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<div class="moz-cite-prefix">
<blockquote type="cite"><br>
Michael Christened our new Q&D burial resistant method
"Duncan"...</blockquote>
<br>
What does "Q&D" mean?<br>
<br>
Am I right in assuming that the Borda counts are based on the
symmetrically completed ballots?<br>
<br>
<blockquote type="cite">
<div dir="auto">Duncan Definition:</div>
<div dir="auto"><br>
</div>
<div dir="auto">In the vast majority of the cases ... those in
which the pairwise counts of the ballots unambiguously
identify the candidate that pairbeats each of the others ...
elect that candidate.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Otherwise, elect the highest score candidate
that pairbeats every candidate with lower score.</div>
</blockquote>
<br>
So another way of putting it is: "If there is no CW, elect the
member of the Smith set with the second-worst score".<br>
<br>
To put it bluntly, that is bound to have monotonicity problems and
doesn't fly philosophically.<br>
<br>
Trying to deter or frustrate order-reversal Burial strategy is
fine, but the algorithm should "appear fair" and be able to be
justified when<br>
we assume that all the votes are sincere (or even just all equally
likely to be sincere).<br>
<br>
So if the score-order is A>B>C and there is a
A>B>C>A top cycle (aka Smith set) then this "Duncan"
method elects B.<br>
<br>
That breaks (at least one version of) "Double Defeat". B is
pairwise beaten by a candidate with a higher "score".<br>
<br>
<br>
Chris B.<br>
<br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">On 14/10/2023 4:43 am, Michael Ossipoff
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAOKDY5Ceg05d69T-AAPAcYWjB-A=j71YPHQsap_Xdf8Ks7DMrg@mail.gmail.com">
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<div dir="auto">Yes, I like Duncan because burying the CW in an
attempt to help your favorite won’t help hir when it causes hir
disqualification, as it probably will.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…& Duncan is remarkably briefly-defined,
needing only a very slight modification of Black’s method.</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Fri, Oct 13, 2023 at
10:11 Forest Simmons <<a
href="mailto:forest.simmons21@gmail.com"
moz-do-not-send="true" class="moz-txt-link-freetext">forest.simmons21@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="auto">
<div>Dear EM List Friends,
<div dir="auto"><br>
</div>
<div dir="auto">We need your feedback on this draft of a
proposal before we submit a version of it to the
voting reform community at large.</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">---------- Forwarded
message ---------<br>
From: <strong class="gmail_sendername" dir="auto">Forest
Simmons</strong> <span dir="auto"><<a
href="mailto:forest.simmons21@gmail.com"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">forest.simmons21@gmail.com</a>></span><br>
Date: Thu, Oct 12, 2023, 5:35 PM<br>
Subject: Duncan Proposal Draft<br>
To: Michael Ossipoff <<a
href="mailto:email9648742@gmail.com"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">email9648742@gmail.com</a>><br>
</div>
<br>
<br>
<div dir="auto">Michael Christened our new Q&D
burial resistant method "Duncan" after Duncan Black
who popularized the idea of using Borda's Method as
a fallback "completion" when the ballots fail to
unambiguously reveal the sincere "Condorcet"
pairbeats-all candidate.
