RL
Rob Lanphier
Thu, Jan 9, 2020 11:17 PM
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting1 activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that all voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
https://en.wikipedia.org/wiki/Unrestricted_domain
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score always chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a feature. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 2) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC3 as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
- Goes faster than the speed of light
- Has infinite capacity
- Has a luxurious and comfortable passenger cabin
- Fits in a small coat pocket
- Is easy to produce
- Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that all voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
precipitously in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki4
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting[1] activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that *all* voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
<https://en.wikipedia.org/wiki/Unrestricted_domain>
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score *always* chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a *feature*. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 [2]) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
* Goes faster than the speed of light
* Has infinite capacity
* Has a luxurious and comfortable passenger cabin
* Fits in a small coat pocket
* Is easy to produce
* Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that *all* voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
*precipitously* in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki[4]
[1]: https://electowiki.org/wiki/Score_voting
[2]: https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election
[3]: https://electowiki.org/wiki/IIAC
[4]: https://electowiki.org/wiki/Arrow%27s_impossibility_theorem
FJ
Faran, James
Fri, Jan 10, 2020 4:12 AM
About Score voting failing Unrestricted Domain:
Part of the confusion of those advocating score and you is not a confusion on anyone's part, but rather a difference in what each considers a preference. (It's not possible to have a good reasoned argument until both sides agree on what the words mean.) Score voters would say
A:100; B:95; C:0
and
A:100; B:5; C:0
are different preferences, but you seem to say that these are both A>B>C and so are the same. I would say the Electowiki page on Unrestricted Domain needs to be edited to include both possibilities, but I can't be bothered.
You also seem to think that most voters would not be able to understand that sort of nuance. You may be right there, especially in today's political climate (especially in the United States?), where there are two sides and the other side is always demonized.
Note that any new voting system will almost always try to be replaced by the loser under the new system. ("The current government is illegitimate! If it wasn't for the biased voting system we would have won!" -- cf. the recently revived call for the elimination of the U. S. Electoral College after Mr. Trump won with a minority of the popular vote.) If the winner can't keep support, the losing side will be able to push through a change.
However, a question: If we had the following score ballots:
9000: A:100; B:95; C:0
1000: B:100; C:85; A:0
giving A a score of 900,000 and B a score of 955,000, hence a victory for B, would there really be enough antipathy to B to cause outrage? All the A voters seemed to think B was pretty good. Of course (see above), the losing side could always complain. Anyone wedded to Condorcet winners would be outraged. And, of course, no real world election would end up like this. Score may be a little too ripe for manipulation. Gibbard-Satterthwaite, anyone?
Jim Faran
From: Election-Methods election-methods-bounces@lists.electorama.com on behalf of Rob Lanphier robla@robla.net
Sent: Thursday, January 9, 2020 6:17 PM
To: Election Methods
Subject: [EM] Arrow's theorem and cardinal voting systems
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting1 activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that all voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
https://en.wikipedia.org/wiki/Unrestricted_domain
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score always chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a feature. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 2) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC3 as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
- Goes faster than the speed of light
- Has infinite capacity
- Has a luxurious and comfortable passenger cabin
- Fits in a small coat pocket
- Is easy to produce
- Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that all voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
precipitously in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki4
Election-Methods mailing list - see https://electorama.com/em for list info
About Score voting failing Unrestricted Domain:
Part of the confusion of those advocating score and you is not a confusion on anyone's part, but rather a difference in what each considers a preference. (It's not possible to have a good reasoned argument until both sides agree on what the words mean.) Score voters would say
A:100; B:95; C:0
and
A:100; B:5; C:0
are different preferences, but you seem to say that these are both A>B>C and so are the same. I would say the Electowiki page on Unrestricted Domain needs to be edited to include both possibilities, but I can't be bothered.
You also seem to think that most voters would not be able to understand that sort of nuance. You may be right there, especially in today's political climate (especially in the United States?), where there are two sides and the other side is always demonized.
Note that any new voting system will almost always try to be replaced by the loser under the new system. ("The current government is illegitimate! If it wasn't for the biased voting system we would have won!" -- cf. the recently revived call for the elimination of the U. S. Electoral College after Mr. Trump won with a minority of the popular vote.) If the winner can't keep support, the losing side will be able to push through a change.
However, a question: If we had the following score ballots:
9000: A:100; B:95; C:0
1000: B:100; C:85; A:0
giving A a score of 900,000 and B a score of 955,000, hence a victory for B, would there really be enough antipathy to B to cause outrage? All the A voters seemed to think B was pretty good. Of course (see above), the losing side could always complain. Anyone wedded to Condorcet winners would be outraged. And, of course, no real world election would end up like this. Score may be a little too ripe for manipulation. Gibbard-Satterthwaite, anyone?
Jim Faran
________________________________________
From: Election-Methods <election-methods-bounces@lists.electorama.com> on behalf of Rob Lanphier <robla@robla.net>
Sent: Thursday, January 9, 2020 6:17 PM
To: Election Methods
Subject: [EM] Arrow's theorem and cardinal voting systems
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting[1] activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that *all* voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
<https://en.wikipedia.org/wiki/Unrestricted_domain>
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score *always* chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a *feature*. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 [2]) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
* Goes faster than the speed of light
* Has infinite capacity
* Has a luxurious and comfortable passenger cabin
* Fits in a small coat pocket
* Is easy to produce
* Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that *all* voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
*precipitously* in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki[4]
[1]: https://electowiki.org/wiki/Score_voting
[2]: https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election
[3]: https://electowiki.org/wiki/IIAC
[4]: https://electowiki.org/wiki/Arrow%27s_impossibility_theorem
----
Election-Methods mailing list - see https://electorama.com/em for list info
F
fdpk69p6uq@snkmail.com
Fri, Jan 10, 2020 4:42 AM
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's
theorem.
Many Score voting1 activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that all voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
https://en.wikipedia.org/wiki/Unrestricted_domain
In particular, let's say that 90% of voters prefer candidate A over
candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score always chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a feature. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 2) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC3 as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
- Goes faster than the speed of light
- Has infinite capacity
- Has a luxurious and comfortable passenger cabin
- Fits in a small coat pocket
- Is easy to produce
- Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that all voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
precipitously in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki4
Election-Methods mailing list - see https://electorama.com/em for list
info
Didn't Arrow agree that rated systems aren't included?
https://www.electionscience.org/commentary-analysis/voting-theory-podcast-2012-10-06-interview-with-nobel-laureate-dr-kenneth-arrow/
On Thu, Jan 9, 2020, 6:17 PM Rob Lanphier wrote:
> Hi folks,
>
> As some of you might have seen, Electowiki is a lot more active than
> it used to be. I'm 99% convinced that's a good thing. The 1% of me
> that has reservations is regarding how some advocates talk about
> Arrow's theorem. I'm hoping you all can do one of the following:
> a) change my view about Arrow's theorem, -or-
> b) offer me some help in better articulating my view about Arrow's
> theorem.
