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<div class="moz-cite-prefix">Forest,<br>
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<div>Is Condorcet(MaxPO(tw)) equivalent to Condorcet(MinLV(eq
rank whole))? If so the margins versions would be equivalent
too.<br>
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"PO" stands for "Pairwise Opposition," and "tw" for "Truncation
Whole," which means that if two candidates are truncated
together on a ballot they are both counted in opposition to each
other.</blockquote>
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It looks like yes.<br>
<br>
35 A>B<br>
25 B<br>
40 C<br>
<br>
C > A 40-35, A>B 35-25, B>C 60-40. MinMax
(Losing Votes) scores: C40 > A35 > B25. (Margins Sort
keeps this order).<br>
<br>
Forest's suggested "truncation whole" version:<br>
C>A 65-60, A>B 75-65, B>C 60-40. Max Pairwise
Opposition (truncation whole) scores: C60 < A65 < B75 .<br>
<br>
The smaller a candidate's Max PO score the better for it. I'll
look at your other method suggestion later.<br>
<br>
Chris Benham<br>
<br>
<br>
On 5/1/2014 6:05 AM, Forest Simmons wrote:<br>
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<div>Is Condorcet(MaxPO(tw)) equivalent to
Condorcet(MinLV(eq rank whole))? If so the
margins versions would be equivalent too.<br>
<br>
</div>
"PO" stands for "Pairwise Opposition," and "tw"
for "Truncation Whole," which means that if two
candidates are truncated together on a ballot
they are both counted in opposition to each
other.<br>
<br>
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With this convention the Pairwise Opposition (tw)
from candidate A against candidate B is the number
N of ballots on which A is ranked strictly above B
plus the number of ballots on which A and B are
truncated together.<br>
<br>
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With the equal rank whole convention, the LV
strength of the defeat of B by A is the number M of
ballots on which B is ranked (but not truncated!)
above or equal to A.<br>
<br>
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Careful consideration reveals N+M is a constant,
namely the total number of ballots, since no case was
left out or counted more than once.<br>
<br>
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This suggests a formulation of Benham's new method that
we could call <br>
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MPO(tw) Sorted Pairwise Margins. in analogy to Approval
Sorted Pairwise Margins.<br>
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List the candidates in order of MPO(tw) scores, and then
adjust the list by reversal of adjacent pairs that are out
of pairwise defeat order taking into account how close they
are in their scores.<br>
<br>
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I believe that the above discussion shows that this
formulation is equivalent to Benham's MaxMinLV(erw) Margins
method.<br>
<br>
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<div>The truncation whole (tw) convention forces MMPO(tw) to
comply with Plurality. The pairwise sorting feature makes it
comply with Smith.<br>
<br>
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<div>But this brings up another method: Majority Enhanced
MPO(tv), in analogy with Majority Enhanced Approval:<br>
<br>
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<div>Initiate a list L with the name of the candidate with the
least MPO(tv). Then while there is any candidate that covers
all of the candidates listed, from among such candidates add
to the list the name of the one with the least MPO(tw). Elect
the last candidate added to the list.<br>
<br>
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<div>Forest<br>
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