Suppose, for a moment, there were never any cycles...
So I am trying to grok this Benoit paper https://people.cs.pitt.edu/~kirk/CS1699Fall2014/gibbard-sat.pdf and I might be able to do it. But I would like to ask the authorities here a simple hypothetical question.
We know that Condorcet cycles can occur and in the U.S. there is one known RCV election that demonstrated a cycle, the 2021 Minneapolis Ward 2 City Council election. It was a simple Rock-Paper-Scissors cycle; Smith set of 3.
I think it's the case that we know that the necessary ingredients for a cycle is a very close 3-way race and that there is at least a 2-dimensional political spectrum (Nolan chart) with candidates and voters spread out all over the map in 2 dimensions, not in mostly a linear spatial distribution. There has to be a sorta political schizophrenia where a lotta voters are saying something like "If I can't have my favorite, Bernie, then I'm voting for T****."
Here is my question: Suppose that cycles never happened. Suppose we were somehow guaranteed that there is always a Condorcet winner. And also suppose we're far enough from a cycle that no collective strategy would succeed at pushing the election into a cycle. Then, if there is always a CW, is there any strategy that will serve a voter's political interest than better than ranking the candidates sincerely?
Like, if there is always a CW, how can IIA be violated? It seems to me that, if you remove any loser from all ballots and the voters express their same preferences with the remaining candidates, that the same CW will be elected. Without exception (other than a cycle).
Sorry to give you folks such a meatball question, but remember, I am an activist, not a trained and published scholar in psephology or social choice theory.
Thank you in advance.
robert
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Hi Robert,
I think it's the case that we know that the necessary ingredients for a cycle is a very
close 3-way race and that there is at least a 2-dimensional political spectrum (Nolan
chart) with candidates and voters spread out all over the map in 2 dimensions, not in
mostly a linear spatial distribution. There has to be a sorta political schizophrenia where
a lotta voters are saying something like "If I can't have my favorite, Bernie, then I'm
voting for T****."
Those might be the prerequisites for a cycle to exist in the sincere preferences.
Here is my question: Suppose that cycles never happened. Suppose we were somehow
guaranteed that there is always a Condorcet winner. And also suppose we're far enough
from a cycle that no collective strategy would succeed at pushing the election into a cycle.
I'm not sure what that last sentence can really mean. We see even under IRV that not all
voters will give all their rankings, despite IRV offering no incentive to withhold them.
This is enough to create a voted cycle.
Then, if there is always a CW, is there any strategy that will serve a voter's political
interest than better than ranking the candidates sincerely?
Like, if there is always a CW, how can IIA be violated? It seems to me that, if you remove
any loser from all ballots and the voters express their same preferences with the
remaining candidates, that the same CW will be elected. Without exception (other than a
cycle).
Yes, if you don't allow the existence of any scenarios without a voted CW, then there should
be no strategies to use.
Kevin
votingmethods.net
On 21.01.2023 20:49, robert bristow-johnson wrote:
So I am trying to grok this Benoit paper
https://people.cs.pitt.edu/~kirk/CS1699Fall2014/gibbard-sat.pdf and I
might be able to do it. But I would like to ask the authorities here a
simple hypothetical question.
We know that Condorcet cycles can occur and in the U.S. there is one
known RCV election that demonstrated a cycle, the 2021 Minneapolis Ward
2 City Council election. It was a simple Rock-Paper-Scissors cycle;
Smith set of 3.
I think it's the case that we know that the necessary ingredients
for a cycle is a very close 3-way race and that there is at least a
2-dimensional political spectrum (Nolan chart) with candidates and
voters spread out all over the map in 2 dimensions, not in mostly a
linear spatial distribution. There has to be a sorta political
schizophrenia where a lotta voters are saying something like "If I can't
have my favorite, Bernie, then I'm voting for T****."
There could also be simple noise, i.e. some candidates are extremely
close, the voters randomly fill in what's really equal-rank, and the
random fill happens to create a Condorcet cycle.
IIRC, Worlobah and Arab were very close in the Minneapolis election, so
the cycle could be a result of noise, but I don't know the circumstances
well enough to say for sure.