>
> Many Score voting[1] activists claim that cardinal methods somehow
> dodge Arrow's theorem. It seems to me that *all* voting systems (not
> a mere subset) are subject to some form of impossibility problem.
> Arrow's impossibility theorem deserved great acclaim for subjecting
> all mainstream voting systems of the 1950s to mathematical rigor, and
> it's clear that his 1950 paper and 1951 book profoundly influenced
> economics and game theory for the better. His 1972 Nobel prize was
> well deserved. It seems that it has become fashionable to find
> loopholes in Arrow's original formulation and declare the loopholes
> important. Even if the loopholes exist, talking up those loopholes
> doesn't seem compelling, given the subsequent work by other theorists
> broaden the scope beyond Arrow's version.
>
> But, what the heck, let's actually talk about Arrow's original
> formulation. I believe Score voting fails unrestricted domain:
> <https://en.wikipedia.org/wiki/Unrestricted_domain>
>
> In particular, let's say that 90% of voters prefer candidate A over
> candidate B:
> 90:A>B
> 10:B>A
>
> Arrow posits that there should only be one way to express that, and
> Score fails it. In Score, it's possible to sometimes pick A, and
> sometimes pick B, depending on the score values on the ballots. If
> Score *always* chose either A or B, then it would pass Universality.
>
> Score advocates claim that this isn't a bug, it's a *feature*. If
> (for example), voters for A only mildly prefer A over B, but voters
> for B strongly detest A, then the correct social choice is B.
> However, it doesn't seem practical to inflict this level of nuance on
> voters. I suspect that the first election where the Condorcet winner
> is beaten by a minority-preferred candidate (e.g. like what happened
> in Burlington 2009 [2]) will result in a repeal (like what happened in
> Burlington). Back to the A/B example above, It's hard to imagine
> voters would consider the selection of "B" to be fair in a large
> election.
>
> It's fine to hold the opinion that Universality is an uninteresting
> criterion, and that therefore, Arrow's set of criteria isn't very
> interesting. For example, a few years ago, we went through a phase
> where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
> interesting criterion, and advocating for Condorcet variants that meet
> that criterion. Regardless, just because we find one criterion less
> compelling than another, we should talk accurately about the failed
> criterion.
>
> My way of thinking about Arrow's theorem (and being thankful for it)
> is to think of it like the physics of voting systems. For example, in
> real-world physics, a "perfect" vehicle is impossible, because it's
> impossible to meet these criteria:
> * Goes faster than the speed of light
> * Has infinite capacity
> * Has a luxurious and comfortable passenger cabin
> * Fits in a small coat pocket
> * Is easy to produce
> * Is cheap (or even free)
>
> Just because a perfect vehicle is not possible, I'm glad
> transportation innovation didn't stop with Ford's Model T. Of course,
> automobile sellers compete on the tradeoffs between the criteria
> above, and much public policy debate is about mode-of-transport
> tradeoffs between planes, trains and automobiles (and bicycles, and
> scooters, and and and...). We need public policy debates around
> election method tradeoffs, too.
>
> I'm hoping we can try to stop trying to declare clever loopholes in
> Arrow's theorem, and just acknowledge the reality that *all* voting
> systems involve tradeoffs. I hope we all can acknowledge that Arrow's
> central insight (there's no "perfect" system given perfectly
> reasonable criteria) is valid, and that it's only on the specifics of
> the exact criteria chosen for the 1951 proof that might be flawed. I
> believe that election method activists should speak (and write) with
> clarity about the tradeoffs involved. Whenever I see someone
> gleefully declare that Arrow's theorem doesn't apply to their voting
> method (and imply perfection), the credibility of the writer drops
> *precipitously* in my mind.
>
> Am I wrong?
>
> Rob
>
> p.s. I've been meaning to write this email for a while. What inspired
> me to finally write it has been reading the current state of
> Electowiki and Wikipedia articles on the topic, like the "Arrow's
> impossiblity theorem" article on Electowiki[4]
>
> [1]: https://electowiki.org/wiki/Score_voting
> [2]: https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election
> [3]: https://electowiki.org/wiki/IIAC
> [4]: https://electowiki.org/wiki/Arrow%27s_impossibility_theorem
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
RB
robert bristow-johnson
Fri, Jan 10, 2020 4:46 AM
On January 9, 2020 11:12 PM Faran, James jjfaran@buffalo.edu wrote:
About Score voting failing Unrestricted Domain:
Part of the confusion of those advocating score and you is not a confusion on anyone's part, but rather a difference in what each considers a preference. (It's not possible to have a good reasoned argument until both sides agree on what the words mean.) Score voters would say
A:100; B:95; C:0
and
A:100; B:5; C:0
are different preferences, but you seem to say that these are both A>B>C and so are the same. I would say the Electowiki page on Unrestricted Domain needs to be edited to include both possibilities, but I can't be bothered.
You also seem to think that most voters would not be able to understand that sort of nuance. You may be right there, especially in today's political climate (especially in the United States?), where there are two sides and the other side is always demonized.
Note that any new voting system will almost always try to be replaced by the loser under the new system. ("The current government is illegitimate! If it wasn't for the biased voting system we would have won!" -- cf. the recently revived call for the elimination of the U. S. Electoral College after Mr. Trump won with a minority of the popular vote.) If the winner can't keep support, the losing side will be able to push through a change.
However, a question: If we had the following score ballots:
9000: A:100; B:95; C:0
1000: B:100; C:85; A:0
giving A a score of 900,000 and B a score of 955,000, hence a victory for B, would there really be enough antipathy to B to cause outrage? All the A voters seemed to think B was pretty good. Of course (see above), the losing side could always complain. Anyone wedded to Condorcet winners would be outraged. And, of course, no real world election would end up like this. Score may be a little too ripe for manipulation. Gibbard-Satterthwaite, anyone?
words have meaning. "preference" without a quantitative adjective is Ranked ballot.
