Scientific American and the "Perfect Electoral System"
Hi Toby,
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.
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.
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?
Rob
On Tue, Nov 7, 2023 at 5:36 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
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.
Toby
On Tuesday, 7 November 2023 at 04:29:31 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
Rob,
Thanks for clearing up a lot of the confusion... and for putting the
current status in perspective.
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.
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.
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.
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.
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.
Pockets of possibility like these .... adequate "For All Practical
Purposes" pervade mathematics ... including the mathematics of voting
systems.
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.
Thanks,
Forest
On Sun, Nov 5, 2023, 11:34 PM Rob Lanphier roblan@gmail.com wrote:
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@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@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
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
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.
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.
All Arrow's theorem really does is make explicit the background assumptions required to make this IIA failure inevitable (such as non-dictatorship).
Toby
On Friday, 10 November 2023 at 22:19:40 GMT, Rob Lanphier roblan@gmail.com wrote:
Hi Toby,
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.
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.
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?
Rob
On Tue, Nov 7, 2023 at 5:36 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
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.
Toby
On Tuesday, 7 November 2023 at 04:29:31 GMT, Forest Simmons forest.simmons21@gmail.com wrote:
Rob,
Thanks for clearing up a lot of the confusion... and for putting the current status in perspective.
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.
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.
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.
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.
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.
Pockets of possibility like these .... adequate "For All Practical Purposes" pervade mathematics ... including the mathematics of voting systems.
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.
Thanks,
Forest
On Sun, Nov 5, 2023, 11:34 PM Rob Lanphier roblan@gmail.com wrote:
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@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@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 LanphierFounder of election-methods mailing list and electowiki.org
https://robla.nethttps://electowiki.org/wiki/User:RobLahttps://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
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
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.
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.
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.
Too bad ... because the misconception thus perpetuated is still beimg used
with impunity to excuse all kinds of garbage.
fws
On Sat, Nov 11, 2023, 3:22 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
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.
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.
All Arrow's theorem really does is make explicit the background
assumptions required to make this IIA failure inevitable (such as
non-dictatorship).
Toby
On Friday, 10 November 2023 at 22:19:40 GMT, Rob Lanphier <
roblan@gmail.com> wrote:
Hi Toby,
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.
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.
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?
Rob
On Tue, Nov 7, 2023 at 5:36 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
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.
Toby
On Tuesday, 7 November 2023 at 04:29:31 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
Rob,
Thanks for clearing up a lot of the confusion... and for putting the
current status in perspective.
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.
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.
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.
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.
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.
Pockets of possibility like these .... adequate "For All Practical
Purposes" pervade mathematics ... including the mathematics of voting
systems.
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.
Thanks,
Forest
On Sun, Nov 5, 2023, 11:34 PM Rob Lanphier roblan@gmail.com wrote:
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@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@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
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
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.
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.)
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.
Regards,
Richard Lung.
On 11/11/2023 23:57, Forest Simmons wrote:
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.
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.
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.
Too bad ... because the misconception thus perpetuated is still beimg
used with impunity to excuse all kinds of garbage.
fws
On Sat, Nov 11, 2023, 3:22 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
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.
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.
All Arrow's theorem really does is make explicit the background
assumptions required to make this IIA failure inevitable (such as
non-dictatorship).
Toby
On Friday, 10 November 2023 at 22:19:40 GMT, Rob Lanphier
<roblan@gmail.com> wrote:
Hi Toby,
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.
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.
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?
Rob
On Tue, Nov 7, 2023 at 5:36 AM Toby Pereira <tdp201b@yahoo.co.uk>
wrote:
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.
Toby
On Tuesday, 7 November 2023 at 04:29:31 GMT, Forest Simmons
<forest.simmons21@gmail.com> wrote:
Rob,
Thanks for clearing up a lot of the confusion... and for
putting the current status in perspective.
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.
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.
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.
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.
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.
Pockets of possibility like these .... adequate "For All
Practical Purposes" pervade mathematics ... including the
mathematics of voting systems.
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.
Thanks,
Forest
On Sun, Nov 5, 2023, 11:34 PM Rob Lanphier <roblan@gmail.com>
wrote:
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@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@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 <http://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
----
Election-Methods mailing list - see
https://electorama.com/em for list info
----
Election-Methods mailing list - see https://electorama.com/em
for list info
Election-Methods mailing list - seehttps://electorama.com/em for list info
Just because it's impossible to get zero IIA failure rates doesn't mean
"we have to let go of" it, in the sense of not trying to reduce IIA
failures.
Although all methods fail IIA, measuring HOW OFTEN those failures occur
is insightful. Some methods have much higher failure rates than others.
As I've said before, I believe reducing failure rates is more important
than regarding fairness criteria as pass/fail (yes/no) flags that are
worth counting simplistically.
Richard Fobes
The VoteFair guy
On 11/11/2023 3:57 PM, Forest Simmons wrote:
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.
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.
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.
Too bad ... because the misconception thus perpetuated is still beimg
used with impunity to excuse all kinds of garbage.
fws
On Sat, Nov 11, 2023, 3:22 AM Toby Pereira <tdp201b@yahoo.co.uk
mailto:tdp201b@yahoo.co.uk> wrote:
...
On 2023-11-13 19:35, Richard, the VoteFair guy wrote:
Just because it's impossible to get zero IIA failure rates doesn't mean
"we have to let go of" it, in the sense of not trying to reduce IIA
failures.
Although all methods fail IIA, measuring HOW OFTEN those failures occur
is insightful. Some methods have much higher failure rates than others.
As I've said before, I believe reducing failure rates is more important
than regarding fairness criteria as pass/fail (yes/no) flags that are
worth counting simplistically.