Here is my question: Suppose that cycles never happened. Suppose
we were somehow guaranteed that there is always a Condorcet winner.
And also suppose we're far enough from a cycle that no collective
strategy would succeed at pushing the election into a cycle. Then,
if there is always a CW, is there any strategy that will serve a
voter's political interest than better than ranking the candidates
sincerely?
If there is a CW, then IIA always holds, yes. Suppose X is the CW and Y
is someone else. Then running the election without Y doesn't change
anything: X still beats everybody else pairwise and wins.
Thus if somehow you could prevent both sincere and tactical Condorcet
cycles, the method would be strategy-proof. (Strictly speaking, this
doesn't invalidate Arrow's theorem because a method that magically
forbids Condorcet cycles would fail universal domain.)
-km
On 1/21/2023 4:18 PM, Kristofer Munsterhjelm wrote:
There could also be simple noise, i.e. some candidates are extremely
close, the voters randomly fill in what's really equal-rank, and the
random fill happens to create a Condorcet cycle.
IIRC, Worlobah and Arab were very close in the Minneapolis election,
so the cycle could be a result of noise, but I don't know the
circumstances well enough to say for sure
= = = = =
[KB] That's correct. There was very little difference in political
positions among most of the Ward 2 candidates. I didn't pay close
attention to their specific positions because I live in a different ward.
- Ken Bearman, Minneapolis MN
On 21.01.2023 20:49, robert bristow-johnson wrote:
Here is my question: Suppose that cycles never happened. Suppose
we were somehow guaranteed that there is always a Condorcet winner.
And also suppose we're far enough from a cycle that no collective
strategy would succeed at pushing the election into a cycle. Then,
if there is always a CW, is there any strategy that will serve a
voter's political interest than better than ranking the candidates
sincerely?
On 01/21/2023 5:18 PM EST Kristofer Munsterhjelm km_elmet@t-online.de wrote:
If there is a CW, then IIA always holds, yes. Suppose X is the CW and Y
is someone else. Then running the election without Y doesn't change
anything: X still beats everybody else pairwise and wins.
Thus if somehow you could prevent both sincere and tactical Condorcet
cycles, the method would be strategy-proof. (Strictly speaking, this
doesn't invalidate Arrow's theorem because a method that magically
forbids Condorcet cycles would fail universal domain.)
Well I don't really expect to prevent cycles, but just by doing nothing, I can plan on them being extremely rare, 0.2% of the time. So it's a faux-suppression of cycles, a pseudo-effect. Either way, I can say that the reason that IRV is good at avoiding the spoiler effect is solely because 99.4% of the time IRV elects the Condorcet winner. It's as effective at suppressing the spoiler effect as it is effective at electing the Condorcet winner. FairVote has to credit any success they claim for IRV to Condorcet. Because when IRV fails to elect the CW, it doesn't do shit about preventing the spoiler effect and all the pathologies cascading from that failure to prevent the election from being spoiled.
And I do consider that 0.4% of the time a CW exists and is not elected to be simply a failure of Hare RCV to do what it promises to do, when correcting that (by making the RCV method Condorcet-consistent), can only be a beneficial thing.
We know that Condorcet cycles can occur and in the U.S. there is one
known RCV election that demonstrated a cycle, the 2021 Minneapolis Ward
2 City Council election. It was a simple Rock-Paper-Scissors cycle;
Smith set of 3.
I think it's the case that we know that the necessary ingredients
for a cycle is a very close 3-way race and that there is at least a
2-dimensional political spectrum (Nolan chart) with candidates and
voters spread out all over the map in 2 dimensions, not in mostly a
linear spatial distribution. There has to be a sorta political
schizophrenia where a lotta voters are saying something like "If I can't
have my favorite, Bernie, then I'm voting for T****."
There could also be simple noise, i.e. some candidates are extremely
close, the voters randomly fill in what's really equal-rank, and the
random fill happens to create a Condorcet cycle.
IIRC, Worlobah and Arab were very close in the Minneapolis election, so
the cycle could be a result of noise, but I don't know the circumstances
well enough to say for sure.
On 01/21/2023 7:42 PM EST KenB kdbearman@gmail.com wrote:
= = = = =
[KB] That's correct. There was very little difference in political
positions among most of the Ward 2 candidates. I didn't pay close
attention to their specific positions because I live in a different ward.