"strong preference" vs. "weak preference" implies a Score ballot.
my question that i have asked the Score Voting or Approval Voting advocates years ago remains: "How much should I score my second choice?" or "Should I approve my second choice or not?" that tactical question faces the voter in a Score or Approval election the second he/she steps into the voting booth. but not so for the ordinal Ranked ballot.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
> On January 9, 2020 11:12 PM Faran, James <jjfaran@buffalo.edu> wrote:
>
>
> About Score voting failing Unrestricted Domain:
>
> Part of the confusion of those advocating score and you is not a confusion on anyone's part, but rather a difference in what each considers a preference. (It's not possible to have a good reasoned argument until both sides agree on what the words mean.) Score voters would say
>
> A:100; B:95; C:0
>
> and
>
> A:100; B:5; C:0
>
> are different preferences, but you seem to say that these are both A>B>C and so are the same. I would say the Electowiki page on Unrestricted Domain needs to be edited to include both possibilities, but I can't be bothered.
>
> You also seem to think that most voters would not be able to understand that sort of nuance. You may be right there, especially in today's political climate (especially in the United States?), where there are two sides and the other side is always demonized.
>
> Note that any new voting system will almost always try to be replaced by the loser under the new system. ("The current government is illegitimate! If it wasn't for the biased voting system we would have won!" -- cf. the recently revived call for the elimination of the U. S. Electoral College after Mr. Trump won with a minority of the popular vote.) If the winner can't keep support, the losing side will be able to push through a change.
>
> However, a question: If we had the following score ballots:
>
> 9000: A:100; B:95; C:0
> 1000: B:100; C:85; A:0
>
> giving A a score of 900,000 and B a score of 955,000, hence a victory for B, would there really be enough antipathy to B to cause outrage? All the A voters seemed to think B was pretty good. Of course (see above), the losing side could always complain. Anyone wedded to Condorcet winners would be outraged. And, of course, no real world election would end up like this. Score may be a little too ripe for manipulation. Gibbard-Satterthwaite, anyone?
>
words have meaning. "preference" without a quantitative adjective is Ranked ballot.
"strong preference" vs. "weak preference" implies a Score ballot.
my question that i have asked the Score Voting or Approval Voting advocates years ago remains: "How much should I score my second choice?" or "Should I approve my second choice or not?" that tactical question faces the voter in a Score or Approval election the second he/she steps into the voting booth. but not so for the ordinal Ranked ballot.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
RB
robert bristow-johnson
Fri, Jan 10, 2020 5:06 AM
On January 9, 2020 11:12 PM Faran, James jjfaran@buffalo.edu wrote:
Note that any new voting system will almost always try to be replaced by the loser under the new system. ("The current government is illegitimate! If it wasn't for the biased voting system we would have won!" -- cf. the recently revived call for the elimination of the U. S. Electoral College after Mr. Trump won with a minority of the popular vote.) If the winner can't keep support, the losing side will be able to push through a change.
well, assuming that you can't change the rules of an election once it's decided, the "losing side" can only advocate changing the rules for future elections. but the circumstances will not be the same and sometimes the losing side will hurt themselves in advocating changing the rules.
an example in Vermont is the 2014 gubernatorial election in which the GOP candidate would almost certainly have won if the state practiced Ranked-Choice Voting of some form. it's the GOP who opposed RCV the most. i opined about that in this commentary: https://vtdigger.org/2014/11/11/robert-bristow-johnson-ways/
the loser under the new system now might be the winner under the same system later.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
i forgot something...
> On January 9, 2020 11:12 PM Faran, James <jjfaran@buffalo.edu> wrote:
>
>
> Note that any new voting system will almost always try to be replaced by the loser under the new system. ("The current government is illegitimate! If it wasn't for the biased voting system we would have won!" -- cf. the recently revived call for the elimination of the U. S. Electoral College after Mr. Trump won with a minority of the popular vote.) If the winner can't keep support, the losing side will be able to push through a change.
>
well, assuming that you can't change the rules of an election once it's decided, the "losing side" can only advocate changing the rules for future elections. but the circumstances will not be the same and sometimes the losing side will hurt themselves in advocating changing the rules.
an example in Vermont is the 2014 gubernatorial election in which the GOP candidate would almost certainly have won if the state practiced Ranked-Choice Voting of some form. it's the GOP who opposed RCV the most. i opined about that in this commentary: https://vtdigger.org/2014/11/11/robert-bristow-johnson-ways/
the loser under the new system now might be the winner under the same system later.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
RL
Rob Lanphier
Fri, Jan 10, 2020 7:02 AM
Hi fdpk69p6uq,
I have to confess that your reply in this thread bothers me a little
bit. More inline below....
On Thu, Jan 9, 2020, 6:17 PM Rob Lanphier wrote:
Many Score voting[1] activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that all voting systems (not
a mere subset) are subject to some form of impossibility problem.
Are you saying that a single interview of an 90-year-old Kenneth Arrow
by a much younger interviewer with a possible bias on the matter
should be the final word on this subject? How much of his
professional credibility did Arrow stake on that interview? How much
preparation for that line of questioning do you think Arrow gave for
that interview? Who's going to interview Gibbard? Who's going to
interview Satterthwaite?
It was really clear to me a the point that Aaron Hamlin tried to get
Dr. Arrow's take on the "favorite betrayal criterion" that Dr. Arrow
wasn't actively reading this mailing list, and instead was enjoying
his waning years. ;-) It's interesting that Arrow had been here in
the Bay Area for a very long time, and witnessed San Francisco (and
Oakland, and others) move to Instant Runoff, and that he clearly had
some reservations about IRV. He also seemed more concerned with
Electoral College and California's jungle primary than he did with any
of the municipal election reforms.
I really appreciate that Aaron did that interview before Dr. Arrow
died, and I told Aaron I was a little jealous, and was kicking myself
for not seeking Arrow out myself after I moved to San Francisco in
2011. Given that, my assessment of the interview above probably seems
a bit harsh. All I'm saying is that the interview wasn't set up for
the level of scrutiny necessary to establish rote truth. I'm not
willing to accept that interview as definitive proof that Arrow's key
insight on voting systems is strictly limited to ordinal voting
systems, and that cardinal voting systems are provably free of any
sort of impossibility paradox.
Rob
Hi fdpk69p6uq,
I have to confess that your reply in this thread bothers me a little
bit. More inline below....
> On Thu, Jan 9, 2020, 6:17 PM Rob Lanphier wrote:
>> Many Score voting[1] activists claim that cardinal methods somehow
>> dodge Arrow's theorem. It seems to me that *all* voting systems (not
>> a mere subset) are subject to some form of impossibility problem.
On Thu, Jan 9, 2020 at 8:43 PM <fdpk69p6uq@snkmail.com> wrote:
> Didn't Arrow agree that rated systems aren't included?
>
> https://www.electionscience.org/commentary-analysis/voting-theory-podcast-2012-10-06-interview-with-nobel-laureate-dr-kenneth-arrow/
Are you saying that a single interview of an 90-year-old Kenneth Arrow
by a much younger interviewer with a possible bias on the matter
should be the final word on this subject? How much of his
professional credibility did Arrow stake on that interview? How much
preparation for that line of questioning do you think Arrow gave for
that interview? Who's going to interview Gibbard? Who's going to
interview Satterthwaite?
