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<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Why
has theorem Arrow gained so much traction over the years?</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">The
short answer, history is written by the victors.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">The
history answer takes some explaining but is evident enough.</span></p>
<p class="MsoNormal"><span style="font-size:16.0pt;
font-family:"Arial Rounded MT Bold"">New York</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">, for instance,
had a Personal Representation society, by the late nineteenth
century. In fact
the organised campaign writings, of its early successes, over
a century old,
have been bought-up, and are still subject to publishers pay
walls, of little
if any commercial value and contrary to the public interest.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">By
the 1937 edition of Proportional Representation. The key to
democracy. Clarence
Hoag and George Hallett were introducing a single transferable
vote to the
boroughs of </span><span style="font-size:16.0pt;
font-family:"Arial Rounded MT Bold"">New York</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">These
two campaigning great men, both mathematicians in their day
job, did not get a
mention in Wikipedia, when I last looked.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">As
a result of battering-ram referendums with the money and
publicity on their
side, The Machine virtually abolished the key to democracy.</span></p>
<p class="MsoNormal"><span style="font-size:16.0pt;
font-family:"Arial Rounded MT Bold"">Massachusetts</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> legislature forbad
other cities than </span><span style="font-size:16.0pt;
font-family:"Arial Rounded MT Bold"">Cambridge</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> to use their electoral
reform. There are several home-rule bills but they are bogged
down in state
committee.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Kenneth
Arrow stepped in, in the nineteen fifties, to effectively
finish the job of The
Machine. He took the Kurt Godel Incompleteness theorem an
extreme step further
by advertising an “Impossibility theorem,” which he himself,
cited in
Scientific American, belatedly admitted it did not amount to.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">In
other words, he by-passed, nearly a century of election method
study, stemming
from Thomas Hare and John Stuart Mill. That tradition
continues and so does the
naïve ignorance of it.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">As
a Scottish STV programmer commented, theorem Arrow does not
even apply to
proportional representation, but merely to bare majority
elections.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Any
theorem is only as good as its assumptions, and those of the
Impossibility
theorem neglect the possibility that statistical methods might
be more accurate
than deterministic ones, as is indeed the case in physics.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Regards, <br>
</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Richatrd Lung.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 07/11/2023 13:35, Toby Pereira
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:1600372198.575581.1699364150541@mail.yahoo.com">
<div class="ydpd48923f3yahoo-style-wrap">
<div dir="ltr" data-setdir="false">As is often the case, I think
the importance of Arrow's Theorem is overstated in that
article. Arrow's Theorem essentially says "With a few
reasonable background assumptions, no ranked-ballot method
passes Independence of Irrelevant Alternatives." But this was
already known for centuries from the Condorcet Paradox. I
don't really know why it's gained so much traction over the
years, as it was nothing like the paradigm shift people credit
it as.</div>
<div dir="ltr" data-setdir="false"><br>
</div>
<div dir="ltr" data-setdir="false">Toby</div>
<div><br>
</div>
</div>
<div id="ydpafe61227yahoo_quoted_9697965469"
class="ydpafe61227yahoo_quoted">
<div>
<div> On Tuesday, 7 November 2023 at 04:29:31 GMT, Forest
Simmons <a class="moz-txt-link-rfc2396E" href="mailto:forest.simmons21@gmail.com"><forest.simmons21@gmail.com></a> wrote: </div>
<div><br>
</div>
<div><br>
</div>
<div>
<div id="ydpafe61227yiv0954465204">
<div>
<div>Rob,
<div><br>
</div>
<div>Thanks for clearing up a lot of the confusion...
and for putting the current status in perspective.</div>
<div><br>
</div>
<div>I like the comparison of the "impossibilities of
voting" with the impossibilities of faster than
light travel, etc. The 2nd law of thermodynamics is
especially relevant... because as Prigogene showed
in the 70's, the impossibility of decreasing entropy
in closed systems still allows for local pockets of
possibility ... that make life possible .... until
the "heat death" of our island space-time big bang
remnant ... while miriads of new "inflationary
bubbles" appear from random virtual quantum
fluctuations.</div>
<div><br>
</div>
<div>We used to "know" that the event horizon was a
boundary of no return .... nut now evaporation of
black holes through quantum tunneling is taken for
granted.</div>
<div><br>
</div>
<div>In the early 1800's Gauss proved the
impossibility of trisecting an arbitrarily given
angle .... inside the rules of classical geometric
ruler and compass constructions.</div>
<div><br>
</div>
<div>But it turns out that (as any first year topology
student can show) any angle can be transformed into
atrisectable one by an arbitrarily small
perturbation.</div>
<div><br>
</div>
<div>I'm fact, once you learn the binary point
expansion of 1/3 ..., you can get within a relative
error tolerance of 1/2^n precision with n
bisections... bisections being the first
constructions you learn in geometty.</div>
<div><br>
</div>
<div>Pockets of possibility like these .... adequate
"For All Practical Purposes" pervade mathematics ...
