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<DIV dir=ltr align=left><SPAN class=558452422-14082007><FONT face=Arial
color=#0000ff size=2>This is enough to convince me that approval is an
appropriate method.</FONT></SPAN></DIV><BR>
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<FONT face=Tahoma size=2><B>From:</B>
election-methods-bounces@lists.electorama.com
[mailto:election-methods-bounces@lists.electorama.com] <B>On Behalf Of </B>Chris
Benham<BR><B>Sent:</B> Tuesday, August 14, 2007 5:11 PM<BR><B>To:</B>
Juho<BR><B>Cc:</B> Forest W Simmons; Election Methods Mailing
List<BR><B>Subject:</B> Re: [Election-Methods] RE : Corrected "strategy
inCondorcet" section<BR></FONT><BR></DIV>
<DIV></DIV><BR><BR>Juho wrote:<BR>
<BLOCKQUOTE type="cite"><PRE wrap="">On Aug 2, 2007, at 6:44 , Kevin Venzke wrote:
</PRE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><PRE wrap="">1000 A>B, 1000 C>D, 1 D>B
</PRE></BLOCKQUOTE></BLOCKQUOTE><PRE wrap=""><!---->
</PRE>
<BLOCKQUOTE type="cite"><PRE wrap="">Yes, I do think D is the proper winner.</PRE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite"><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 :-).
</PRE></BLOCKQUOTE><BR>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><BR>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><BR><BR><BR><BR><BR></BODY></HTML>