It was really clear to me a the point that Aaron Hamlin tried to get
Dr. Arrow's take on the "favorite betrayal criterion" that Dr. Arrow
wasn't actively reading this mailing list, and instead was enjoying
his waning years. ;-) It's interesting that Arrow had been here in
the Bay Area for a very long time, and witnessed San Francisco (and
Oakland, and others) move to Instant Runoff, and that he clearly had
some reservations about IRV. He also seemed more concerned with
Electoral College and California's jungle primary than he did with any
of the municipal election reforms.
I really appreciate that Aaron did that interview before Dr. Arrow
died, and I told Aaron I was a little jealous, and was kicking myself
for not seeking Arrow out myself after I moved to San Francisco in
2011. Given that, my assessment of the interview above probably seems
a bit harsh. All I'm saying is that the interview wasn't set up for
the level of scrutiny necessary to establish rote truth. I'm not
willing to accept that interview as definitive proof that Arrow's key
insight on voting systems is strictly limited to ordinal voting
systems, and that cardinal voting systems are provably free of any
sort of impossibility paradox.
Rob
KM
Kristofer Munsterhjelm
Fri, Jan 10, 2020 11:20 AM
On 10/01/2020 00.17, Rob Lanphier wrote:
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting[1] activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that all voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved.
It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
https://en.wikipedia.org/wiki/Unrestricted_domain
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score always chose either A or B, then it would pass Universality.
I agree. Arrow's theorem requires unrestricted domain to work, and what
unrestricted domain says (as far as I know it) is that the inputs are
lists of orderings, that every such list must be admissible, and that's
all that's required. I.e. "The rankings, all rankings, and nothing but
the rankings".
Score advocates claim that this isn't a bug, it's a feature. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 [2]) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
Sure, you might say that unrestricted domain is uninteresting. If you
do, and you design a voting system that doesn't pass unrestricted
domain, then Arrow won't apply. You could well get IIA out of it (with
certain assumptions). That doesn't mean that Arrow's is wrong, it just
means that it no longer applies.
I think that it's a good idea to think: "is my objection about strategy
or not?" If it's about strategy-proofness, the right theorem isn't
Arrow's, it's Gibbard's. And Gibbard's theorem holds for Range as well,
so Range doesn't get around it. So just because Range is outside of the
scope of Arrow, that doesn't mean that it's invulnerable to strategy.
And, to go on a bit of a tangent, I think that ordinary (normalized)
Range has both a cardinal and ordinal component to it. The ordinal
component might violate IIA.
Consider, for instance, something like: election one has a pro-war
candidate and an anti-war candidate, and their positions are otherwise
pretty much the same. But election two has ten pro-war candidates
ranging from economic left to right and ten anti-war candidates ranging
from economic left to right. It may be the case that in election one,
people judge the candidates by whether their war stance agree, and in
election two, people judge the candidates more heavily by left vs right
than by war stance. The distribution of the candidates affects what the
voters consider important features, and thus irrelevant candidates could
alter who the winner is.
On the other hand, "The Possibility of Social Choice" (Sen) suggests
that only very weak utility-like comparisons are required to salvage
IIA. So who knows? Perhaps with a method that's not Range, you can have
it even with the scenario above.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
- Goes faster than the speed of light
- Has infinite capacity
- Has a luxurious and comfortable passenger cabin
- Fits in a small coat pocket
- Is easy to produce
- Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
The feeling I get from it is roughly:
- Wouldn't it be nice if we had perfection even under honesty?
- Well, here's one reason we can't have perfection.
- So have fun with the complexity.
That is, Arrow's theorem is useful to say what you can't have. In your
vehicle analog, we would want to find out how to create that perfect
FTL-equipped free car if we could. Arrow's theorem just tells us that we
can stop looking. (And Gibbard's is like: even if your "vehicle" moves
the world instead of moving itself, thus making Arrow no longer apply,
you still can't get perfection under strategy.)
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that all voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
precipitously in my mind.
It does seem that there are no perfect methods, even if we can
circumvent Arrow, and even if we don't care about strategy. For
instance, Approval requires calculation even by honest voters, and for
Range it's not even obvious what the one honest vote is.
It would be useful to get a proof of this, but I wouldn't know where to
start. So the observation that it's impossible to attain perfection must
be inductive rather than deductive, i.e. we have a hunch because nothing
has attained perfection until now.
I think the problem ultimately is: someone thinks "Arrow implies
imperfection, so if I get rid of Arrow, I have perfection". They confuse
implication for equivalence.
On 10/01/2020 00.17, Rob Lanphier wrote:
> Hi folks,
>
> As some of you might have seen, Electowiki is a lot more active than
> it used to be. I'm 99% convinced that's a good thing. The 1% of me
> that has reservations is regarding how some advocates talk about
> Arrow's theorem. I'm hoping you all can do one of the following:
> a) change my view about Arrow's theorem, -or-
> b) offer me some help in better articulating my view about Arrow's theorem.
>
> Many Score voting[1] activists claim that cardinal methods somehow
> dodge Arrow's theorem. It seems to me that *all* voting systems (not
> a mere subset) are subject to some form of impossibility problem.
> Arrow's impossibility theorem deserved great acclaim for subjecting
> all mainstream voting systems of the 1950s to mathematical rigor, and
> it's clear that his 1950 paper and 1951 book profoundly influenced
> economics and game theory for the better. His 1972 Nobel prize was
> well deserved.
First a little pet peeve of sorts: It's not a Nobel prize. The Nobel
foundation says as much at the very bottom of
https://www.nobelprize.org/nomination/economic-sciences/ :-)
> It seems that it has become fashionable to find
> loopholes in Arrow's original formulation and declare the loopholes
> important. Even if the loopholes exist, talking up those loopholes
> doesn't seem compelling, given the subsequent work by other theorists
> broaden the scope beyond Arrow's version.
>
> But, what the heck, let's actually talk about Arrow's original
> formulation. I believe Score voting fails unrestricted domain:
> <https://en.wikipedia.org/wiki/Unrestricted_domain>
>
> In particular, let's say that 90% of voters prefer candidate A over candidate B:
> 90:A>B
> 10:B>A
>
> Arrow posits that there should only be one way to express that, and
> Score fails it. In Score, it's possible to sometimes pick A, and
> sometimes pick B, depending on the score values on the ballots. If
> Score *always* chose either A or B, then it would pass Universality.
