Positive Involvement; No-Show

[DEMOREP1 at aol.com]

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
------
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).