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<p><br>
</p>
<p>IIA may be compared to the primitive after-tthought of an
exclusion count to be found in traditional and conventional STV.
This is a sort of "Last past the post" elimination of candidates.
The IIA test might ask what of the exclusion of a runner-up? But
the principle seems to be the same, namely that the order of
election might be changed by excluding any candidate.</p>
<p>But the criterion can be met by abandoning the irrational
exclusion count and replacing it with a rational exclusion count,
as well as the rational election count. The Meek method of surplus
transfers is equally valid for a preference count and the reverse
preference count, because one voters preference is another voters
reverse preference. (It just means you have to count the
abstentions as well, to calculate the relative importance of
election or exclusion of candidates to the voter.)</p>
<p>The Meek surplus transfer count elects candidates in the desired
order, and as (a reverse preference) exclusion count would also
exclude candidates in the desired order without opportunity for
strategy, theoretically possible with irrational exclusions.</p>
<p>Regards,</p>
<p>Richard Lung.<br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 11/11/2023 23:57, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfoeG0B9+jDko-PGT2=daF-00wQWpO1mg7hhTTa3QAEktA@mail.gmail.com">
<div dir="auto">At the time it seemed revolutionary. ... but with
hindsight it is clear that IIA is the sole culprit ... it's the
one we have to let go of.
<div dir="auto"><br>
</div>
<div dir="auto">Even Majority Judgment which comes as close as
possible to IIA ... will predictably fail when voters are
given the opportunity to change their judgment after their
ballots have been exhausted at the top or bottom from
candidate withdrawals.</div>
<div dir="auto"><br>
</div>
<div dir="auto">It's too bad that after all of this time nobody
but Toby and Markus Schulze (who first pointed it out to me
more than twenty years ago) seems to have noticed this almost
embarrassing take-away from Arrow's most famous theorem.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Too bad ... because the misconception thus
perpetuated is still beimg used with impunity to excuse all
kinds of garbage.</div>
<div dir="auto"><br>
</div>
<div dir="auto">fws</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Nov 11, 2023, 3:22 AM
Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk"
target="_blank" rel="noreferrer" moz-do-not-send="true"
class="moz-txt-link-freetext">tdp201b@yahoo.co.uk</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote">
<div>
<div>
<div dir="ltr">I suppose it's that I'm not convinced about
how foundational Arrow's work really was. The theorem is
basically that you can't have all these
reasonable-sounding criteria together in one
ranked-ballot method. But the one criterion that sticks
out is Independence of Irrelevant Alternatives (IIA).
It's not that some methods pass x and y but fail z,
others pass y and z but fail x etc. They all fail IIA
and pass the others. For a ranked-ballot method to pass
IIA it would have to fail some really basic stuff. So my
point is that I'm not sure what his theorem added to
what we already knew from the existence of the Condorcet
paradox.</div>
<div dir="ltr"><br>
</div>
<div dir="ltr">In summary: If you have an A>B>C>A
cycle, then each of the three candidates will win one
election if you held separate head-to-head elections, so
if you put them together for a three-way election, an
IIA failure is inevitable.</div>
<div dir="ltr"><br>
</div>
<div dir="ltr">All Arrow's theorem really does is make
explicit the background assumptions required to make
this IIA failure inevitable (such as non-dictatorship).</div>
<div dir="ltr"><br>
</div>
<div dir="ltr">Toby</div>
<div><br>
</div>
</div>
<div
id="m_-7770504167945343178m_-6094388280336351274ydp5971a859yahoo_quoted_0211444469">
<div>
<div> On Friday, 10 November 2023 at 22:19:40 GMT, Rob
Lanphier <<a href="mailto:roblan@gmail.com"
rel="noreferrer noreferrer" target="_blank"
moz-do-not-send="true" class="moz-txt-link-freetext">roblan@gmail.com</a>>
wrote: </div>
<div><br>
</div>
<div><br>
</div>
<div>
<div
id="m_-7770504167945343178m_-6094388280336351274ydp5971a859yiv1205666266">
<div>
<div dir="ltr">
<div>Hi Toby,</div>
<div><br>
</div>
<div>I guess I understand some of your
frustration how articles like the SciAm
article overemphasize Arrow. I suspect the
feeling is similar to what I feel when I see
the emphasis on Condorcet cycles. Too many
articles encourage fatalism about comparative
quality because ALL systems will have flaws.