I agree. Arrow's theorem requires unrestricted domain to work, and what
unrestricted domain says (as far as I know it) is that the inputs are
lists of orderings, that every such list must be admissible, and that's
all that's required. I.e. "The rankings, all rankings, and nothing but
the rankings".
> Score advocates claim that this isn't a bug, it's a *feature*. If
> (for example), voters for A only mildly prefer A over B, but voters
> for B strongly detest A, then the correct social choice is B.
> However, it doesn't seem practical to inflict this level of nuance on
> voters. I suspect that the first election where the Condorcet winner
> is beaten by a minority-preferred candidate (e.g. like what happened
> in Burlington 2009 [2]) will result in a repeal (like what happened in
> Burlington). Back to the A/B example above, It's hard to imagine
> voters would consider the selection of "B" to be fair in a large
> election.
Sure, you might say that unrestricted domain is uninteresting. If you
do, and you design a voting system that doesn't pass unrestricted
domain, then Arrow won't apply. You could well get IIA out of it (with
certain assumptions). That doesn't mean that Arrow's is wrong, it just
means that it no longer applies.
I think that it's a good idea to think: "is my objection about strategy
or not?" If it's about strategy-proofness, the right theorem isn't
Arrow's, it's Gibbard's. And Gibbard's theorem holds for Range as well,
so Range doesn't get around it. So just because Range is outside of the
scope of Arrow, that doesn't mean that it's invulnerable to strategy.
And, to go on a bit of a tangent, I think that ordinary (normalized)
Range has both a cardinal and ordinal component to it. The ordinal
component might violate IIA.
Consider, for instance, something like: election one has a pro-war
candidate and an anti-war candidate, and their positions are otherwise
pretty much the same. But election two has ten pro-war candidates
ranging from economic left to right and ten anti-war candidates ranging
from economic left to right. It may be the case that in election one,
people judge the candidates by whether their war stance agree, and in
election two, people judge the candidates more heavily by left vs right
than by war stance. The distribution of the candidates affects what the
voters consider important features, and thus irrelevant candidates could
alter who the winner is.
On the other hand, "The Possibility of Social Choice" (Sen) suggests
that only very weak utility-like comparisons are required to salvage
IIA. So who knows? Perhaps with a method that's not Range, you can have
it even with the scenario above.
> It's fine to hold the opinion that Universality is an uninteresting
> criterion, and that therefore, Arrow's set of criteria isn't very
> interesting. For example, a few years ago, we went through a phase
> where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
> interesting criterion, and advocating for Condorcet variants that meet
> that criterion. Regardless, just because we find one criterion less
> compelling than another, we should talk accurately about the failed
> criterion.
>
> My way of thinking about Arrow's theorem (and being thankful for it)
> is to think of it like the physics of voting systems. For example, in
> real-world physics, a "perfect" vehicle is impossible, because it's
> impossible to meet these criteria:
> * Goes faster than the speed of light
> * Has infinite capacity
> * Has a luxurious and comfortable passenger cabin
> * Fits in a small coat pocket
> * Is easy to produce
> * Is cheap (or even free)
>
> Just because a perfect vehicle is not possible, I'm glad
> transportation innovation didn't stop with Ford's Model T. Of course,
> automobile sellers compete on the tradeoffs between the criteria
> above, and much public policy debate is about mode-of-transport
> tradeoffs between planes, trains and automobiles (and bicycles, and
> scooters, and and and...). We need public policy debates around
> election method tradeoffs, too.
The feeling I get from it is roughly:
- Wouldn't it be nice if we had perfection even under honesty?
- Well, here's one reason we can't have perfection.
- So have fun with the complexity.
That is, Arrow's theorem is useful to say what you can't have. In your
vehicle analog, we would want to find out how to create that perfect
FTL-equipped free car if we could. Arrow's theorem just tells us that we
can stop looking. (And Gibbard's is like: even if your "vehicle" moves
the world instead of moving itself, thus making Arrow no longer apply,
you still can't get perfection under strategy.)
> I'm hoping we can try to stop trying to declare clever loopholes in
> Arrow's theorem, and just acknowledge the reality that *all* voting
> systems involve tradeoffs. I hope we all can acknowledge that Arrow's
> central insight (there's no "perfect" system given perfectly
> reasonable criteria) is valid, and that it's only on the specifics of
> the exact criteria chosen for the 1951 proof that might be flawed. I
> believe that election method activists should speak (and write) with
> clarity about the tradeoffs involved. Whenever I see someone
> gleefully declare that Arrow's theorem doesn't apply to their voting
> method (and imply perfection), the credibility of the writer drops
> *precipitously* in my mind.
It does seem that there are no perfect methods, even if we can
circumvent Arrow, and even if we don't care about strategy. For
instance, Approval requires calculation even by honest voters, and for
Range it's not even obvious what the one honest vote *is*.
It would be useful to get a proof of this, but I wouldn't know where to
start. So the observation that it's impossible to attain perfection must
be inductive rather than deductive, i.e. we have a hunch because nothing
has attained perfection until now.
I think the problem ultimately is: someone thinks "Arrow implies
imperfection, so if I get rid of Arrow, I have perfection". They confuse
implication for equivalence.
TP
Toby Pereira
Fri, Jan 10, 2020 11:39 AM
Arrow published a mathematical theorem so presumably everything was rigorously defined and not open to interpretation, so that would include unrestricted domain. On the Wikipedia it says "In social choice theory, unrestricted domain, or universality, is a property of social welfare functions in which all preferences of all voters (but no other considerations) are allowed." And while it might be defined differently and more precisely in Arrow's paper, I wouldn't say score fails by that definition. But it doesn't really matter anyway. You can define it in a way that score fails or define it in a way that it doesn't apply to score. Similarly you could define a condition where degrees of liking must be allowed, and ranked methods would fail that. And as has been said, it's not as if Arrow's Theorem is the be all and end all. All methods have their own problems, and whether they happen to be covered by one particular theorem is neither here nor there.
But what I would say is that I consider Arrow's Theorem to be possibly the most overrated and overstated theorem of all time. If you look at the criteria that ranked methods must fail one of according to Arrow's Theorem, most of them are just criteria that any remotely reasonable method would pass. The theorem, stated more informally, is basically that with a few reasonable background assumptions, all ranked-ballot methods fail independence of irrelevant alternatives. Which is interesting enough itself, except that this was known for centuries anyway from the Condorcet Paradox. If head to head A beats B, B beats C, and C beats A, then any winner in the three-way election has to overturn one of the head to head results as a result of an irrelevant alternative being added.