- Ken Bearman, Minneapolis MN
I actually have family living in Minneapolis, but have no idea of what ward they are in or where they are regarding city politics. But that you're there, Ken, is very interesting. I wonder if the candidates themselves understand the unique situation the were in.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Hi Robert,
Well I don't really expect to prevent cycles, but just by doing nothing, I can plan on them
being extremely rare, 0.2% of the time. So it's a faux-suppression of cycles, a
pseudo-effect. Either way, I can say that the reason that IRV is good at avoiding the
spoiler effect is solely because 99.4% of the time IRV elects the Condorcet winner.
That sounds to me like a pretty big concession.
To the extent a method deals badly with spoilers, the interested parties will aim to avoid
the issue through their nomination choices or voting advice.
For example FPP always elects the CW on those ballots. Spoiled FPP elections aren't that
common. But we would probably say that's because they tried not to have 3+ candidates on
the ballot, not because FPP is so Condorcet-efficient.
I can't say with any certainty how different the nomination incentives under IRV are in
comparison to any specific Condorcet method, but they shouldn't be the exact same. One
obvious element is that a would-be IRV candidate expecting few first preferences is
probably not viable, and so might choose not to run for that reason. I hope Condorcet
incentives are noticeably different in this sort of vein. Otherwise this statement above
seems to tell me that IRV is 99.4% right already, that all we can do is fix the 0.6%, and
that seems a little demotivating to me.
Kevin
votingmethods.net
On 22.01.2023 10:08, robert bristow-johnson wrote:
On 01/21/2023 5:18 PM EST Kristofer Munsterhjelm km_elmet@t-online.de wrote:
If there is a CW, then IIA always holds, yes. Suppose X is the CW and Y
is someone else. Then running the election without Y doesn't change
anything: X still beats everybody else pairwise and wins.
Thus if somehow you could prevent both sincere and tactical Condorcet
cycles, the method would be strategy-proof. (Strictly speaking, this
doesn't invalidate Arrow's theorem because a method that magically
forbids Condorcet cycles would fail universal domain.)
Well I don't really expect to prevent cycles, but just by doing
nothing, I can plan on them being extremely rare, 0.2% of the time. So
it's a faux-suppression of cycles, a pseudo-effect. Either way, I can
say that the reason that IRV is good at avoiding the spoiler effect is
solely because 99.4% of the time IRV elects the Condorcet winner. It's
as effective at suppressing the spoiler effect as it is effective at
electing the Condorcet winner. FairVote has to credit any success they
claim for IRV to Condorcet. Because when IRV fails to elect the CW, it
doesn't do shit about preventing the spoiler effect and all the
pathologies cascading from that failure to prevent the election from
being spoiled.
Like Kevin, I would say it's worse. The way Plurality goes, after a few
spoiled elections, people figure out that they can't throw away their
vote by voting for a third party.
For IRV, I imagine that the typical progression would be that IRV allows
minor parties to grow (since they don't affect the outcome), then a
viable three-way contest happens, and then IRV more or less becomes a
random draw. Then the voters either figure out that they have to
compromise after all (which leads back to two-party rule), or they
repeal IRV.
But somehow, the step from small third party to three-way contest
doesn't seem to happen all that often in the US. I don't know why, but
whatever it is, it masks IRV's flaws.
In any case, if people go back to two-party voting to protect themselves
from IRV's failures, then those 0.6% have an outsize influence -- just
like with Plurality.
-km
I wrote:
Well I don't really expect to prevent cycles, but just by doing nothing, I can plan on them
being extremely rare, 0.2% of the time. So it's a faux-suppression of cycles, a
pseudo-effect. Either way, I can say that the reason that IRV is good at avoiding the
spoiler effect is solely because 99.4% of the time IRV elects the Condorcet winner.
On 01/22/2023 9:08 AM EST Kevin Venzke stepjak@yahoo.fr wrote:
That sounds to me like a pretty big concession.
We gotta be honest with the facts. I don't consider it a concession.
To the extent a method deals badly with spoilers, the interested parties will aim to avoid
the issue through their nomination choices or voting advice.
