Hay guys, look at this...
On 02/17/2023 11:05 PM EST KenB kdbearman@gmail.com wrote:
Robert, ordinarily I not only find most of your posts very interesting
(when I understand them, as I'm not a mathematician or well-versed on
all the technical stuff that most everyone here posts) but I also admire
your patience.
I don't think I have ever been known, by people who know and love me, to have much patience.
But in the case of your last two posts (below) I object
twice. Then I have a question about cycles.
(1) Your wrote, "If a simple majority of voters mark their ballots
preferring Candidate A over Candidate B, then Candidate B is not
elected. Why should Candidate B be elected? The IRV people twist
themselves into pretzels trying to answer that." My objection is this:
You describe a Condorcet election rule and then ask why [implicitly in
an IRV election] the Condorcet rule isn't followed.
It sorta is, 99.4% of the time with IRV. 99.4% of the time IRV succeeds at not electing Candidate B. 0.4% of the time, IRV fails when the failure was unnecessary and avoidable, and 0.2% of the time Arrow prevails and no method would have avoided electing a candidate that was not defeated by some other candidate in a head-to-head.
Your question isn't entirely honest. If you're talking about an
election where the criteria/rules are Condorcet, then no IRV (or FPTP)
proponent I know of will say B should be elected.
Oh, but they do, Ken. In Burlington 2009, Bob Kiss was Candidate B. In Alaska 2022 (August), Mary Peltola was Candidate B.
Now, I know at least two IRV proponents (one posted to this forum years ago and was the person who told me about this EM mailing list) that have told me that Candidate B was better because they had more "core support" than Candidate A and basically called Candidate A "Milquetoast" or "kiss the baby".
In this vid https://www.youtube.com/watch?v=j3s5jornaUY at index 56:41, Deb Otis does exactly that.
If you're not talking
about a Condorcet election, then your question is inapt and the
"pretzels" comment is just a bit insulting, I hate to say.
Well, they say RCV will elect candidates having more popular support, will discourage the election of fringe candidates (which seems to me that the opposite of "fringe" is more centrist), and then when their method exactly fails to do that, they come up with this excuse. Watch the video. (My presentation to Senate Gov Ops was earlier.)
They twist themselves into pretzels because their method failed at 3 times to do what they say it would do, 2 of the 3 times, a different method would have succeeded at doing what they say IRV is meant to do, but they don't want it and then, to justify not adopting the method that does even better, they go back on or twist what their message is. They say Montroll is bad because he's too bland. Why? Only because he's centrist.
--
(2) In your second post, responding to Forest Simmons, you wrote, "IRV
tried to simplify the debate with a method that essentially has no
overall principle." My objection is this: IRV proponents employ a
simple principle to explain the process, viz. that the vote counting in
the absence of a first-count majority is a series of runoff elections
using one ballot/precinct appearance.
That's a process. (And you didn't explain how the runoffs are carried out.) What's the principle?
At least FPTP has a simple principle that everyone can understand: "The candidate with the most votes wins." Condorcet has Majority Rule (which is simply what the Condorcet criterion is). What explicit principle does Hare IRV have?
If I misunderstood what your "no ... principle" comment was about,
please clarify for me. (I know you detest IRV, but that comment also
was just a bit insulting.)
Listen, I'll take IRV over Approval or STAR. Or even FPTP, but it's soooo hard to change something as fundamental as how we vote, that when we have a lesson to learn (and we do, in Vermont, but we're forgetting the lesson), what I detest is the disingenuity and the short memory people have about it.
--
(3) As I wrote above, I don't grok a lot of the technical stuff you
all discuss in the EM list.
I don't grok most of the stuff the other guys are talking about. Remember, I am just an activist, I am not one of the scholars like you see here arguing about esoteric stuff that I don't usually get.
I wrote my paper to connect the schlubs like me to the stuff these scholars debate about. But I only scratch the surface.
I think, though, that I understand what a cycle is.
Rock-Paper-Scissors. Condorcet Paradox.
So I'd like to give you more information about the
one-in-500+ you've referred to, the Minneapolis Ward 2 election in 2021,
before I ask a question.
There were five candidates on the ballot. (Scroll down to "Original
tabulation" here:
https://vote.minneapolismn.gov/results-data/election-results/2021/council-ward-2/)
The five were, in descending order, a Democratic Socialist; a Democrat
(called Democratic-Farmer-Labor or DFL in MN), who fell just short of
party endorsement; a Green; another DFLer; and a Republican.
The top three differed very little on issues or policies. However, there
were three Charter amendments on the ballot*; Question 2 would have
abolished the police department and replaced it with a Department of
Public Safety. (Q2, the only one that failed, was extremely
controversial and probably helped increase city-wide turnout.**)
BTW, the City of Burlington is also having similar controversial questions on our ballot in March. Just like that.