Toby
On Thursday, 9 January 2020, 23:17:56 GMT, Rob Lanphier robla@robla.net wrote:
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting1 activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that all voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
https://en.wikipedia.org/wiki/Unrestricted_domain
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score always chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a feature. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 2) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC3 as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
- Goes faster than the speed of light
- Has infinite capacity
- Has a luxurious and comfortable passenger cabin
- Fits in a small coat pocket
- Is easy to produce
- Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that all voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
precipitously in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki4
Election-Methods mailing list - see https://electorama.com/em for list info
Arrow published a mathematical theorem so presumably everything was rigorously defined and not open to interpretation, so that would include unrestricted domain. On the Wikipedia it says "In social choice theory, unrestricted domain, or universality, is a property of social welfare functions in which all preferences of all voters (but no other considerations) are allowed." And while it might be defined differently and more precisely in Arrow's paper, I wouldn't say score fails by that definition. But it doesn't really matter anyway. You can define it in a way that score fails or define it in a way that it doesn't apply to score. Similarly you could define a condition where degrees of liking must be allowed, and ranked methods would fail that. And as has been said, it's not as if Arrow's Theorem is the be all and end all. All methods have their own problems, and whether they happen to be covered by one particular theorem is neither here nor there.
But what I would say is that I consider Arrow's Theorem to be possibly the most overrated and overstated theorem of all time. If you look at the criteria that ranked methods must fail one of according to Arrow's Theorem, most of them are just criteria that any remotely reasonable method would pass. The theorem, stated more informally, is basically that with a few reasonable background assumptions, all ranked-ballot methods fail independence of irrelevant alternatives. Which is interesting enough itself, except that this was known for centuries anyway from the Condorcet Paradox. If head to head A beats B, B beats C, and C beats A, then any winner in the three-way election has to overturn one of the head to head results as a result of an irrelevant alternative being added.
Toby
On Thursday, 9 January 2020, 23:17:56 GMT, Rob Lanphier <robla@robla.net> wrote:
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting[1] activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that *all* voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
<https://en.wikipedia.org/wiki/Unrestricted_domain>
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score *always* chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a *feature*. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 [2]) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
* Goes faster than the speed of light
* Has infinite capacity
* Has a luxurious and comfortable passenger cabin
* Fits in a small coat pocket
* Is easy to produce
* Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that *all* voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
*precipitously* in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki[4]
[1]: https://electowiki.org/wiki/Score_voting
[2]: https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election
[3]: https://electowiki.org/wiki/IIAC
[4]: https://electowiki.org/wiki/Arrow%27s_impossibility_theorem
----
Election-Methods mailing list - see https://electorama.com/em for list info
SE
Steve Eppley
Fri, Jan 10, 2020 11:41 AM
I think the spirit of Rob's question is (or should be): Can any plausibly democratic voting method satisfy this Independence criterion: "Assuming voters' preferences don't change, the winner must not change if another candidate chooses not to compete." (Let's call methods plausibly democratic if they don't privilege any candidates or voters. In other words, the Neutrality and Anonymity criteria in the literature of social choice theory.)
None can satisfy that Independence.
The last time I checked, advocates of Range Voting acknowledge that when there are only two candidates, optimal voting strategy is to give the highest possible score to the voter's most preferred candidate and the lowest possible score to the voter's least preferred candidate. (Some of those advocates may even think that's sincere voting, bless their little hearts.) Since that's such an obvious strategy, it's reasonable to assume at least some of the voters will eventually learn to use it (just as many voters have learned to vote for a compromise to help defeat a "greater evil" given Plurality Rule). Now consider an example: Suppose that given a majoritarian voting method such as Plurality Rule, Rock would beat Scissors, Scissors would beat Paper, and Paper would beat Rock, by a narrow majority in each pairing. Suppose also that Rock would be the winner if Rock, Paper and Scissors compete given Range Voting (or Approval). Which one wins if only Rock and Paper compete
given Range Voting (or Approval)? Obviously, Paper can win, since the majority who prefer Paper can elect Paper using their optimal voting strategy. Thus the winner can change from Rock to Paper when Scissors doesn't compete, which violates Independence.
Given the fact that strategic voting is possible, many (most?) criteria definitions are "naive." For instance, a "Condorcet winner given sincere voting" can lose given a voting method that satisfies the Condorcet criterion. I hope we can all agree that the spirit of the Condorcet criterion is that the sincere Condorcet winner should win (when it exists). Call that the Sincere Condorcet criterion. No plausibly democratic voting method can satisfy Sincere Condorcet, but some voting methods can perform better on it than others, by making defensive strategies easier and/or more palatable, or offensive strategies riskier.
I presume the same is true regarding Independence: some plausibly democratic voting methods perform better than others on Independence, even though none satisfy Independence.
For the criterion that matters most to me, I don't have a rigorous definition. Here's a non-rigorous definition: The voting method should give candidates who want to win a strong incentive to take positions that the voters themselves would collectively choose given a well-functioning direct democracy... even on issues that most voters don't care strongly about. Here's how I relate that to voting methods like Maximize Affirmed Majorities (MAM), which facilitate competition, count all pairwise majorities, and pay attention to the sizes of the majorities: Suppose candidate Alice wants to win, and is considering taking position p on some issue. Although she knows a majority of the voters prefer alternative q over p, her wealthy campaign donors favor p and most voters care more about other issues. Given a voting method like MAM, the risk to Alice is that by advocating p, she would create an opportunity for another candidate Bob to enter the race, take position q and copy
Alice's positions on all other issues. The larger the majority who prefer q over p, the larger the majority who would tend to rank Bob over Alice. Defeating Alice. A deterrent against taking unpopular positions to benefit donors.
--Steve
On 1/9/2020 6:17 PM, Rob Lanphier wrote:
Hi folks,
As some of you might have seen, Electowiki is a lot more active than
it used to be. I'm 99% convinced that's a good thing. The 1% of me
that has reservations is regarding how some advocates talk about
Arrow's theorem. I'm hoping you all can do one of the following:
a) change my view about Arrow's theorem, -or-
b) offer me some help in better articulating my view about Arrow's theorem.
Many Score voting1 activists claim that cardinal methods somehow
dodge Arrow's theorem. It seems to me that all voting systems (not
a mere subset) are subject to some form of impossibility problem.
Arrow's impossibility theorem deserved great acclaim for subjecting
all mainstream voting systems of the 1950s to mathematical rigor, and
it's clear that his 1950 paper and 1951 book profoundly influenced
economics and game theory for the better. His 1972 Nobel prize was
well deserved. It seems that it has become fashionable to find
loopholes in Arrow's original formulation and declare the loopholes
important. Even if the loopholes exist, talking up those loopholes
doesn't seem compelling, given the subsequent work by other theorists
broaden the scope beyond Arrow's version.