including the mathematics of voting systems.</div>
<div><br>
</div>
<div>Sometimes you have to discover new tools not
included in the classical tool kit. In the case of
angle trisections, if you are allowed to make a few
marks on the ruler... hen the general ruler and
compass trisection suddenly resolves itself.</div>
<div><br>
</div>
<div>Thanks,</div>
<div><br>
</div>
<div>Forest</div>
</div>
<br>
<div class="ydpafe61227yiv0954465204gmail_quote">
<div id="ydpafe61227yiv0954465204yqt91197"
class="ydpafe61227yiv0954465204yqt7468526250">
<div dir="ltr"
class="ydpafe61227yiv0954465204gmail_attr">On Sun,
Nov 5, 2023, 11:34 PM Rob Lanphier <<a
shape="rect" href="mailto:roblan@gmail.com"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">roblan@gmail.com</a>>
wrote:<br>
</div>
<blockquote
class="ydpafe61227yiv0954465204gmail_quote">
<div dir="ltr">
<div>Hi folks,</div>
<div><br>
</div>
<div>I just wrote a letter to the editor(s) of
Scientific American, which I've included
below. My letter was in a response to the
following article that was recently published
on their website:<br>
</div>
<div>
<div><a shape="rect"
href="https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/</a></div>
<div><br>
</div>
<div>Y'all may have other thoughts on the
article.<br>
</div>
<div><br>
</div>
</div>
<div>Rob<br>
<div
class="ydpafe61227yiv0954465204gmail_quote">
<div dir="ltr"
class="ydpafe61227yiv0954465204gmail_attr">----------
Forwarded message ---------<br>
From: <b
class="ydpafe61227yiv0954465204gmail_sendername">Rob
Lanphier</b> <span><<a shape="rect"
href="mailto:roblan@gmail.com"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">roblan@gmail.com</a>></span><br>
Date: Sun, Nov 5, 2023 at 11:22 PM<br>
Subject: Regarding using math to create a
"Perfect Electoral System"<br>
To: Scientific American Editors <<a
shape="rect"
href="mailto:editors@sciam.com"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">editors@sciam.com</a>><br>
</div>
<br>
<br>
<div dir="ltr">
<div>To whom it may concern:</div>
<div><br>
</div>
<div>I appreciate your article "Could Math
Design the Perfect Electoral System?",
since I agree that math is important for
understanding electoral reform, and
there's a lot of good information and
great diagrams in your article:</div>
<div><a shape="rect"
href="https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/</a></div>
<div><br>
</div>
<div>There's some things that the article
gets wrong, but the good news is that
the article title and its relation to <span>Betteridge</span><span>'s
law. This law states </span>"Any
headline that ends in a question mark
can be answered by the word <i>'</i>no<i>'</i>."
The bad news: the URL slug
("see-how-math-could-design-the-perfect-electoral-system")
implies the answer is "yes". The answer
is "no"; Kenneth Arrow and Allan Gibbard
proved there is no perfect electoral
system (using math).</div>
<div><br>
</div>
<div>I appreciate that your article
highlights the mayoral election in
Burlington, Vermont in 2009. That is an
important election for all voters
considering FairVote's favorite
single-winner system ("instant-runoff
voting" or rather "ranked-choice voting,
as they now call it). When I
volunteered with FairVote in the late
1990s, I remember when they introduced
the term "instant-runoff voting". I
thought the name was fine. After
Burlington 2009, it would seem that
FairVote has abandoned the name.
Regardless, anyone considering
instant-runoff needs to consider
Burlington's experience.<br>
</div>
<div><br>
</div>
<div>Sadly, your article describes
"cardinal methods" in a confusing
manner. It erroneously equates
cardinal's counterpart ("ordinal
voting") with "ranked-choice voting".
Intuitively, all "ordinal methods"
should be called "ranked choice voting",
but during this century, the term has
been popularized by FairVote and the
city of San Francisco to refer to a
specific method formerly referred to as
"instant-runoff voting". These days,
when Americans speak of "RCV", they're
generally referring to the system known
on English Wikipedia as "IRV" (or
"Instant-runoff voting"):</div>
<div><a shape="rect"
href="https://en.wikipedia.org/wiki/Instant-runoff_voting"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://en.wikipedia.org/wiki/Instant-runoff_voting</a><br>
</div>
<br>
<div>There have been many methods that use
ranked ballots, including the methods
developed by Nicolas de Condorcet
and Jean-Charles de Borda in the 1780s
and the 1790s. I'm grateful that the
Marquis de Condorcet's work is featured
so prominently in your article.
Condorcet's work was brilliant, and I'm
sure he would have become more prominent
if he hadn't died in a French prison in
the 1790s. Many single-winner methods
that strictly comply with the "Condorcet
winner criterion" are probably as close
to "perfect" as any system (from a
mathematical perspective).<br>
</div>
<div><br>
</div>
<div>Most methods that pass the "Condorcet
winner criterion" typically use ranked
ballots (and thus are "ordinal"), but
it's important to note that almost all
"ordinal" methods can use cardinal
ballots. Instant-runoff voting doesn't
work very well with cardinal ballots
(because tied scores cannot be allowed),
but most other ordinal systems work
perfectly well with tied ratings or
rankings. Even though passing the
Condorcet winner criterion is very
important, there are many methods that
come very, very close in reasonable
simulations. I would strongly recommend
that you contact Dr. Ka-Ping Yee, who is
famous in electoral reform circles for
"Yee diagrams":</div>
<div><a shape="rect"
href="https://electowiki.org/wiki/Yee_diagram"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://electowiki.org/wiki/Yee_diagram</a></div>
<div>(a direct link to Yee's 2005 paper: <a
shape="rect"
href="http://zesty.ca/voting/sim/"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">http://zesty.ca/voting/sim/</a>
)</div>
<div><br>
</div>
<div>Note that "approval voting" and
"Condorcet" provide pretty much the same
results in Yee's 2005 paper.
