[EM] Marcus Schulze 2003 on Bucklin's technical shortcomings

[Chris Benham]

http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010803.html

Dear John B. Hodges,

you wrote (1 Sep 2003):
> This method has been called "Generalized Bucklin", and AFAICT
> could also be called "Majority Choice Approval". My question,
> for one and all: Is there any desirable quality, that any
> single-winner method has, that this method does not have?

Condorcet, Condorcet Loser, Consistency, Independence of Clones,
Reversal Symmetry, Smith, later-no-harm, Participation.

Markus Schulze


http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010811.html

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.

Kevin Venzke

http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010812.html

Dear Kevin,

you wrote (2 Sep 2003):
> I think MCA meets Clone Independence and Participation,
> but I'd like to hear reasoning to the contrary.

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.

Markus Schulze


http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010821.html


"Reversal symmetry" says: When candidate X is the unique
winner then when the individual preferences of each voter
are inverted then candidate X must not be elected.

Example:

     19  A > C > B
     20  B > C > A
     1   C > A > B
     1   C > B > A
     1   B > A > C
     1   A > B > C

     Candidate C is the unique Bucklin winner. When all
     individual preferences are inverted then candidate C
     is still the unique Bucklin winner.

Markus Schulze


http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010822.html


Dear John B. Hodges,

the following example demonstrates that Bucklin
violates consistency.

Situation 1:

     4   A > B > C
     5   B > C > A
     6   C > A > B

     Candidate C is the unique Bucklin winner.

Situation 2:

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

     Candidate C is the unique Bucklin winner.

Situation 1+2:

     Candidate A is the unique Bucklin winner.

Markus Schulze


http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010823.html


Dear John B. Hodges,

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.

******

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.

Markus Schulze



<http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010803.html> 

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