Suppose that a majoritarian method fails Condorcet. Then there exist
elections where the CW is X, but the method elects Y. Then eliminating
every candidate but Y and X makes X beat Y, so these elections have IIA
failure.
Suppose that there's a Condorcet cycle. Then every majoritarian ranked
election method fails IIA: suppose without loss of generality that the
method elects A, and that B beats A pairwise. Eliminating every
candidate but A and B leads B to win, hence an IIA failure.
Suppose a majoritarian ranked method passes Condorcet and the election
has a Condorcet winner. Then the method passes IIA for that election,
because eliminating any set of non-winning candidates still leaves that
candidate a Condorcet winner.
So if we want to minimize IIA failure, and IIA failure exists whenever
we can remove a set of candidates who did not win and thus change the
winner, we would want to pass Condorcet.
-km
As Kristofer says, minimising IIA failure (at least with ranked ballots) just means using Condorcet, and I think they would all be equal in that respect. However, even if there is a Condorcet winner, one could still argue, at least sometimes, that there has been an IIA failure. Say there are three main candidates - A, B and C. Polls suggest that it's close and that there will be no Condorcet winner, but that A will likely win under the particular method used. C then drops out before the election causing B to win. One might call this an IIA failure.
The other question is whether C dropping out was a good thing. We went from probably not having a Condorcet winner to having one as a result of C dropping out. Arguably C standing gives us more information overall about voter preferences. And as A would have won if C had stood, A is arguably the most likely "best" winner.
So while it might be nicer to have a clear Condorcet winner, in situations where it's close enough for there to be a possible cycle if certain candidates stand, arguably it's better if they do stand, causing the cycle and giving us more information.
Toby
On Monday, 13 November 2023 at 20:55:48 GMT, Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 2023-11-13 19:35, Richard, the VoteFair guy wrote:
Just because it's impossible to get zero IIA failure rates doesn't mean
"we have to let go of" it, in the sense of not trying to reduce IIA
failures.
Although all methods fail IIA, measuring HOW OFTEN those failures occur
is insightful. Some methods have much higher failure rates than others.
As I've said before, I believe reducing failure rates is more important
than regarding fairness criteria as pass/fail (yes/no) flags that are
worth counting simplistically.
Suppose that a majoritarian method fails Condorcet. Then there exist
elections where the CW is X, but the method elects Y. Then eliminating
every candidate but Y and X makes X beat Y, so these elections have IIA
failure.
Suppose that there's a Condorcet cycle. Then every majoritarian ranked
election method fails IIA: suppose without loss of generality that the
method elects A, and that B beats A pairwise. Eliminating every
candidate but A and B leads B to win, hence an IIA failure.
Suppose a majoritarian ranked method passes Condorcet and the election
has a Condorcet winner. Then the method passes IIA for that election,
because eliminating any set of non-winning candidates still leaves that
candidate a Condorcet winner.
So if we want to minimize IIA failure, and IIA failure exists whenever
we can remove a set of candidates who did not win and thus change the
winner, we would want to pass Condorcet.
-km
Election-Methods mailing list - see https://electorama.com/em for list info
On 2023-11-14 17:25, Toby Pereira wrote:
As Kristofer says, minimising IIA failure (at least with ranked ballots)
just means using Condorcet, and I think they would all be equal in that
respect. However, even if there is a Condorcet winner, one could still
argue, at least sometimes, that there has been an IIA failure. Say there
are three main candidates - A, B and C. Polls suggest that it's close
and that there will be no Condorcet winner, but that A will likely win
under the particular method used. C then drops out before the election
causing B to win. One might call this an IIA failure.
The other question is whether C dropping out was a good thing. We went
from probably not having a Condorcet winner to having one as a result of
C dropping out. Arguably C standing gives us more information overall
about voter preferences. And as A would have won if C had stood, A is
arguably the most likely "best" winner.
So while it might be nicer to have a clear Condorcet winner, in
situations where it's close enough for there to be a possible cycle if
certain candidates stand, arguably it's better if they do stand, causing
the cycle and giving us more information.
I agree. If there is a cycle, it's better to have it be known.
For non-Condorcet methods like Plurality, you could have apparent ballot
Condorcet winners that are only CWs because of the pressure the system
puts on candidates who'd otherwise ruin the result to stay out of the way.
This is part of why I don't find FairVote's argument that IRV is good
enough because it elects the ballot CW so often very convincing. There's
enormous two-party inertia. And if, in addition, something bad happens
when third parties get strong, then third parties aren't going to get
strong.
There are definitely limits to what voting methods can do on their own,
though. Suppose there's an upcoming election and someone, if he were to
run and could get the vote out, would be the CW, beating all the known
candidates. But because he doesn't have access to the required
resources, or he doesn't know how popular his political position would
be, or a number of other reasone, he doesn't run.
There's no way a voting method, being just a mapping from elections
(sets of ballots) to winners or social orders, can detect that such a
"hidden candidate" exists. In a similar way, if there's a hidden cycle
of three very good would-be candidates, all of whom would beat every
current candidate pairwise, the method can't detect this because it
doesn't know that they exist.
If we want to look at IIA in such a wide context, we'd have to consider
not just the voting method, but the surrounding dynamics as well. But at
least the good Condorcet methods should have relatively good strategic
entry and exit resistance, going by JGA's simulations.
-km
On 2023-11-14 19:19, Kristofer Munsterhjelm wrote:
If we want to look at IIA in such a wide context, we'd have to consider
not just the voting method, but the surrounding dynamics as well. But at
least the good Condorcet methods should have relatively good strategic
entry and exit resistance, going by JGA's simulations.
I don't suppose my "hidden CW" and "hidden cycle" examples are really
IIA failures because the candidates removed aren't irrelevant. But if
the hidden candidates would form a cycle with the current top candidate,
then they would be... like you (Toby) said.
-km