<div dir="auto"><div><br><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Jun 4, 2023, 11:03 PM C.Benham <<a href="mailto:cbenham@adam.com.au">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">
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<p><br>
</p>
<div>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></div></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Me too. I cannot make that kind of method (weakest link cycle breaking) sufficiently burial resistant ... no matter how I define defeat strength.</div><div dir="auto"><br></div><div dir="auto">My current thinking (based on geometrically motivated ballot sets) is that non trivial top cycles are more likely to be artificial than sincere, and the simplest, most likely mechanism (for creating promising cycles) is unilateral burial or strategic truncation of the sincere CW by some faction.</div><div dir="auto"><br></div><div dir="auto">And it seems to me if this guess is more or less accurate, our top Condorcet design priority should be to "not reward the buriers" ... as opposed to detecting a sincere signal in a noisy ballot set ... i.e. one riddled by mistaken but sincere judgments ... the kind of ballot set where weakest link cycle breaking would be indicated.</div><div dir="auto"><br></div><div dir="auto">Forest </div><div dir="auto"><br></div><div dir="auto"><br></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>
<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 is generally accepted that Winning Votes meets the ("normal",
original) Plurality criterion.<br>
<br>
Chris Benham<br>
<br>
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<blockquote type="cite">
<div dir="auto">
<div><br>
<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" target="_blank" rel="noreferrer">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>
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</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>
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