Of the
top three, Arab opposed it and Worlobah and Gordon supported it. That's
the only substantial issue difference I know of among the three.
I'm giving you all these local details because I wonder, Does "cycle"
mean much when the candidates in the cycle are essentially
interchangeable?
In a loose sense. It means that there is a sorta circular symmetry about it. No matter who you elect in the Smith set (who was Gordon, Worlobah, and Arab), there is someone else who beats that candidate.
Gordon beats Worlobah, Worlobah beats Arab, Arab beats Gordon. Condorcet is stumped. Who do you elect? IRV and Plurality elect Worlobah.
And a spoiler is unavoidable. Whether it's IRV or Condorcet. Since Worlobah was elected, then Arab was the spoiler, if Arab never ran and Ward 2 voters came to the polls and voted their same preferences with the remaining candidates, then Gordon would have won.
But if the method (whatever method) had elected Gordon instead, then that means Worlobah is the spoiler. And if Arab was elected, then Gordon is the spoiler.
Arrow Impossibility. Condorcet Paradox. Here is that paper: https://arxiv.org/abs/2111.09846
I.e., whichever of the three won, the supporters of
the other two would have approved of most official policy outcomes
anyway, so what does "cycle" mean outside of election theory?
It means a circular collective preference. Our ranked ballots are linear, not circular, so individually we can't do a cycle. If you like A better than B and you also like B better than C, then, as an individual we must assume you also like A better than C.
But collectively, we can be a little more schizoid about it. It's like a bunch of Bernie voters saying "If I can't have Bernie, then I'm voting for Trump."
OTOH, if
that interchangeability is irrelevant in discussing cycles, please
explain for me.
Without considering the actual politics, but just how people voted, it means that there is no way that you can satisfy this simple principle of Majority Rule:
If more voters mark their ballots preferring Candidate A
to Candidate B than the number of voters marking their
ballots to the contrary, then Candidate B is not elected.
That's a simple and fair rule. And that rule is necessary in order to consistently value our votes equally. If Candidate B were to be elected, even with fewer voters preferring him/her, then those fewer voters had votes that had more juice, that counted more, than the votes coming from the larger number of voters preferring Candidate A.
In all of the US RCV elections except Minneapolis Ward 2 2021, that simple and fair rule could have been satisfied. In all of the other elections (when the rule could have been satisfied) except two (Burlington 2009 and Alaska 2022) that rule was satisfied with IRV. So three anomalous elections. But only one of those elections would have to be anomalous, if we had a Condorcet-consistent method rather than Hare.
Now, what I told the folks on the Senate Gov Ops, if you needed surgery to correct a critical condition and you had a choice of procedures, one with a 0.2% table mortality and the other with a 0.6% table mortality, all other factors being the same, which procedure would you choose?
Minneapolis 2021 was the one time that the patient dies on the operating table and there ain't diddley squat that the surgeons can do to save the patient. But the table fatalities in Burlington 2009 and Alaska 2022 were preventable.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Let me rephrase the question ... suppose that there were only three
candidates and you already knew that they were in a rock paper scissors
pairwise preference cycle.
How would you decide which one to vote for if you could only vote for one?
That's the one you should make your first choice on an RCV ballot if the
cycle breaker is FPTP as you have been suggesting.
That decision is at least as difficult as the approval decision would be,
because under approval strategy you should approve that candidate X (the
one you would vote for if you had only one vote) AND also approve your
favorite if X was not already your favorite.
These are the same candidates that you would naturally rank on an RCV
ballot ... leaving the 3rd choice unranked ... the one that is neither your
favorite nor your compromise.
If you mis-triangulate the compromise in an FPTP election ... too bad: you
wasted your vote. But the approval ballot also counts towards everybody you
like better than your compromise, including your favorite.
That's why Approval is often proposed as a Condorcet completion method in
the absence of a runoff.
Implicit approval takes advantage of the natural strategy of truncating the
candidates you don't like, while ranking your preferred of the two front
runners AND anybody you liked better ... including your favorite ...
whether or not it was a frontrunner.
Yes, the cycle is already there ... but it cannot split the votes unless
the method allows vote splitting by not having any contingent backup vote.
Approval has the simplest backup vote capability ... any other method
requires some kind of runoff/elimination step to ameliorate the potential
vote split.
Example ballot profile:
40 A>B (Sincere is A>C)
35 B>C
25 C>A
Under Plurality A wins.
The Implicit Approval (fewest truncations) winner is B with only 25
truncations, compared with 35 A truncations and 40 C truncations.
This is a typical kind of ballot profile resulting from the burial by the
largest faction ... of the sincere Condorcet Winner (C in this example).
If the C supporters wanted to protect C, they could have truncated A:
25 C instead of 25 C>A.
This would not change the Plurality winner, but reinforces the Implicit
Approval winner, which gives the sincere CW a defense against burial by
punishing the burying faction ... electing their sincere last choice
instead of their sincere second choice.
