[EM] [EM]Re: Marcus Schulze 2003 on Bucklin

[Chris Benham]

Mike Ossipoff wrote (Thu.Apr.8):

>Chris Benham posted an archived discussion as a criticism of Bucklin. 
>Actually Bucklin isn't what is being discussed in that quote, and so it has 
>no relevance to Bucklin's merit.
>
>By the way, if anyone knows of an example in which Buckling fails 
>Independence from Clones, would they post it?
>
>Mike Ossipoff
>
Presumably he refers to:

>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
>
>  
>
"Generalized Bucklin"  just means Bucklin  that allows equal-ranking 
with whole votes (precisely the version that Mike
has been talking up). The demonstrations in that post all apply to that 
method. John Hodges apparently didn't realise that
the name "Majority Choice Approval"  was already taken by a 3-slot 
 method, that is equivalent  to "ER Bucklin (whole)"
when there are three candidates.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012595.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.
>  
>
>Markus Schulze
>
 I  think this shows that, without the "AERLO"  strategy gimmick, 
 ER-Bucklin(whole)  doesn't meet "strong  FBC".
I don't recall it ever being explained exactly how  the AERLO  operates 
in Bucklin (or IRV).

Mike,
Given your well known standards, I  am surprised  you haven't  shown any 
interest in the easy-to-count, clone-proof  Bucklin-like
plain  Weighted  Median  Approval (WMA).
To refresh your memory of the rules:
Ranked ballots, equal preferences and truncation ok. Each candidate is 
given a weight equal to the number of first preferences
(fractional) they get. The total weight of  all the candidates is equal 
to the total number of  valid ballots.
A candidate whose weight exceeds half the total weight wins outright.
If  none do that, then all ballots fully approve  the candidate/s they 
rank first or equal first. (There are no partial approvals.
All ballots do not approve candidate/s they rank last or equal last.)
(Subject to above) each ballot, starting with the highest-ranked, keeps 
approving the most preferred candidates until  their
weight equals or exceeds half the total weight of the candidates.
The candidate with the highest  approval  score wins.

Chris Benham



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