<div dir="auto"><br>
</div>
<div dir="auto">Our Duncan method has the same form
as Black's in that the official version directly
specifies electing the unambiguous Condorcet
Candidate when there is one, and falls back to
another procedure that relies on Borda Scores,
otherwise.</div>
<div dir="auto"><br>
</div>
<div dir="auto">It should be emphasized that in both
cases the fall back Borda based expedient is
rarely needed. For that reason some misguided
voting reform advocates have cavalierly opined
that any decisive completion/ fallback method
would be plenty adequate to supplement the
Condorcet Criterion requirement.</div>
<div dir="auto"><br>
</div>
<div dir="auto">However, this casual attitude
ignores the feedback aspects of voting systems in
that various voting methods vary in the degree
that they encourage or discourage the creation of
artificial beat cycles that subvert/ hide the
Condorcet Candidate from view, bringing the
completion method into greater prominence in a
potentially unstable cycle.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Unfortunately most of the extant
methods fall into this "positive" feedback
category, including Borda itself. Some less
sensitive methods like Approval and IRV/RCV have
a built in "friction" that dampens the feedback;
but as systems engineers know, the high
performance components are the ones that need the
addition of some carefully engineered negative
feedback "circuit" to stabilize the system as a
whole.</div>
<div dir="auto"><br>
</div>
<div dir="auto">In our Condorcet Completion context,
our use of the Borda Count scores is carefully
designed with that stabilizing influence in mind:
adventurous strategists who are aware of this
feature, when acting rationally will be deterred
from creating these cycles that come back to bite
them. Those not aware will find out when their
ploys backfire or otherwise disappoint them.</div>
<div dir="auto"><br>
</div>
<div dir="auto">How do these pesky cycles arise so
easily in Borda and other rank based methods?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Suppose that your personal
preference schedule for the alphabetized
candidates looks like ...</div>
<div dir="auto"><br>
</div>
<div dir="auto">A>C>X>Y>Z, and that C is
the Condorcet Candidate projected to win the
election if nobody acts nefariously.</div>
<div dir="auto"><br>
</div>
<div dir="auto">You, and like minded friends, get
the idea to insincerely move your second choice to
the bottom of your ballot (so it now reads
A>X>Y>Z>C) ... not to be "nefarious"
so much as to just increase the winning chances of
your favorite A.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Could this work?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Yes, under Black's method if your
friends follow your lead, this "nurial" of C under
the "busses" X, Y, and Z, could easily subvert one
or more of C's pairwise victories over X,Y, and Z,
into defeats of C by them, thereby hiding C's
identity of sincere Universal "pairbeater" status
to just one more member of a "beatcycle" of the
form A beats X beats Y beats Z beats C beats A.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Note that the buried candidate C
still beats the buriers' favorite, A ... because
lowering C does not decrease the number of
ballots that support C over A ... which is how
easily and innocently beatcycles like this can be
created in Condorcet style elections ... at least
in the absence of negative feedback from the cycle
resolution fallback method.</div>
<div dir="auto"><br>
</div>
<div dir="auto">In traditional Black that fallback
method is Borda. Does that fix the problem? ... or
does it exacerbate it.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Well ... the same burial that put C
at disadvantage in the pairwise contests with X
thru Z, also lowered C's Borda score by 3 counts
per ballot, and raised</div>
<div dir="auto"> the Borda score of each of X thru Z
to the tune of one count per ballot.</div>
<div dir="auto"><br>
</div>
<div dir="auto">The likely outcome is that C will
end up with the lowest score, and come in last in
the finish order.</div>
<div dir="auto"><br>
</div>
<div dir="auto">By way of contrast, under our new
Duncan method, the most likely winner is X, and
the least likely winner is A, the burier faction's
favorite ... thus disappointing the burier faction
supporters ... teaching them that if they try to
outsmart new Duncan with insincere ballot
rankings, they are apt to end up helping elect
their third (or later) choice instead of their
first choice or their second choice ... the one
that they so cleverly buried (however innocently
or without malice).</div>
<div dir="auto"><br>
</div>
<div dir="auto">Too many dabblers in voting method
reform (as well as most professionals) are unaware
of these dynamics.</div>
<div dir="auto"><br>
</div>
<div dir="auto">But now, with your new
understanding, you, at least, can become part of
the solution.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Duncan Definition:</div>
<div dir="auto"><br>
</div>
<div dir="auto">In the vast majority of the cases
... those in which the pairwise counts of the
ballots unambiguously identify the candidate that
pairbeats each of the others ... elect that
candidate.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Otherwise, elect the highest score
candidate that pairbeats every candidate with
lower score.</div>
<div dir="auto"><br>
</div>
<div dir="auto">[Nominally "score" = Borda Count,
though STAR Voting scores, for example, could also
serve]</div>
<div dir="auto"><br>
</div>
<div dir="auto">How does this Duncan fallback
procedure work to prevent A from getting elected
in our scenario regarding A thru Z?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Well, could A pairbeat every lower
score candidate? In particular, could A pairbeat
C, which is now at the bottom of the Borda score
pile ... certainly lower than A ...?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Well, remember that "C beats A" was
the last step in the beatcycle created by A's
friends.</div>
<div dir="auto"><br>
</div>
<div dir="auto">So A does not pairbeat every lower
score candidate, and therefore cannot win.</div>
</div>
</div>
</div>
</div>
<div dir="auto">
<div>
<div class="gmail_quote">
<div dir="auto">
<div dir="auto"><br>
</div>
<div dir="auto">New Duncan is burial resistant.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Next time ... more examples and
insights ...</div>
<div dir="auto"><br>
</div>
<div dir="auto">fws</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
</div>
</blockquote>
<p><br>
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