With this defensive truncation B still has the fewest truncations 25, but
now the burial perpetrator A has way more truncations (60) than either of
the others ... no chance of success in their burial gambit.
Electing the Plurality choice (lacking a ballot CW) rewards the burial
perpetrator in this example .... so it encourages candidates with large
first place support to bury the sincere CW.
This example is typical in this respect ... the insincere burial (of
sincere CW) gambit is most tempting to the faction with the greatest first
place support.
On the other hand it is not tempting to bury the CW when lacking a CW the
implicit approval candidate is elected ... because this burial gambit will
almost certainly fail if not outright backfire.
It seems to me that anybody who understands why Approval is superior to
FPTP Plurality as an election method ... such a person should be able to
see how Approval is a better fall back alternative than Plurality (absent a
CW) .... an appreciable positive difference at no extra cost.
The little Dutch boy was right to put his finger in the dike ... a stitch
in time is in deed worth nine.
On Fri, Feb 17, 2023, 7:07 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
On 02/17/2023 9:44 PM EST Forest Simmons forest.simmons21@gmail.com
wrote:
Suppose the whole election was to choose one of the three candidates ...
no noncycle members were in the election at all.
Would you recommend FPTP Plurality over Approval?
I dunno. I would recommend Condorcet RCV and, only in the super-rare case
of a cycle, I would recommend plurality of first-choice votes because it's
no worse than we already have now with FPTP and it's simple to explain to
voters why that one candidate (the one with more first-choice votes than
anyone else) is, in some sense, uniquely more preferred by the electorate
over any other candidate.
In a competitive 3-way race, I dunno if Approval would be better than
FPTP. I do know, if it were Approval, that I would have a tactical
decision to make regarding my second-favorite candidate.
But with RCV, I would have no tactical decision to make. I would know
immediately what I would do with my second-fav.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
I think Robert was wise to propse Condorcet+FPTP. It's the Judgement of
Solomon, allowing him to step aside from endless debates about which
Condorcet method is best.
I don't agree with his reasoning "If a simple majority of voters
mark their ballots preferring Candidate A over Candidate B... Why should
B be elected?" This is the argument of the Condorcet Loser Criterion,
which implicitly assumes that a decision can be determined purely by the
signums of the margins, ignoring their amplitudes. Minimax violates
Condorcet Loser and I'm not the only person to support it.
But then I don't favour Kristofer's proposal either. My evaluation
suggests that burial is a particular threat for Condorcet methods, and
that in its presence their accuracies are: minimax 64%, condorcet+fptp
59%, copeland,fptp 48%. [Usual disclaimers apply.]
[I would say a word in favour of SPE with an FPTP preranking. This is a
symmetrisation of the method of Llull's De Arte Eleccionis of 1299, so
it's essentially the oldest Condorcet method in existence which isn't
vitiated by indecisiveness. Its virtue lies in its linear-time
countability, which is only a factor if counting is manual and there is
a risk of a sizeable number of candidates standing. SPE is about as
resistant to burial as is minimax.]
Wiser judgements than Solomon's are imaginable. If there was a an expert
consensus that among those methods simple enough to gain the approval of
voters and legislators, XYZ was best, then Robert would probably listen;
but the onus is on experts to build a consensus, not on advocates to
take sides.
CJC
On 18/02/2023 06:05, Forest Simmons wrote:
Let me rephrase the question ... suppose that there were only three
candidates and you already knew that they were in a rock paper
scissors pairwise preference cycle.
How would you decide which one to vote for if you could only vote for one?
That's the one you should make your first choice on an RCV ballot if
the cycle breaker is FPTP as you have been suggesting.
That decision is at least as difficult as the approval decision would
be, because under approval strategy you should approve that candidate
X (the one you would vote for if you had only one vote) AND also
approve your favorite if X was not already your favorite.
These are the same candidates that you would naturally rank on an RCV
ballot ... leaving the 3rd choice unranked ... the one that is neither
your favorite nor your compromise.
If you mis-triangulate the compromise in an FPTP election ... too bad:
you wasted your vote. But the approval ballot also counts towards
everybody you like better than your compromise, including your favorite.
That's why Approval is often proposed as a Condorcet completion method
in the absence of a runoff.
Implicit approval takes advantage of the natural strategy of
truncating the candidates you don't like, while ranking your preferred
of the two front runners AND anybody you liked better ... including
your favorite ... whether or not it was a frontrunner.
Yes, the cycle is already there ... but it cannot split the votes
unless the method allows vote splitting by not having any contingent
backup vote. Approval has the simplest backup vote capability ... any
other method requires some kind of runoff/elimination step to
ameliorate the potential vote split.
Example ballot profile:
40 A>B (Sincere is A>C)
35 B>C
25 C>A
Under Plurality A wins.
