<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">voting@ukscientists.com</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>
<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"></blockquote></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">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">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>
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</pre>
</blockquote>
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