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<div class="moz-cite-prefix">On 5/06/2023 9:16 am, Forest Simmons
wrote:<br>
<blockquote type="cite">35 A <br>
10 A=B <br>
30 B>C <br>
25 C <br>
<br>
C>A 55-45, A>B 45-40 (note 10A=B effect), B>C
40-25.
<div dir="auto"><br>
</div>
<div dir="auto">I noticed that A has more losing votes (45) than
B has wining votes (40).</div>
<div dir="auto"><br>
</div>
<div dir="auto">It seems to me that this fact (by itself) should
disqualify B.</div>
<div dir="auto"><br>
</div>
<div dir="auto">So how about this as a tournament versión of
Plurality:</div>
<div dir="auto"><br>
</div>
<div dir="auto">If B's maxPairwiseSuppoft is less than A's
minPS, then B should not win.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Anybody ever proposed this Criterion before?</div>
</blockquote>
<br>
I and/or Kevin Venzke may have mentioned it in passing. The
example is originally from Kevin.<br>
<br>
I agree that is a good criterion and should be a strong standard.
I quite a while ago rejected the idea<br>
that the best Condorcet methods were those that focused purely on
"defeat strengths" with a view to<br>
simply "break the cycle at its weakest link".<br>
<br>
<blockquote type="cite">
<div dir="auto">Also B is Ranked on fewer ballots (40) than A is
ranked Top (45) so Plurality requires B to lose as well.</div>
<div dir="auto"><br>
</div>
</blockquote>
The Plurality criterion was coined by Douglas Woodall, who only
discussed ballots with strict ranking from<br>
the top with truncation allowed. So it says that that B isn't
allowed to win if B is voted above bottom on fewer<br>
ballots than A is voted alone above all others.<br>
<br>
So it generally accepted that Winning Votes meets the ("normal",
original) Plurality criterion.<br>
<br>
Chris Benham<br>
<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfp2b8vgJbN+bcK4u-btBaHobKj-+y6UCwARZMgqHhGpAA@mail.gmail.com">
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<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, May 4, 2023, 1:25
AM C.Benham <<a href="mailto:cbenham@adam.com.au"
moz-do-not-send="true" class="moz-txt-link-freetext">cbenham@adam.com.au</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<p><br>
</p>
<div style="font-family:-moz-fixed;font-size:14px"
lang="x-unicode"> <br>
<br>
My favourite method that meets both Condorcet and
Chicken Dilemma is 'Min Losing-Votes (equal-ranking
whole) Sorted Margins Elimination': <br>
<br>
*Voters rank from the top whatever number of
candidates they like. Equal-ranking and truncation are
allowed. <br>
<br>
For the purpose of determining candidates' pairwise
scores: <br>
<br>
a ballot that votes both X and Y above no other
(remaining) candidates contributes nothing to X's
pairwise score versus Y and vice versa, <br>
<br>
a ballot that ranks X and Y equal and above at least
one (remaining) candidate contributes a whole vote to
X's pairwise score versus Y and vice versa, <br>
<br>
a ballot that ranks X above Y contributes a whole vote
to X's pairwise score versus Y and nothing to Y's
pairwise score <br>
versus X. <br>
<br>
Give each candidate X a score equal to X's smallest
losing pairwise score. <br>
<br>
Initially order the candidates from highest-scored to
lowest scored. If any adjacent pair is out-of-order
pairwise, then swap <br>
the out-of-order pair with the smallest
score-difference. If there is a tie for that then swap
the tied pair that is lowest in <br>
the order. Repeat until no adjacent pair is pairwise
out-of-order, and then eliminate the lowest-ordered
candidate. <br>
<br>
Repeat (disregarding any pairwise scores with
eliminated candidates) until one candidate remains. *
<br>
<br>
Some examples: <br>
<br>
46 A>B <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 90-10, C>A 54-46. <br>
<br>
MinLV(erw) scores: B49 > A46 > C10. <br>
<br>
Both adjacent pairs (B>A and A>C) are pairwise
out of order. The B>A score-difference is the
smallest of the two<br>
(3 versus 36) so we first swap that order to give<br>
<br>
A49 > B51 > C10<br>
<br>
Now neither pair of adjacent candidates is pairwise
out of order so C is eliminated and A wins. <br>
<br>
Winning Votes, Margins, MMPO elect the Burier's
candidate.<br>
<br>
25 A>B <br>
26 B>C <br>
23 C>A <br>
26 C <br>
<br>
C>A 75-25, A>B 48-26, B>C 51-49. <br>
<br>
MinLV(erw) scores: C49 > B26 > A25. <br>
<br>
Both adjacent pairs (C>B and B>A) are pairwise
out-of-order. The B-A score difference is by <br>
far the smallest, so we swap the B>A order to give
<br>
<br>
C > A > B. That order is final and C wins. C
is the most top ranked and the most above-bottom
ranked <br>
candidate. WV, MMPO, IRV, Benham elect B. <br>
<br>
35 A <br>
10 A=B <br>
30 B>C <br>
25 C <br>
<br>
C>A 55-45, A>B 45-40 (note 10A=B
effect), B>C 40-25.
</div>
</div>
</blockquote>
</div>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">I noticed that A has more losing votes (45) than
B has wining votes (40).</div>
<div dir="auto"><br>
</div>
<div dir="auto">It seems to me that this fact (by itself) should
disqualify B.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Also B is Ranked on feet ballots (40) than A is
ranked Top (45) so Plurality requires B to los as well.</div>
<div dir="auto"><br>
</div>
<div dir="auto">So how about this as a tournament versión of
Plurality:</div>
<div dir="auto"><br>
</div>
<div dir="auto">If B's maxPairwiseSuppoft is less than A's
minPS, then B should not win.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Anybody ever proposed this Criterion before?</div>
<div dir="auto">
<div class="gmail_quote">
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<div style="font-family:-moz-fixed;font-size:14px"
lang="x-unicode"> <br>
<br>
MinLV(erw) scores: A45 > B40 > C25. Neither
adjacent pair is pairwise out-of-order so the order
is final <br>
and A wins. <br>
<br>
A both pairwise-beats and positionally dominates B,
but WV, Margins, MMPO all elect B. <br>
<br>
Chris Benham <br>
<br>
<br>
<br>
</div>
</div>
</blockquote>
</div>
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