The Implicit Approval (fewest truncations) winner is B with only 25
truncations, compared with 35 A truncations and 40 C truncations.
This is a typical kind of ballot profile resulting from the burial by
the largest faction ... of the sincere Condorcet Winner (C in this
example).
If the C supporters wanted to protect C, they could have truncated A:
25 C instead of 25 C>A.
This would not change the Plurality winner, but reinforces the
Implicit Approval winner, which gives the sincere CW a defense against
burial by punishing the burying faction ... electing their sincere
last choice instead of their sincere second choice.
With this defensive truncation B still has the fewest truncations 25,
but now the burial perpetrator A has way more truncations (60) than
either of the others ... no chance of success in their burial gambit.
Electing the Plurality choice (lacking a ballot CW) rewards the burial
perpetrator in this example .... so it encourages candidates with
large first place support to bury the sincere CW.
This example is typical in this respect ... the insincere burial (of
sincere CW) gambit is most tempting to the faction with the greatest
first place support.
On the other hand it is not tempting to bury the CW when lacking a CW
the implicit approval candidate is elected ... because this burial
gambit will almost certainly fail if not outright backfire.
It seems to me that anybody who understands why Approval is superior
to FPTP Plurality as an election method ... such a person should be
able to see how Approval is a better fall back alternative than
Plurality (absent a CW) .... an appreciable positive difference at no
extra cost.
The little Dutch boy was right to put his finger in the dike ... a
stitch in time is in deed worth nine.
On Fri, Feb 17, 2023, 7:07 PM robert bristow-johnson
<rbj@audioimagination.com mailto:rbj@audioimagination.com> wrote:
On 02/17/2023 9:44 PM EST Forest Simmons
<forest.simmons21@gmail.com <mailto:forest.simmons21@gmail.com>>
wrote:
Suppose the whole election was to choose one of the three
candidates ... no noncycle members were in the election at all.
Would you recommend FPTP Plurality over Approval?
I dunno. I would recommend Condorcet RCV and, only in the
super-rare case of a cycle, I would recommend plurality of
first-choice votes because it's no worse than we already have now
with FPTP and it's simple to explain to voters why that one
candidate (the one with more first-choice votes than anyone else)
is, in some sense, uniquely more preferred by the electorate over
any other candidate.
In a competitive 3-way race, I dunno if Approval would be better
than FPTP. I *do* know, if it were Approval, that I would have a
tactical decision to make regarding my second-favorite candidate.
But with RCV, I would have no tactical decision to make. I would
know immediately what I would do with my second-fav.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
<mailto:rbj@audioimagination.com>
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for list info
On 2/18/23 10:42, Colin Champion wrote:
But then I don't favour Kristofer's proposal either. My evaluation
suggests that burial is a particular threat for Condorcet methods, and
that in its presence their accuracies are: minimax 64%, condorcet+fptp
59%, copeland,fptp 48%. [Usual disclaimers apply.]
That's fair; I was simply trying to find a minimal change to the method
that would at least grant Smith or something like it.
Really, what I'm concerned about is that there's such a, for lack of a
better term, steep cliff from the Condorcet domain down to the Plurality
domain. So everything's nice as long as you play on top of the mountain,
but if you misstep (i.e. produce a cycle), then you don't gradually
degrade, you fall directly into plain old Plurality, with all of its
vote splitting problems. The discontinuity seems like something that's
just asking to be exploited.
Do you know of any alternate "bang for the buck" methods that would be
simple enough to be accepted?
-km
Kristofer - firstly an apology, I gave the result for Condorcet//fptp
rather than Condorcet,fptp. The correct results are: minimax 64%,
condorcet+fptp 59%, copeland,fptp 53% (vice 47%).
As for other good, simple methods, I find it hard to say. Lots of
reasonably accurate methods are aesthetically objectionable for a range
of reasons; for instance I think that Condorcet+random is at least as
good as Condorcet+fptp (presumably because it's hard to manipulate), but
no one would be happy to see so prominent a role given to chance.
'Minisum' - which I think is the same as Tideman's "Simplified
Dodgson Rule" - is almost as good as minimax, but I can't see why anyone
would choose it in preference (it looks rather similar). It has the
drawback of having received little discussion in the literature.
Copeland,dblv is somewhat better than Copeland,fptp. The double vote
elects the candidate with the greatest sum of first and second
preferences. It's a lousy voting method but an effective tie-break
because it tends to blow up in the face of anyone who attempts tactical
voting.
Copeland,minimax is very good, but again why bother? Its resistance
to tactical voting comes from minimax; Copeland's method is little more
than a sleeping partner.
Copeland//Borda (which is one interpretation of Dasgupta/Maskin) is
probably slightly better than Copeland,fptp.
Benham's method and Black's are both pretty good. So are some of the
more complicated methods such as RP.
