[EM] Improved Generalised Bucklin

[Eric Gorr]

At 4:05 AM +0930 8/21/03, Chris Benham wrote:
>Example 3.
>31:  B>A>E>C>D
>23:  C>B>A>E>D
>25:  D>A>C>E>B
>11:  D>C>B>A>E
>10:  E>A>C>B>D
>100 voters, all 5 candidates in the Smith set.
>IGB
>Round 1:    A:0       B:31     C:23     D:36     E:10
>Round 2:    A:66     B:65     C:34     D:36     E:10
>  Eliminate C D E. All ballots have contributed  to the totals of  A 
>and/or  B, except the 11 DCB ballots, so 11 votes are added to B's 
>tally.  Round 3:    A:66    B:76 ,  so  B is the first finalist.
>Reverse IGB Elimination
>Round 1:    A:0       B:25      C:0      D:64    E:11
>  Eliminate D.
>Round 1:    A:0       B:35      C:31    E:34
>           2:    A:23     B:35      C:41    E:90
>  Eliminate E.
>Round 1:   A:34      B:35      C:31
>           2:   A:65      B:69      C:41
>     Those 41 C votes are all on ballots that have contributed to A or B, so
>  Eliminate B, and then A>C 66-34 and so A is the other finalist.
>The two finalists runoff:    B>A  64-36 , so elect B.

This example contains a simple cycle between ABC. It is clear that DE 
are not preferred over ABC by any majority and shouldn't have the 
possibility of winning.

So, the question becomes, who should be victorious in the cycle. I 
cannot come up with any good reason to believe that should be anyone 
other then A.