But, what the heck, let's actually talk about Arrow's original
formulation. I believe Score voting fails unrestricted domain:
https://en.wikipedia.org/wiki/Unrestricted_domain
In particular, let's say that 90% of voters prefer candidate A over candidate B:
90:A>B
10:B>A
Arrow posits that there should only be one way to express that, and
Score fails it. In Score, it's possible to sometimes pick A, and
sometimes pick B, depending on the score values on the ballots. If
Score always chose either A or B, then it would pass Universality.
Score advocates claim that this isn't a bug, it's a feature. If
(for example), voters for A only mildly prefer A over B, but voters
for B strongly detest A, then the correct social choice is B.
However, it doesn't seem practical to inflict this level of nuance on
voters. I suspect that the first election where the Condorcet winner
is beaten by a minority-preferred candidate (e.g. like what happened
in Burlington 2009 2) will result in a repeal (like what happened in
Burlington). Back to the A/B example above, It's hard to imagine
voters would consider the selection of "B" to be fair in a large
election.
It's fine to hold the opinion that Universality is an uninteresting
criterion, and that therefore, Arrow's set of criteria isn't very
interesting. For example, a few years ago, we went through a phase
where Condorcet advocates promoted "Local IIAC" as a IIAC3 as a more
interesting criterion, and advocating for Condorcet variants that meet
that criterion. Regardless, just because we find one criterion less
compelling than another, we should talk accurately about the failed
criterion.
My way of thinking about Arrow's theorem (and being thankful for it)
is to think of it like the physics of voting systems. For example, in
real-world physics, a "perfect" vehicle is impossible, because it's
impossible to meet these criteria:
- Goes faster than the speed of light
- Has infinite capacity
- Has a luxurious and comfortable passenger cabin
- Fits in a small coat pocket
- Is easy to produce
- Is cheap (or even free)
Just because a perfect vehicle is not possible, I'm glad
transportation innovation didn't stop with Ford's Model T. Of course,
automobile sellers compete on the tradeoffs between the criteria
above, and much public policy debate is about mode-of-transport
tradeoffs between planes, trains and automobiles (and bicycles, and
scooters, and and and...). We need public policy debates around
election method tradeoffs, too.
I'm hoping we can try to stop trying to declare clever loopholes in
Arrow's theorem, and just acknowledge the reality that all voting
systems involve tradeoffs. I hope we all can acknowledge that Arrow's
central insight (there's no "perfect" system given perfectly
reasonable criteria) is valid, and that it's only on the specifics of
the exact criteria chosen for the 1951 proof that might be flawed. I
believe that election method activists should speak (and write) with
clarity about the tradeoffs involved. Whenever I see someone
gleefully declare that Arrow's theorem doesn't apply to their voting
method (and imply perfection), the credibility of the writer drops
precipitously in my mind.
Am I wrong?
Rob
p.s. I've been meaning to write this email for a while. What inspired
me to finally write it has been reading the current state of
Electowiki and Wikipedia articles on the topic, like the "Arrow's
impossiblity theorem" article on Electowiki4
Election-Methods mailing list - see https://electorama.com/em for list info
I think the spirit of Rob's question is (or should be): Can any plausibly democratic voting method satisfy this Independence criterion: "Assuming voters' preferences don't change, the winner must not change if another candidate chooses not to compete." (Let's call methods plausibly democratic if they don't privilege any candidates or voters. In other words, the Neutrality and Anonymity criteria in the literature of social choice theory.)
None can satisfy that Independence.
The last time I checked, advocates of Range Voting acknowledge that when there are only two candidates, optimal voting strategy is to give the highest possible score to the voter's most preferred candidate and the lowest possible score to the voter's least preferred candidate. (Some of those advocates may even think that's sincere voting, bless their little hearts.) Since that's such an obvious strategy, it's reasonable to assume at least some of the voters will eventually learn to use it (just as many voters have learned to vote for a compromise to help defeat a "greater evil" given Plurality Rule). Now consider an example: Suppose that given a majoritarian voting method such as Plurality Rule, Rock would beat Scissors, Scissors would beat Paper, and Paper would beat Rock, by a narrow majority in each pairing. Suppose also that Rock would be the winner if Rock, Paper and Scissors compete given Range Voting (or Approval). Which one wins if only Rock and Paper compete
given Range Voting (or Approval)? Obviously, Paper can win, since the majority who prefer Paper can elect Paper using their optimal voting strategy. Thus the winner can change from Rock to Paper when Scissors doesn't compete, which violates Independence.
Given the fact that strategic voting is possible, many (most?) criteria definitions are "naive." For instance, a "Condorcet winner given sincere voting" can lose given a voting method that satisfies the Condorcet criterion. I hope we can all agree that the spirit of the Condorcet criterion is that the sincere Condorcet winner should win (when it exists). Call that the Sincere Condorcet criterion. No plausibly democratic voting method can satisfy Sincere Condorcet, but some voting methods can perform better on it than others, by making defensive strategies easier and/or more palatable, or offensive strategies riskier.
I presume the same is true regarding Independence: some plausibly democratic voting methods perform better than others on Independence, even though none satisfy Independence.
For the criterion that matters most to me, I don't have a rigorous definition. Here's a non-rigorous definition: The voting method should give candidates who want to win a strong incentive to take positions that the voters themselves would collectively choose given a well-functioning direct democracy... even on issues that most voters don't care strongly about. Here's how I relate that to voting methods like Maximize Affirmed Majorities (MAM), which facilitate competition, count all pairwise majorities, and pay attention to the sizes of the majorities: Suppose candidate Alice wants to win, and is considering taking position p on some issue. Although she knows a majority of the voters prefer alternative q over p, her wealthy campaign donors favor p and most voters care more about other issues. Given a voting method like MAM, the risk to Alice is that by advocating p, she would create an opportunity for another candidate Bob to enter the race, take position q and copy
Alice's positions on all other issues. The larger the majority who prefer q over p, the larger the majority who would tend to rank Bob over Alice. Defeating Alice. A deterrent against taking unpopular positions to benefit donors.
--Steve
On 1/9/2020 6:17 PM, Rob Lanphier wrote:
> Hi folks,
>
> As some of you might have seen, Electowiki is a lot more active than
> it used to be. I'm 99% convinced that's a good thing. The 1% of me
> that has reservations is regarding how some advocates talk about
> Arrow's theorem. I'm hoping you all can do one of the following:
> a) change my view about Arrow's theorem, -or-
> b) offer me some help in better articulating my view about Arrow's theorem.
>
> Many Score voting[1] activists claim that cardinal methods somehow
> dodge Arrow's theorem. It seems to me that *all* voting systems (not
> a mere subset) are subject to some form of impossibility problem.