All this subject to the usual caveats about software reliablilty. The
results table is at
https://www.masterlyinactivity.com/condorcet/condorcet.html#results
Colin
On 18/02/2023 11:47, Kristofer Munsterhjelm wrote:
On 2/18/23 10:42, Colin Champion wrote:
But then I don't favour Kristofer's proposal either. My
evaluation suggests that burial is a particular threat for Condorcet
methods, and that in its presence their accuracies are: minimax 64%,
condorcet+fptp 59%, copeland,fptp 48%. [Usual disclaimers apply.]
That's fair; I was simply trying to find a minimal change to the
method that would at least grant Smith or something like it.
Really, what I'm concerned about is that there's such a, for lack of a
better term, steep cliff from the Condorcet domain down to the
Plurality domain. So everything's nice as long as you play on top of
the mountain, but if you misstep (i.e. produce a cycle), then you
don't gradually degrade, you fall directly into plain old Plurality,
with all of its vote splitting problems. The discontinuity seems like
something that's just asking to be exploited.
Do you know of any alternate "bang for the buck" methods that would be
simple enough to be accepted?
-km
Colin makes one argument for learning to live with the plurality winner
when there is no Condorcet winner. But it is only part of the reason.
Even if the social choice theorists could agree among themselves on one
best (or good enough) solution to the riddle of cycles, politicians and
the voting public would still not accept anything more complicated than
Robert's draft bill, or -- possibly -- "choose the IRV winner when there
is no Condorcet winner." (The latter only because IRV is already a
somewhat familiar procedure.) The fact that the theorists cancel each
other out is only part of this situation.
Robert said earlier that there is a "political problem that might
eclipse the technical problem" (emphasis added). I would say instead
that the political problem absolutely eclipses the technical problem.
--Bob Richard
------ Original Message ------
From "Colin Champion" colin.champion@routemaster.app
To election-methods@lists.electorama.com
Date 2/18/2023 1:42:36 AM
Subject Re: [EM] Hay guys, look at this...
I think Robert was wise to propse Condorcet+FPTP. It's the Judgement of
Solomon, allowing him to step aside from endless debates about which
Condorcet method is best.
I don't agree with his reasoning "If a simple majority of voters
mark their ballots preferring Candidate A over Candidate B... Why
should B be elected?" This is the argument of the Condorcet Loser
Criterion, which implicitly assumes that a decision can be determined
purely by the signums of the margins, ignoring their amplitudes.
Minimax violates Condorcet Loser and I'm not the only person to support
it.
But then I don't favour Kristofer's proposal either. My evaluation
suggests that burial is a particular threat for Condorcet methods, and
that in its presence their accuracies are: minimax 64%, condorcet+fptp
59%, copeland,fptp 48%. [Usual disclaimers apply.]
[I would say a word in favour of SPE with an FPTP preranking. This is a
symmetrisation of the method of Llull's De Arte Eleccionis of 1299, so
it's essentially the oldest Condorcet method in existence which isn't
vitiated by indecisiveness. Its virtue lies in its linear-time
countability, which is only a factor if counting is manual and there is
a risk of a sizeable number of candidates standing. SPE is about as
resistant to burial as is minimax.]
Wiser judgements than Solomon's are imaginable. If there was a an
expert consensus that among those methods simple enough to gain the
approval of voters and legislators, XYZ was best, then Robert would
probably listen; but the onus is on experts to build a consensus, not
on advocates to take sides.
CJC
On 18/02/2023 06:05, Forest Simmons wrote:
Let me rephrase the question ... suppose that there were only three
candidates and you already knew that they were in a rock paper
scissors pairwise preference cycle.
How would you decide which one to vote for if you could only vote for
one?
That's the one you should make your first choice on an RCV ballot if
the cycle breaker is FPTP as you have been suggesting.
That decision is at least as difficult as the approval decision would
be, because under approval strategy you should approve that candidate
X (the one you would vote for if you had only one vote) AND also
approve your favorite if X was not already your favorite.
These are the same candidates that you would naturally rank on an RCV
ballot ... leaving the 3rd choice unranked ... the one that is neither
your favorite nor your compromise.
If you mis-triangulate the compromise in an FPTP election ... too bad:
you wasted your vote. But the approval ballot also counts towards
everybody you like better than your compromise, including your
favorite.
That's why Approval is often proposed as a Condorcet completion method
in the absence of a runoff.
Implicit approval takes advantage of the natural strategy of
truncating the candidates you don't like, while ranking your preferred
of the two front runners AND anybody you liked better ... including
your favorite ... whether or not it was a frontrunner.
Yes, the cycle is already there ... but it cannot split the votes
unless the method allows vote splitting by not having any contingent
backup vote. Approval has the simplest backup vote capability ... any
other method requires some kind of runoff/elimination step to
ameliorate the potential vote split.
Example ballot profile:
40 A>B (Sincere is A>C)
35 B>C
25 C>A
Under Plurality A wins.
