C>A, A>D, D>B>C circular tie
Reverse Bucklin CH = Choice
4 CH 4+3 CH
A 13 33
B 6 73 majority against, B loses
C 35 54 majority against, C loses
D 52 52
106 212
A/D 58/48, A wins (again)
General comment- With 4 or more tied choices Reverse Bucklin causes the
successive defeat of the candidates who have majorities against them (leaving
the head to head math to be looked at again).