> Arrow's impossibility theorem deserved great acclaim for subjecting
> all mainstream voting systems of the 1950s to mathematical rigor, and
> it's clear that his 1950 paper and 1951 book profoundly influenced
> economics and game theory for the better. His 1972 Nobel prize was
> well deserved. It seems that it has become fashionable to find
> loopholes in Arrow's original formulation and declare the loopholes
> important. Even if the loopholes exist, talking up those loopholes
> doesn't seem compelling, given the subsequent work by other theorists
> broaden the scope beyond Arrow's version.
>
> But, what the heck, let's actually talk about Arrow's original
> formulation. I believe Score voting fails unrestricted domain:
> <https://en.wikipedia.org/wiki/Unrestricted_domain>
>
> In particular, let's say that 90% of voters prefer candidate A over candidate B:
> 90:A>B
> 10:B>A
>
> Arrow posits that there should only be one way to express that, and
> Score fails it. In Score, it's possible to sometimes pick A, and
> sometimes pick B, depending on the score values on the ballots. If
> Score *always* chose either A or B, then it would pass Universality.
>
> Score advocates claim that this isn't a bug, it's a *feature*. If
> (for example), voters for A only mildly prefer A over B, but voters
> for B strongly detest A, then the correct social choice is B.
> However, it doesn't seem practical to inflict this level of nuance on
> voters. I suspect that the first election where the Condorcet winner
> is beaten by a minority-preferred candidate (e.g. like what happened
> in Burlington 2009 [2]) will result in a repeal (like what happened in
> Burlington). Back to the A/B example above, It's hard to imagine
> voters would consider the selection of "B" to be fair in a large
> election.
>
> It's fine to hold the opinion that Universality is an uninteresting
> criterion, and that therefore, Arrow's set of criteria isn't very
> interesting. For example, a few years ago, we went through a phase
> where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
> interesting criterion, and advocating for Condorcet variants that meet
> that criterion. Regardless, just because we find one criterion less
> compelling than another, we should talk accurately about the failed
> criterion.
>
> My way of thinking about Arrow's theorem (and being thankful for it)
> is to think of it like the physics of voting systems. For example, in
> real-world physics, a "perfect" vehicle is impossible, because it's
> impossible to meet these criteria:
> * Goes faster than the speed of light
> * Has infinite capacity
> * Has a luxurious and comfortable passenger cabin
> * Fits in a small coat pocket
> * Is easy to produce
> * Is cheap (or even free)
>
> Just because a perfect vehicle is not possible, I'm glad
> transportation innovation didn't stop with Ford's Model T. Of course,
> automobile sellers compete on the tradeoffs between the criteria
> above, and much public policy debate is about mode-of-transport
> tradeoffs between planes, trains and automobiles (and bicycles, and
> scooters, and and and...). We need public policy debates around
> election method tradeoffs, too.
>
> I'm hoping we can try to stop trying to declare clever loopholes in
> Arrow's theorem, and just acknowledge the reality that *all* voting
> systems involve tradeoffs. I hope we all can acknowledge that Arrow's
> central insight (there's no "perfect" system given perfectly
> reasonable criteria) is valid, and that it's only on the specifics of
> the exact criteria chosen for the 1951 proof that might be flawed. I
> believe that election method activists should speak (and write) with
> clarity about the tradeoffs involved. Whenever I see someone
> gleefully declare that Arrow's theorem doesn't apply to their voting
> method (and imply perfection), the credibility of the writer drops
> *precipitously* in my mind.
>
> Am I wrong?
>
> Rob
>
> p.s. I've been meaning to write this email for a while. What inspired
> me to finally write it has been reading the current state of
> Electowiki and Wikipedia articles on the topic, like the "Arrow's
> impossiblity theorem" article on Electowiki[4]
>
> [1]: https://electowiki.org/wiki/Score_voting
> [2]: https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election
> [3]: https://electowiki.org/wiki/IIAC
> [4]: https://electowiki.org/wiki/Arrow%27s_impossibility_theorem
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info
KM
Kristofer Munsterhjelm
Fri, Jan 10, 2020 12:04 PM
On 10/01/2020 05.46, robert bristow-johnson wrote:
my question that i have asked the Score Voting or Approval Voting
advocates years ago remains: "How much should I score my second choice?"
or "Should I approve my second choice or not?" that tactical question
faces the voter in a Score or Approval election the second he/she steps
into the voting booth. but not so for the ordinal Ranked ballot.
I tended to phrase this as: Approval requires that the voters engage in
manual DSV (or earlier, that they "dither" - in the sense of reducing a
full-color image to black-and-white). Approval satisfies so many
properties on paper by placing the burden on the voter instead.
But I've recently found a paper that puts this very clearly:
https://www.jstor.org/stable/1955800 (use Sci-Hub if you don't have
access). The paper shows that if the voter preferences aren't naturally
dichotomous (a bunch of equal ranked candidates at top above a bunch of
equal ranked candidates at bottom), then the Condorcet winner may end up
being dead last by approval score; and that for a particular type of
strategy, any candidate may be an equilibrium Approval winner.
To quote from the conclusion: "Strategic calculations are endemic to AV
even though all of the votes considered are called sincere. Given the
literature's emphasis on approval and disapproval sets - even the name,
approval - and the fact that voting for all approved candidates and no
others is optimal for dichotomous preferences, one gets the false
impression that AV will eliminate strategic thinking and voting. The
results here show that this is far from true, however."
On 10/01/2020 05.46, robert bristow-johnson wrote:
> my question that i have asked the Score Voting or Approval Voting
> advocates years ago remains: "How much should I score my second choice?"
> or "Should I approve my second choice or not?" that tactical question
> faces the voter in a Score or Approval election the second he/she steps
> into the voting booth. but not so for the ordinal Ranked ballot.
I tended to phrase this as: Approval requires that the voters engage in
manual DSV (or earlier, that they "dither" - in the sense of reducing a
full-color image to black-and-white). Approval satisfies so many
properties on paper by placing the burden on the voter instead.
But I've recently found a paper that puts this very clearly:
https://www.jstor.org/stable/1955800 (use Sci-Hub if you don't have
access). The paper shows that if the voter preferences aren't naturally
dichotomous (a bunch of equal ranked candidates at top above a bunch of
equal ranked candidates at bottom), then the Condorcet winner may end up
being dead last by approval score; and that for a particular type of
strategy, any candidate may be an equilibrium Approval winner.
To quote from the conclusion: "Strategic calculations are endemic to AV
even though all of the votes considered are called sincere. Given the
literature's emphasis on approval and disapproval sets - even the name,
approval - and the fact that voting for all approved candidates and no
others is optimal for dichotomous preferences, one gets the false
impression that AV will eliminate strategic thinking and voting. The
results here show that this is far from true, however."