The Implicit Approval (fewest truncations) winner is B with only 25
truncations, compared with 35 A truncations and 40 C truncations.
This is a typical kind of ballot profile resulting from the burial by
the largest faction ... of the sincere Condorcet Winner (C in this
example).
If the C supporters wanted to protect C, they could have truncated A:
25 C instead of 25 C>A.
This would not change the Plurality winner, but reinforces the
Implicit Approval winner, which gives the sincere CW a defense against
burial by punishing the burying faction ... electing their sincere
last choice instead of their sincere second choice.
With this defensive truncation B still has the fewest truncations 25,
but now the burial perpetrator A has way more truncations (60) than
either of the others ... no chance of success in their burial gambit.
Electing the Plurality choice (lacking a ballot CW) rewards the burial
perpetrator in this example .... so it encourages candidates with
large first place support to bury the sincere CW.
This example is typical in this respect ... the insincere burial (of
sincere CW) gambit is most tempting to the faction with the greatest
first place support.
On the other hand it is not tempting to bury the CW when lacking a CW
the implicit approval candidate is elected ... because this burial
gambit will almost certainly fail if not outright backfire.
It seems to me that anybody who understands why Approval is superior
to FPTP Plurality as an election method ... such a person should be
able to see how Approval is a better fall back alternative than
Plurality (absent a CW) .... an appreciable positive difference at no
extra cost.
The little Dutch boy was right to put his finger in the dike ... a
stitch in time is in deed worth nine.
On Fri, Feb 17, 2023, 7:07 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
On 02/17/2023 9:44 PM EST Forest Simmons
forest.simmons21@gmail.com wrote:
Suppose the whole election was to choose one of the three
candidates ... no noncycle members were in the election at all.
Would you recommend FPTP Plurality over Approval?
I dunno. I would recommend Condorcet RCV and, only in the super-rare
case of a cycle, I would recommend plurality of first-choice votes
because it's no worse than we already have now with FPTP and it's
simple to explain to voters why that one candidate (the one with more
first-choice votes than anyone else) is, in some sense, uniquely more
preferred by the electorate over any other candidate.
In a competitive 3-way race, I dunno if Approval would be better than
FPTP. I do know, if it were Approval, that I would have a tactical
decision to make regarding my second-favorite candidate.
But with RCV, I would have no tactical decision to make. I would
know immediately what I would do with my second-fav.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
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I agree with Kristofer about the cliff analogy and take it a little
further ... are we going to say that because it will be needed only rarely
we can settle for any old simple alternative?
Even if there were no significantly better equally simple solution ... it
would still be shameful engineering practice:
"Boss I cannot give the green light to the Challenger until we fix that
O-Ring problem."
"But we have a deadline to keep ... and there is only a 0.4 percent chance
the thing will cause a problem ... so far, so good ... just cross your
fingers and sign here."
Here's a simple, acceptable method that beats many elaborate Condorcet
proposals including Copeland,Baldwin, Black, Nanson, MinMax, and many
others. If it turned out that twenty percent of Condorcrt election had
cycles in a certain odd ball electorate, it would still be a credible,
upstanding choice.
It has a natural segue from the simplest definition of a Condorcet Winner
into what to do if there is no CW:
A Condorcet Winner C is a candidate that is unbeaten pairwise. This means
that for any other candidate X, the number of ballots on which C outranks X
is greater than the number of ballots on which X outranks C.
In other words, C has a positive margin of support compared to any other
candidate X.
If there is no candidate with a positive margin of support compared to
every other candidate, then elect the candidate with the single greatest
margin of support relative to any other candidate.
Example:
48 C
28 A>B
24 B
A's margin of support relative to B is
28-24=4
B's margin over C is 28+24 vs 48 or 52-48 which equals 4, the same as A's
margin over B.
C's margin over A is 48-28=20, which is greater than either of the other
positive margins, so the Plurality winner C wins in this example.
Example2.
40 A>B
35 B>C
25 C
A's margin over B is 40-35=5
B's margin over C is 40+35-25=50
C's margin over A is 25+35-40=20
Candidate B is the max defeat margin winner with a max margin of 50.
So this time it would have been an embarrassment to elect the Plurality
winner A ... whose max support margin was a mere 5 votes, the least of all.
So can we agree to elect the candidate with the max fefest margin when
there is no candidate with all positive margins?
-Forest
On Sat, Feb 18, 2023, 3:47 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 2/18/23 10:42, Colin Champion wrote:
But then I don't favour Kristofer's proposal either. My evaluation
suggests that burial is a particular threat for Condorcet methods, and
that in its presence their accuracies are: minimax 64%, condorcet+fptp
59%, copeland,fptp 48%. [Usual disclaimers apply.]
That's fair; I was simply trying to find a minimal change to the method
that would at least grant Smith or something like it.