Condorcet cycles seem like they would be rare
enough in real-world conditions, and I suppose
some aspects of Arrow might overemphasize
similarly rare possibilities.<br>
</div>
<div><br>
</div>
<div>I don't think it's fair to brush off
Arrow's work, though, because it was
foundational to other impossibility theorems.
Arrow made a very helpful generalization of
the Condorcet paradox, and Gibbard made a very
helpful generalization of Arrow's work. I've
found impossibility theorems helpful in
constraining and classifying the tradeoffs
made about various systems.</div>
<div><br>
</div>
<div>Do you feel like SciAm went too far when
they even mentioned Arrow's theorem, or is it
that you don't think they weren't careful
enough about contextualizing it?<br>
</div>
<div><br>
</div>
<div>Rob<br>
</div>
<br>
<div
id="m_-7770504167945343178m_-6094388280336351274ydp5971a859yiv1205666266yqt68035">
<div>
<div dir="ltr">On Tue, Nov 7, 2023 at
5:36 AM Toby Pereira <<a shape="rect"
href="mailto:tdp201b@yahoo.co.uk"
rel="nofollow noreferrer noreferrer"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">tdp201b@yahoo.co.uk</a>>
wrote:<br>
</div>
<blockquote>
<div>
<div>
<div dir="ltr">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"><br>
</div>
<div dir="ltr">Toby</div>
<div><br>
</div>
</div>
<div
id="m_-7770504167945343178m_-6094388280336351274ydp5971a859yiv1205666266m_-2021678076462734438ydpafe61227yahoo_quoted_9697965469">
<div>
<div> On Tuesday, 7 November 2023 at
04:29:31 GMT, Forest Simmons <<a
shape="rect"
href="mailto:forest.simmons21@gmail.com"
rel="nofollow noreferrer
noreferrer" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">forest.simmons21@gmail.com</a>>
wrote: </div>
<div><br>
</div>
<div><br>
</div>
<div>
<div
id="m_-7770504167945343178m_-6094388280336351274ydp5971a859yiv1205666266m_-2021678076462734438ydpafe61227yiv0954465204">
<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>
<div
id="m_-7770504167945343178m_-6094388280336351274ydp5971a859yiv1205666266m_-2021678076462734438ydpafe61227yiv0954465204yqt91197">
<div dir="ltr">On Sun, Nov
5, 2023, 11:34 PM Rob
Lanphier <<a
shape="rect"
href="mailto:roblan@gmail.com"
rel="nofollow
noreferrer noreferrer"
target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">roblan@gmail.com</a>> wrote:<br>
</div>
<blockquote>
<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
noreferrer
noreferrer"
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>
<div dir="ltr">----------
Forwarded
message
---------<br>
From: <b>Rob
Lanphier</b> <span><<a
shape="rect"
href="mailto:roblan@gmail.com"
rel="nofollow
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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>
<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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
target="_blank"
moz-do-not-send="true">electowiki.org</a><br>
</div>
<div><a
shape="rect"
href="https://robla.net"
rel="nofollow
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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
noreferrer
noreferrer"
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>
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info<br>
</blockquote>
</div>
</div>
</div>
</div>
<div
id="m_-7770504167945343178m_-6094388280336351274ydp5971a859yiv1205666266m_-2021678076462734438ydpafe61227yqt56102">----<br>
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noreferrer" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://electorama.com/em</a>
for list info<br>
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<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
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