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
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