[EM] Re: Improved Generalised Bucklin

[Chris Benham]

I  would just like to point out  that a method  I posted  on  Fri.Aug. 
22,  which for the time being  I shall dub "Improved Generalised 
Bucklin" ( the full "2-way" version),  succeeds in many of  the examples 
(given in the "Query for one and all" thread) 
of  plain  (Generalised) Bucklin failing some important  criteria.
To recap what  IGB is, it features a final runoff  between  finalists 
chosen by  2 different (but related) methods. The same candidate can be 
"both" finalists. The first finalist is determined by Generalised 
Bucklin with an extra rule:

When any candidate has a majority, eliminate all those who do not. Any 
ballots showing a preference among the remaining candidates which have 
not been counted towards any of their tallies, shall be counted toward 
the remaining candidate/s for whom the ballot shows highest or equal 
highest preference.

The second finalist is determined by reversing the first-finalist method to one-at-a-time 
eliminate candidates until one remains.

Kevin Venzke Tues.Sep.2 on Participation:
"I found how MCA fails Participation. It seems pretty mild, though:

5: A>B>C
4: B>C>A

A is a majority favorite and wins.

But add these in:
2: C>A>B

There is no majority favorite and B wins by greatest approval."
(In this example MCA is equivalent to Generalised Bucklin.)

IGB first finalist sub-election.
Round 1.  A:5  B:4  C:2 
Round 2.  A:7  B:9  C:6  As above, B "wins" (and so is first finalist).

IGB second finalist sub-election.
Round 1:  A:4  B:2  C:5
Round 2:  A:6  B:7  C:9  C is eliminated and then A is the second finalist.

A>B 7-4 and so A wins (the same as before the 2 CAB votes were added).

Markus Schulze Wed.Sep.3 on Clone Independence:
"Situation 1:

2 A > B > C
3 B > C > A
4 C > A > B

The winner is candidate C.

Situation 2:

Replacing C by C1, C2, and C3 gives:

2 A > B > C2 > C1 > C3
3 B > C3 > C2 > C1 > A
4 C1 > C2 > C3 > A > B

The winner is candidate B."

In both above "situations", the IGB winner is B.

Marcus Schulze Th.Sep.4 on Compromising:
"the following example demonstrates that Bucklin is
vulnerable to "compromising" (i.e. insincerely ranking
a candidate higher to make him win).

Example:

4 A > B > C
3 B > C > A
2 C > A > B

The unique Bucklin winner is candidate B.
However, if the 2 CAB voters had insincerely voted
ACB then the unique Bucklin winner would have been
candidate A. Since these 2 CAB voters strictly prefer
candidate A to candidate B, voting ACB instead of CAB
to change the winner from candidate B to candidate A
is a useful strategy for them."

In the above example, the IGB winner is A in both cases ( so those 2 C supporters gain 
nothing by Compromising).

Marcus in the same message on Burial:
"The following example demonstrates that Bucklin is
vulnerable to "burying" (i.e. insincerely ranking a
candidate lower to make him lose).

Example:

4 A > D > C > B > E
2 B > C > A > D > E
3 C > A > E > D > B

The unique Bucklin winner is candidate A.
However, if the 3 CAEDB voters had insincerely voted
CEDBA then the unique Bucklin winner would have been
candidate C. Since these 3 CAEDB voters strictly prefer
candidate C to candidate A, voting CEDBA instead of CAEDB
to change the winner from candidate A to candidate C
is a useful strategy for them."

In the above example, the IGB winner is C in both cases ( so there is nothing for those
3 C supporters to gain by Burying A.)

Chris Benham