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<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">With regard to the Saint Lague divisor, this has
been argued, for instance by Carstairs, as the most equitable
share-out. My findings substantiate this system also called
Webster apportionment after its original discoverer.</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">The Droop quota is a minimum proportional
representation, which largely replaced the Hare quota for
maximum representation in large constituencies. (Because
politicians wanted to safeguard their safe seats from the
greater electoral competition of being in large constituencies.)
But the average quota of the two, found by taking their harmonic
mean, is, on examination, a more optimally democratic
representation than maximum or minimum PR. The Harmonic Mean
quota, which I introduced, is V/(s+ ½). This is effectively
equivalent to Webster apportionment.</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">The democratic principle of voters lists (STV)
compared to the oligarchic principle of party lists, may use a
no less proportional principle (the Harmonic Mean quota) than
some party lists use of the Saint Lague divisor count</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">I briefly discussed this in my most recent e-book,
Don't You Ever read Anything But Serious Books?, in the review
of Carstairs brief history of West European voting methods.</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">The Harmonic Mean quota is one of te four averages I
use in the higher order counts of Binomial STV (STV^x]. Hence
Four Averages Binomial STV (FAB STV). The four averages are to
make the count more representative, not so much of candidate
popularity, but for the representation of information in
general.</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">First order Binomial STV (STV^1) is probably
sufficient for representation of candidates. But it is still the
first binomial count and the first one-truth voting method, that
uses the same count for both election and exclusion of
candidates - one persons election being another persons
exclusion, in principle.<br>
</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">Regards,</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold"">Richard Lung.<br>
</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
<p class="MsoNormal"><span
style="font-size:20.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
<div class="moz-cite-prefix">On 13/10/2023 20:22, Michael Ossipoff
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAOKDY5DudohH9RwaZhzQHmu8wRN_iBsb9r04Q-z3AtYC3r+__Q@mail.gmail.com">
<div dir="auto">Richard—</div>
<div dir="auto"><br>
</div>
<div dir="auto">No one is denying the desirability PR.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I don’t know where you reside, but, here in the
U.S., PR for our national legislature, Congress, is much less
short-term feasible, due to Constitutional structure.</div>
<div dir="auto"><br>
</div>
<div dir="auto">The Constitution requires that every state gets a
House representative, regardless of how small it’s population
is. If its population were 1, it would nonetheless get a
representative.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Additionally, the Constitution requires that every
state must get the SAME number of Senate-seats (two)…again,
regardless of how small its population is.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Those two Constitutional requirements would make
nonsense of proportionality.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Constitutional amendment is difficult &
time-consuming. …&, for various reasons we needn’t go into,
a Constitutional convention now would be a rather terrifying
thing.</div>
<div dir="auto"><br>
</div>
<div dir="auto">So, here, electoral-reform is single-winner
reform.</div>
<div dir="auto"><br>
</div>
<div dir="auto">BTW, I hasten to emphasize that I’m not against
the small states. I don’t want to deny them equal
representation. “ Equal” is the operative word..</div>
<div dir="auto"><br>
</div>
<div dir="auto">Equal representation could be achieved, but not
without repairing the Constitution’s built-in
disproportionality. It was “The Great Compromise”, which
compromised-away any chance of equal representation. A very
regrettable compromise.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Here’s an example of equal representation…my
favorite one:</div>
<div dir="auto"><br>
</div>
<div dir="auto">A unicameral at large (no districts or
gerrymandering) Parliament (yes, no president), 150 seats,
elected by open-list party-list PR, allocated by Sainte Lague,
or, preferably, Bias-Free.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Of the divisor-method allocation-rules that are or
have been used, Sainte Lague is the very nearly unbiased one.</div>
<div dir="auto"><br>
</div>
<div dir="auto">SL is only very slightly biased favoring larger
parties.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Bias-Free is entirely absolutely unbiased.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Divisor methods involve the rounding, up or down,
to a whole number, of a party’s number of “quotas” ( details are
outside the scope of this discussion).</div>
<div dir="auto"><br>
</div>
<div dir="auto">Sainte Lague rounds to the nearest whole number.</div>
<div dir="auto"><br>
</div>
<div dir="auto">i.e. the round-up point is the average of the two
surrounding integers. I.e. …</div>
<div dir="auto"><br>
</div>
<div dir="auto">R = (a+b)/2.</div>
<div dir="auto"><br>
</div>
<div dir="auto">For Bias-Free, determine R as follows:</div>
<div dir="auto"><br>
</div>
<div dir="auto">Divide b^b by a^a. Then divide the result by e.</div>
<div dir="auto"><br>
</div>
<div dir="auto">e is the base of the natural logarithms, equal to
about 2.718</div>
<div dir="auto"><br>
</div>
<div dir="auto">But I re-emphasize that, with proportionality now
Constitutionally impossible, national PR is unavailable.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Electoral reform means single-winner reform.</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
<div>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Fri, Oct 13, 2023 at
11:18 Richard Lung <<a
href="mailto:voting@ukscientists.com"
moz-do-not-send="true" class="moz-txt-link-freetext">voting@ukscientists.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote">
<div>
<p><br>
</p>
<p>"Cycles" (in the paper-scissors-rock sense) are a
problem of the (under-candidated) single member systems
own making. They rapidly disappear with a representative
sample of candidates proportionally elected to large
constituencies. The problem is not the 'pesky' cycles,
it is the pesky single member system. Unless the
politics in political science is to dictate to the
science, it is up to academics to point out, as hundreds
of American political scientists have, in conjunction
with The New York Times, I believe, this requirement of
a quota-preferential method.</p>
<p>Remedies to the single member system are cosmetic. They
cannot possibly please more than half the population,
whatever you do -- and probably a good deal less. UK
monopolistic elections are a minorocracy not a
democracy, and that is probably a fair indication of the
US state of affairs.<br>
</p>
<p>Time to move on from the ancient Greek conception of
democracy, as to elect a tyrant, unconditionally --
making Britain what Hailsham called an "elective
dictatorship." Which shares some of the all too evident
failings of any dictatorship, elected or otherwise. This
should be a spur to avoid another Vietnam war or second
Iraq war, which even W. may deplore, in his heart.<br>
</p>
<p>Regards,</p>
<p>Richard Lung.<br>
</p>
</div>
<div>
<p><br>
</p>
<div>On 13/10/2023 18:11, Forest Simmons wrote:<br>
</div>
</div>
<div>
<blockquote type="cite">
<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 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>
<br>
<fieldset></fieldset>
</blockquote>
</div>
<div>
<blockquote type="cite">
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</pre>
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target="_blank" moz-do-not-send="true"
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