Scientific American and the “Perfect Electoral System”

I wrote a letter to the editor(s) of Scientific American last night in response to an article that was recently published on their website. I’ve included my letter in response later in this blog post.

I was probably harsher than what was deserved, because the article makes a valiant attempt to explain electoral reform beyond most of the options that have been tried in recent years. Delightfully, they explain Condorcet methods, and explain the problematic results in the Burlington mayoral election of 2009, when an unpopular incumbent remained in power despite clear majorities preferring the Democratic Party candidate.

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My letter below was in response to an article that Scientific American had recently published about electoral reform, about math and the “perfect electoral system”:
https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/

Proponents of “instant-runoff voting”/”IRV” (now frequently referred to as “ranked-choice voting” or “RCV”) like to point out that situations similar to Burlington’s 2009 situation rarely happen. However, “rarely” is not the same as “never”. If a civil engineer fails to put a guardrail on a narrow bridge over a deep canyon, and claims that “most vehicles never need the guardrail“, we would consider that dangerous engineering. RCV/IRV is a result of dangerous engineering.

There are systems that many 21st-century engineers (and other people) agree have many fewer severe flaws than are much better than RCV/IRV. These include:

• Approval voting — see also https://electionscience.org/approval-voting-101/
• STAR voting — see also https://starvoting.us
• Condorcet methods, such as the Minimax Condorcet method, Ranked Pairs/Maximize Affirmed Majorities, the Schulze method, and Copeland/Ranked Robin

I suppose that is enough of a prelude. Below is the message that I wrote to the folks at Scientific American. Enjoy!

———- Message ———
From: Rob Lanphier
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