"Instant-runoff voting" seems a little
crazy in Yee's simulations.<br>
</div>
<div><br>
</div>
<div>Though Arrow and Gibbard disproved
"perfection", I prefer to think of
Arrow's and Gibbard's work as defining
the physics of election methods. To
explain what I mean, consider the
physics of personal transportation. It
is impossible to design the PERFECT
vehicle (that is spacious, and
comfortable, travels faster than the
speed of light, fits in anyone's garage
or personal handbag). Newton and
Einstein more-or-less proved it.
However, those esteemed scientists' work
didn't cause us to stop working on
improvements in personal
transportation. Buggy whips are now
(more or less) recognized as obsolete,
as is Ford's "Model T".<br>
</div>
<div><br>
</div>
<div>Now that Arrow and Gibbard have
helped us understand the physics of
election methods, we can hopefully start
pursuing alternatives to the buggy whip
(or rather, alternatives to "choose-one"
voting systems, often referred to as
"first past the post" systems). <br>
</div>
<div><br>
</div>
<div>This gets me to the statement from
your article that gets under my skin the
most::</div>
<blockquote
class="ydpafe61227yiv0954465204gmail_quote">
<div>This is called cardinal voting, or
range voting, and although it’s no
panacea and has its own shortcomings,
it circumvents the limitations imposed
by Arrow’s impossibility theorem,
which only applies to ranked choice
voting. <br>
</div>
</blockquote>
<div> </div>
<div>People who study election methods
refer to "cardinal voting" as a <i>category</i>
of voting methods, of which "range
voting" is just one (which is called
"score voting" on English Wikipedia):</div>
<div><a shape="rect"
href="https://en.wikipedia.org/wiki/Score_voting"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://en.wikipedia.org/wiki/Score_voting</a><br>
</div>
<div><br>
</div>
<div>The conflation of "ranked choice
voting" with all ordinal voting methods
is also highly problematic (though I
don't entirely blame you for this). As
I stated earlier, there are many methods
that can use ranked ballots. While this
article may have been helpful for those
of us that prefer ranking methods that
are not "instant-runoff voting" back
when FairVote switched to "ranked-choice
voting" in the early 2010s. Note that
before the fiasco in Burlington in 2009,
FairVote pretty consistently preferred
"instant runoff voting":</div>
<div><a shape="rect"
href="https://web.archive.org/web/20091111061523/http://www.fairvote.org/"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://web.archive.org/web/20091111061523/http://www.fairvote.org/</a></div>
<br>
<div>I appreciate that you're trying to
explain this insanely complicated topic
to your readers. When I edit English
Wikipedia (which I've done for over
twenty years), I would love to be able
to cite Scientific American on this
topic. However, I'm not yet sure I'd
feel good about citing this article.<br>
</div>
<div><br>
</div>
<div>Rob Lanphier</div>
<div>Founder of election-methods mailing
list and <a shape="rect"
href="http://electowiki.org"
rel="nofollow" target="_blank"
moz-do-not-send="true">electowiki.org</a><br>
</div>
<div><a shape="rect"
href="https://robla.net"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://robla.net</a></div>
<div><a shape="rect"
href="https://electowiki.org/wiki/User:RobLa"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://electowiki.org/wiki/User:RobLa</a></div>
<div><a shape="rect"
href="https://en.wikipedia.org/wiki/User:RobLa"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://en.wikipedia.org/wiki/User:RobLa</a><br>
</div>
<div><br>
</div>
<div>p.s. back in the late 1990s, I wrote
an article for a small tech journal
called "The Perl Journal". It's out of
print, but I've reproduced my 1996
article about election methods which I
think holds up pretty well:</div>
<div><a shape="rect"
href="https://robla.net/1996/TPJ"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://robla.net/1996/TPJ</a><br>
</div>
</div>
</div>
</div>
</div>
----<br>
Election-Methods mailing list - see <a
shape="rect" href="https://electorama.com/em"
rel="nofollow" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://electorama.com/em</a>
for list info<br>
</blockquote>
</div>
</div>
</div>
</div>
<div class="ydpafe61227yqt7468526250"
id="ydpafe61227yqt56102">----<br>
Election-Methods mailing list - see <a shape="rect"
href="https://electorama.com/em" rel="nofollow"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://electorama.com/em</a>
for list info<br>
</div>
</div>
</div>
</div>
<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre class="moz-quote-pre" wrap="">----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="https://electorama.com/em">https://electorama.com/em</a> for list info
</pre>
</blockquote>
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