Really, what I'm concerned about is that there's such a, for lack of a
better term, steep cliff from the Condorcet domain down to the Plurality
domain. So everything's nice as long as you play on top of the mountain,
but if you misstep (i.e. produce a cycle), then you don't gradually
degrade, you fall directly into plain old Plurality, with all of its
vote splitting problems. The discontinuity seems like something that's
just asking to be exploited.
Do you know of any alternate "bang for the buck" methods that would be
simple enough to be accepted?
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
Colin,
You just floated a bunch of methods that are way more complicated and
objectively inferior in results compared to the specific method I
suggested, as well as compared to many other methods of the same type:
Absent a CW elect the candidate with the strongest defeat strength ...
period.
All of the other good methods that actually rival my suggestion in
simplicity (by not introducing elimination steps, approval cutoffs, scores,
equal-first rankings, etc.) are of this type ... I have wasted a lot of
time time looking elsewhere.
Here's a slightly less simple example of this promising type ...
Absent a CW, elect the strongest defeat winner where strength of defeat is
gauged by ... winning votes plus losing truncations.
Each pairwise defeat has a winner and a loser ... winning votes (wv) means
the pairwise support of the winner, i.e. the number of ballots on which the
winner out ranks the loser.
Losing truncations simply means the number of ballots on which the Loser is
unranked.
Let's look at our two previous examples in this light ...
48 C
28 A>B
24 B
A defeats B with strength 28 winning votes plus 48 losing truncations ... a
total strength of 76.
B beats C with 52 wv plus 52 losing truncations ... 104 total.
C beats A with total strength 48 plus 72, or 120.
So again, the Plurality winner C has the strongest defeat over any other
candidate by this wv+losing truncations gauge.
Example2:
40 A>B
35 B>C
25 C
A beats B with strength 40 wv plus 25 loser truncations... 65 total.
B beats C with 75 wv plus 40 truncations ... a total strength of 115.
C beats A with 60 wv plus 60 truncations. C wins.
If the C faction truncated A in anticipation of the A faction's burial of
C, it worked ... the defensive truncation saved the sincere CW.
This is (arguably) a strategic improvement over our slightly simpler
margins (wv minus lv) gauge that I am still recommending.
It's like the difference between an error detecting code and an error
correcting code.
-Forest
On Sat, Feb 18, 2023, 9:54 AM Colin Champion colin.champion@routemaster.app
wrote:
Kristofer - firstly an apology, I gave the result for Condorcet//fptp
rather than Condorcet,fptp. The correct results are: minimax 64%,
condorcet+fptp 59%, copeland,fptp 53% (vice 47%).
As for other good, simple methods, I find it hard to say. Lots of
reasonably accurate methods are aesthetically objectionable for a range of
reasons; for instance I think that Condorcet+random is at least as good as
Condorcet+fptp (presumably because it's hard to manipulate), but no one
would be happy to see so prominent a role given to chance.
'Minisum' - which I think is the same as Tideman's "Simplified Dodgson
Rule" - is almost as good as minimax, but I can't see why anyone would
choose it in preference (it looks rather similar). It has the drawback of
having received little discussion in the literature.
Copeland,dblv is somewhat better than Copeland,fptp. The double vote
elects the candidate with the greatest sum of first and second preferences.
It's a lousy voting method but an effective tie-break because it tends to
blow up in the face of anyone who attempts tactical voting.
Copeland,minimax is very good, but again why bother? Its resistance to
tactical voting comes from minimax; Copeland's method is little more than a
sleeping partner.
Copeland//Borda (which is one interpretation of Dasgupta/Maskin) is
probably slightly better than Copeland,fptp.
Benham's method and Black's are both pretty good. So are some of the
more complicated methods such as RP.
All this subject to the usual caveats about software reliablilty. The
results table is at
https://www.masterlyinactivity.com/condorcet/condorcet.html#results
Colin
On 18/02/2023 11:47, Kristofer Munsterhjelm wrote:
On 2/18/23 10:42, Colin Champion wrote:
But then I don't favour Kristofer's proposal either. My evaluation
suggests that burial is a particular threat for Condorcet methods, and that
in its presence their accuracies are: minimax 64%, condorcet+fptp 59%,
copeland,fptp 48%. [Usual disclaimers apply.]
That's fair; I was simply trying to find a minimal change to the method
that would at least grant Smith or something like it.
Really, what I'm concerned about is that there's such a, for lack of a
better term, steep cliff from the Condorcet domain down to the Plurality
domain. So everything's nice as long as you play on top of the mountain,
but if you misstep (i.e. produce a cycle), then you don't gradually
degrade, you fall directly into plain old Plurality, with all of its vote
splitting problems. The discontinuity seems like something that's just
asking to be exploited.
Do you know of any alternate "bang for the buck" methods that would be
simple enough to be accepted?
