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<pre>Dear John B. Hodges,
you wrote (1 Sep 2003):
><i> This method has been called "Generalized Bucklin", and AFAICT
</i>><i> could also be called "Majority Choice Approval". My question,
</i>><i> for one and all: Is there any desirable quality, that any
</i>><i> single-winner method has, that this method does not have?
</i>
Condorcet, Condorcet Loser, Consistency, Independence of Clones,
Reversal Symmetry, Smith, later-no-harm, Participation.
Markus Schulze
</pre>
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href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010811.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010811.html</a><br>
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<pre>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
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href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010812.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010812.html</a>
Dear Kevin,
you wrote (2 Sep 2003):
><i> I think MCA meets Clone Independence and Participation,
</i>><i> but I'd like to hear reasoning to the contrary.
</i>
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
<a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010821.html">
http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010821.html</a>
"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
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href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010822.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010822.html</a>
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
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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
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