[EM] Scientific American and the "Perfect Electoral System"

Sun Nov 5 23:29:50 PST 2023

Hi folks,

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:
https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/

Y'all may have other thoughts on the article.

Rob
---------- Forwarded message ---------
From: Rob Lanphier <roblan at gmail.com>
Date: Sun, Nov 5, 2023 at 11:22 PM
Subject: Regarding using math to create a "Perfect Electoral System"
To: Scientific American Editors <editors at sciam.com>

To whom it may concern:

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:
https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/

There's some things that the article gets wrong, but the good news is that
the article title and its relation to Betteridge's law.  This law states "Any
headline that ends in a question mark can be answered by the word *'*no*'*."
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).

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.

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"):
https://en.wikipedia.org/wiki/Instant-runoff_voting

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).

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":
https://electowiki.org/wiki/Yee_diagram
(a direct link to Yee's 2005 paper: http://zesty.ca/voting/sim/ )

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.

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".

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).

This gets me to the statement from your article that gets under my skin the
most::

> 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.
>

People who study election methods refer to "cardinal voting" as a *category*
of voting methods, of which "range voting" is just one (which is called
"score voting" on English Wikipedia):
https://en.wikipedia.org/wiki/Score_voting

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":
https://web.archive.org/web/20091111061523/http://www.fairvote.org/

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.

Rob Lanphier
Founder of election-methods mailing list and electowiki.org
https://robla.net
https://electowiki.org/wiki/User:RobLa
https://en.wikipedia.org/wiki/User:RobLa

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:
https://robla.net/1996/TPJ
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