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
Hi Forest,
Le samedi 18 février 2023 à 13:19:10 UTC−6, Forest Simmons forest.simmons21@gmail.com a écrit :
Here's a simple, acceptable method that beats many elaborate Condorcet proposals including
Copeland,Baldwin, Black, Nanson, MinMax, and many others. If it turned out that twenty
percent of Condorcrt election had cycles in a certain odd ball electorate, it would still
be a credible, upstanding choice.
It has a natural segue from the simplest definition of a Condorcet Winner into what to do
if there is no CW:
A Condorcet Winner C is a candidate that is unbeaten pairwise. This means that for any
other candidate X, the number of ballots on which C outranks X is greater than the number
of ballots on which X outranks C.
In other words, C has a positive margin of support compared to any other candidate X.
If there is no candidate with a positive margin of support compared to every other
candidate, then elect the candidate with the single greatest margin of support relative to
any other candidate.
I'll call this method C//MaxMargin or C//MM.
One reason I can "live and let live" in regards to C,FPP is that it at least satisfies the
Plurality criterion. I think methods that fail this will be hard to propose.
(I also think that being likely able to guess which candidate will benefit from a burial
strategy in C,FPP might at least create some stability there, even if the ultimate result
might be compromise incentive / nomination disincentive, whenever voters perceive that
supporters of the FPP winner have a burial strategy that can't be defended against in any
other way. Put differently, I don't think we would see backfiring burial strategies under
C,FPP, due to the one-sidedness of which voters would want to try burying.)
Realistically C//MM resolves cycle scenarios by electing the candidate with the biggest win
over the weakest candidate. (The winning score probably won't come from a match-up between
strong candidates.) This gives it a good share of the truncation incentive seen under
C//Approval, as it's very clear that adding a lower preference for some candidate could
hand them the win.
But (experimentally) C//MM doesn't see C//A's reduction in burial incentive, perhaps
because you are using the margin, so burial can be used to undermine a candidate even if
you don't defeat that candidate. This is also easy to imagine: A few random voters casting
insincere votes burying a frontrunner could certainly be enough to take the win away from
them.
When it comes to compromise incentive, C//MM is considerably better than C,FPP, although
hardly amazing. Compromise incentive is most relevant to the concerns about the use of FPP
in the method, so perhaps C//MM accomplishes its mission.
Kevin
votingmethods.net
Thanks, Kevin ... your wide experience is very valuable.
On Sat, Feb 18, 2023, 2:18 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest,
Le samedi 18 février 2023 à 13:19:10 UTC−6, Forest Simmons <
forest.simmons21@gmail.com> a écrit :
Here's a simple, acceptable method that beats many elaborate Condorcet
proposals including
Copeland,Baldwin, Black, Nanson, MinMax, and many others. If it turned
out that twenty
percent of Condorcrt election had cycles in a certain odd ball
electorate, it would still
be a credible, upstanding choice.
It has a natural segue from the simplest definition of a Condorcet
Winner into what to do
if there is no CW:
A Condorcet Winner C is a candidate that is unbeaten pairwise. This
means that for any
other candidate X, the number of ballots on which C outranks X is
greater than the number
of ballots on which X outranks C.
In other words, C has a positive margin of support compared to any other
candidate X.
If there is no candidate with a positive margin of support compared to
every other
candidate, then elect the candidate with the single greatest margin of
support relative to
any other candidate.
I'll call this method C//MaxMargin or C//MM.
One reason I can "live and let live" in regards to C,FPP is that it at
least satisfies the
Plurality criterion. I think methods that fail this will be hard to
propose.
(I also think that being likely able to guess which candidate will benefit
from a burial
strategy in C,FPP might at least create some stability there, even if the
ultimate result
might be compromise incentive / nomination disincentive, whenever voters
perceive that
supporters of the FPP winner have a burial strategy that can't be defended
against in any
other way. Put differently, I don't think we would see backfiring burial
strategies under
C,FPP, due to the one-sidedness of which voters would want to try burying.)
Realistically C//MM resolves cycle scenarios by electing the candidate
with the biggest win
over the weakest candidate. (The winning score probably won't come from a
match-up between
strong candidates.) This gives it a good share of the truncation incentive
seen under
C//Approval, as it's very clear that adding a lower preference for some
candidate could
hand them the win.
But (experimentally) C//MM doesn't see C//A's reduction in burial
incentive, perhaps
because you are using the margin, so burial can be used to undermine a
candidate even if
you don't defeat that candidate. This is also easy to imagine: A few
random voters casting
insincere votes burying a frontrunner could certainly be enough to take
the win away from
them.
When it comes to compromise incentive, C//MM is considerably better than
C,FPP, although
hardly amazing. Compromise incentive is most relevant to the concerns
about the use of FPP
in the method, so perhaps C//MM accomplishes its mission.
Kevin
votingmethods.net