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Juho wrote:<br>
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<pre wrap="">On Aug 2, 2007, at 6:44 , Kevin Venzke wrote:
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<pre wrap="">1000 A>B, 1000 C>D, 1 D>B
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<pre wrap=""><!---->
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<pre wrap="">Yes, I do think D is the proper winner.</pre>
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<pre wrap="">Do you have a verbal (natural language) explanation why D is better
than A and C. This scenario could be an election in a school. One
class has voted A>B (A and B are pupils of that class), another class
has voted C>D, the teacher has voted D>B. What should the teacher
tell the C>D voting class when they ask "didn't you count our votes"?
Maybe this is clear to you. Unfortunately not as clear to me. The
teacher vote seemed to be heavier than the pupils votes :-).
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I agree with Kevin that D is the proper winner, but Winning Votes
isn't my favourite algorithm.<br>
If we are sticking with Condorcet "immune" methods and so are only
focussing on how to compare<br>
(measure) defeat strengths, then I like Approval Margins (Ranking) if
we are using plain ranking ballots.<br>
<br>
So interpreting ranking (above bottom or equal-bottom) as approval, we
get these approval scores:<br>
D1001, B1001, A1000, C1000<br>
<br>
All the candidates have at least one pairwise defeat, and by AM the
weakest is D's single defeat, C>D<br>
by an AM of -1.<br>
I also like Approval-Sorted Margins(Ranking), which is probably
equivalent to AM.<br>
<br>
The initial approval order is D=B>A=C. The smallest approval gaps
(zero) are between D and B, and A<br>
and C. A pairwise ties with C but D pairwise beats B, so our first
modification of the order is D>B>A=C.<br>
A pairwise beats B, so the second modification is D>A>B=C. B
pairwise beats C, so the third modified<br>
order is D>A>B>C. This order accords with the pairwise
comparisons so is the final order and D wins.<br>
<br>
I also like eliminating (and dropping from the ballots) the candidate
lowest in this order and then repeating<br>
the whole process until one remains. In this case that would give the
same winner, with the elimination order<br>
just being the reverse of the ASM(R) order.<br>
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The only candidate with any sort of claim versus D is C, and C is
pairwise beaten by a more approved<br>
candidate (B) so C is outside the "Definite Majority (Ranking)" set.<br>
<br>
Chris Benham<br>
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