I doubt it. I doubt that, on the local, state, or national level, anyone will be looking at this to strategically nominate candidates that somehow will prevail if FPTP fails to get a majority or if IRV fails to elect the CW or if a Condorcet method has to deal with a cycle. I predict zero nominations will be materially affected by such considerations.
But if a failure happens, people will notice. And there will be a loss of trust in the system and the elected candidate may very well suffer from a perception of diminished legitimacy.
For example FPP always elects the CW on those ballots.
Oh, that seems to me to be a little disingenuous. There's only one ranking level other than unranked. You don't know who the CW is if voters were allowed to be more specific about their preferences. It's like the Approval folks insisting that their better at electing the CW than IRV.
Spoiled FPP elections aren't that common.
No. But they do happen and people remember. BTW, for FPTP we don't know for sure they are spoiled because, without the ranked ballot, we don't know for sure who voters for the ostensible spoiler would have voted for had that candidate not run (or if there was a ranked ballot).
In Vermont we remember two fairly recent high-profile races that were likely spoiled: the 2014 gubernatorial election and the 2021 Burlington mayoral election. But to know if they really were spoiled, we would need more information that only a ranked ballot gives us.
But we would probably say that's because they tried not to have 3+ candidates on
the ballot, not because FPP is so Condorcet-efficient.
"They" are who? Each party only nominates a number of candidates equal to the winning seats. Independents (and those signing their petition to get on the ballot) choose independently if they're gonna run or not.
I can't say with any certainty how different the nomination incentives under IRV are in
comparison to any specific Condorcet method, but they shouldn't be the exact same.
I think, without additional information, we have to assume they're the same. It's similar to people telling me that people would mark their ranked ballot differently if they knew it was which Condorcet method or IRV.
One
obvious element is that a would-be IRV candidate expecting few first preferences is
probably not viable, and so might choose not to run for that reason.
Well "few" is both a qualitative and quantitative term. The extreme hypothetical that IRV apologists like to toss at me is the milktoast candidate that is everyone's 2nd-choice and no one's first. Now how does Candidate Milktoast become the CW. The extreme they toss out is:
500 Left > Milktoast > Right
500 Right > Milktoast > Left
1 Milktoast > either Left or Right > the other one
It's a highly polarized and evenly split electorate. Now, even with only 1001 ballots, how likely is that going to happen? It's astronomically low.
Now it get's less astronomical. Assuming 3 significant candidates (all making it to the semifinal round), an IRV election that fails to elect the CW will fail because of the Center Squeeze effect. That is the seminal flaw. Now, what are the odds of that happening? Astronomically low? Or just very low? And that centrist candidate will have a lot of first-choice votes from voters, just less than the other two.
So I consider the Candidate Milktoast argument to be a red herring. In Burlington 2009, Andy Montroll was the centrist candidate but he's not milktoast. I presume the same is true for Nick Begich in Alaska.
I hope Condorcet
incentives are noticeably different in this sort of vein. Otherwise this statement above
seems to tell me that IRV is 99.4% right already, that all we can do is fix the 0.6%, and
that seems a little demotivating to me.
Well, we can only fix 0.4%. Condorcet, Arrow, Gibbard, and Satterthwaite tell us that the other 0.2% can't be fixed. (But we can do the best we can in that one election out of more than 500.)
While this avoidable failure happened only twice (that we know of in the United States), it can happen again. Occasionally we read about surgeons accidentally amputating the wrong limb because of a procedural mixup. When this happens, do we hear hospital officials defending their procedures saying "These procedures have served us well for decades and hundreds of surgeries, so we see no need to change our procedure at all"?
No. Even with a single catastrophic mistake, that is enough to motivate review and make changes in procedure to insure that such an unnecessary failure will not happen again. Now is precisely the time to recognize this failure that occurred in Burlington in 2009 and in Alaska in August 2022.
Suppose you were going to have life-preserving surgery and had a choice of two different surgical procedures, one that has a 0.6% table mortality and the other with 0.2%. All other things equal, which treatment would you choose?
