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<div class="moz-cite-prefix">Forest wrote:<br>
<br>
<blockquote type="cite">
<div>But this brings up another method: Majority Enhanced
MPO(tw), in analogy with Majority Enhanced Approval:<br>
<br>
</div>
Initiate a list L with the name of the candidate with the least
MPO(tw). 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>
</blockquote>
<br>
That doesn't seem to resist Burial as well as MMLV(erw)M. In
this example I gave in an earlier recent post:<br>
<br>
<blockquote type="cite">34 A>B <br>
17 C>A <br>
16 B>C <br>
31 B <br>
02 B>C (sincere is B or B>A) <br>
<br>
A is the sincere Condorcet winner (and a sincere Mutual Dominant
Third winner). <br>
<br>
A>B>C>A. MMLV(erw) scores: B49 > A34 > C17.
The margin between adjacent candidates B and A (15) is smaller
than <br>
that between A and C (17), and A pairwise beats B, so Margins
Sort first flips that order to give A>B>C with no
candidate pairwise <br>
beating the next highest in the order, and so elects the
candidate highest in this final order, A. <br>
<br>
C>A -17, A>B -15, B>C +32. A has the weakest
defeat and so wins. </blockquote>
<br>
MPO (tw) scores: B51 > A66 > 83 B (the buriers'
candidate) has the smallest PO(tw) score and is uncovered and so
wins.<br>
<br>
Likewise in another earlier example:<br>
<br>
<blockquote type="cite">46 A<br>
44 B>C (sincere is B or B>A)<br>
05 C>A<br>
05 C>B<br>
<br>
A>B 51-49, B>C 44-10, C>A 54-46. MinMax (Losing
Votes) scores: <br>
B49, A46, C10.</blockquote>
<br>
MPO(tw) scores: B51 > A56 > C90<br>
<br>
Again the Burier's candidate B wins with Forest's suggested "
Majority Enhanced MPO(tw)" method. MMLV(erw)M elects A, and if
all of 46A change<br>
to A>B it still elects A.<br>
<br>
Chris Benham<br>
<br>
<br>
On 5/1/2014 6:05 AM, Forest Simmons wrote:<br>
</div>
<blockquote
cite="mid:CAP29ondYungB601QY42wXkD63HWoi_NYWf+uNu-WZK2tGmHYFg@mail.gmail.com"
type="cite">
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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>
</div>
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>
</div>
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>
</div>
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>
</div>
This suggests a formulation of Benham's new method that
we could call <br>
</div>
MPO(tw) Sorted Pairwise Margins. in analogy to Approval
Sorted Pairwise Margins.<br>
<br>
</div>
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>
</div>
I believe that the above discussion shows that this
formulation is equivalent to Benham's MaxMinLV(erw) Margins
method.<br>
<br>
</div>
<div>The truncation whole (tw) convention forces MMPO(tw) to
comply with Plurality. The pairwise sorting feature makes it
comply with Smith.<br>
<br>
</div>
<div>But this brings up another method: Majority Enhanced
MPO(tw), in analogy with Majority Enhanced Approval:<br>
<br>
</div>
<div>Initiate a list L with the name of the candidate with the
least MPO(tw). 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>
</div>
<div>Forest<br>
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