Elections are about majorities. If we do not elect the majority candidate, then the votes coming from the voters supporting the minority-favored winning candidate had votes that had more juice, that counted more, than those votes from the greater number of voters supporting the majority candidate. Elections that elect the wrong candidate are failed elections. Fucking up an election is a big deal. Something to be avoided whenever we can possibly avoid it.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
On 01/22/2023 12:28 PM EST Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 22.01.2023 10:08, robert bristow-johnson wrote:
On 01/21/2023 5:18 PM EST Kristofer Munsterhjelm km_elmet@t-online.de wrote:
If there is a CW, then IIA always holds, yes. Suppose X is the CW and Y
is someone else. Then running the election without Y doesn't change
anything: X still beats everybody else pairwise and wins.
Thus if somehow you could prevent both sincere and tactical Condorcet
cycles, the method would be strategy-proof. (Strictly speaking, this
doesn't invalidate Arrow's theorem because a method that magically
forbids Condorcet cycles would fail universal domain.)
Well I don't really expect to prevent cycles, but just by doing
nothing, I can plan on them being extremely rare, 0.2% of the time. So
it's a faux-suppression of cycles, a pseudo-effect. Either way, I can
say that the reason that IRV is good at avoiding the spoiler effect is
solely because 99.4% of the time IRV elects the Condorcet winner. It's
as effective at suppressing the spoiler effect as it is effective at
electing the Condorcet winner. FairVote has to credit any success they
claim for IRV to Condorcet. Because when IRV fails to elect the CW, it
doesn't do shit about preventing the spoiler effect and all the
pathologies cascading from that failure to prevent the election from
being spoiled.
Like Kevin, I would say it's worse. The way Plurality goes, after a few
spoiled elections, people figure out that they can't throw away their
vote by voting for a third party.
For IRV, I imagine that the typical progression would be that IRV allows
minor parties to grow (since they don't affect the outcome), then a
viable three-way contest happens, and then IRV more or less becomes a
random draw. Then the voters either figure out that they have to
compromise after all (which leads back to two-party rule), or they
repeal IRV.
But somehow, the step from small third party to three-way contest
doesn't seem to happen all that often in the US. I don't know why, but
whatever it is, it masks IRV's flaws.
In any case, if people go back to two-party voting to protect themselves
from IRV's failures, then those 0.6% have an outsize influence -- just
like with Plurality.
The problem with repealing IRV to go back to plurality is that of a problem of education, misinformation, and even disinformation. Alaska is not the same as Burlington, but right now they are going through some of the same drama we did in 2009/2010.
There are the GOP persons somehow claiming that they were robbed. At least in Burlington, they had something of a case by just appealing to plurality: "Whoever has the most votes wins." But in Alaska those aggrieved GOP make no sense whatsoever because Sarah Palin never had the plurality of votes. That is the one sense that the topology of failure in Alaska 2022 is different than that in Burlington 2009. Otherwise the two elections look quite the same, with the center squeeze effect, the candidate on the right being the spoiler, and the candidate on the left being the beneficiary of a spoiled election.
In 2009, I was a voice crying in the wilderness. We, in Burlington, were faced with a false dichotomy: Hare IRV or FPTP. Pick the lesser of evils. It's a little different now. A third, smarter, alternative might be available.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Hi Robert,
Ok, you make your position clear that you don't really think choice of method imparts
different incentives on anyone.
I would think you would at least agree that if the Alaska race had been determined under
FPP, Begich would probably receive fewer votes, assuming he would insist on running, given
an expectation of placing third, with a greater likelihood of playing spoiler. (Ditto this
basic idea for most three-way IRV races.)
For example FPP always elects the CW on those ballots.
Oh, that seems to me to be a little disingenuous. There's only one ranking level other than
unranked. You don't know who the CW is if voters were allowed to be more specific about
their preferences. It's like the Approval folks insisting that their better at electing the
CW than IRV.
So what do you think would happen if FPP was actually conducted with rank ballots? I dare
speculate that most FPP elections are won with a full majority, so the use of rank ballots
would probably not dent FPP's observable Condorcet efficiency by much.
Although maybe you have the belief that while method choice doesn't affect voter behavior,
ballot format does, and so using rank ballots for FPP would result in half of elections
getting spoiled by voters refusing to use FPP strategy. I don't believe that, myself.
Kevin
votingmethods.net