Hay guys, look at this...
On 2/20/23 01:21, Kevin Venzke wrote:
I'd wondered whether Robert didn't have any intellectual commitent to the criterion, but
had used it in argument against IRV and therefore found his options limited.
I don't quite follow that since IRV satisfies Condorcet Loser.
I think the point is this: Robert says that if X beats Y pairwise, then
Y shouldn't be elected. This requires the Condorcet winner criterion to
be satisfied, because otherwise X = the CW, Y = anybody else violates it.
But suppose that a method didn't pass Condorcet loser. Then X = someone
who's not the Condorcet loser, Y = the Condorcet loser would violate the
criterion.
So this leads to a problem when proposing Condorcet,Plurality because if
a Condorcet loser is elected, then it seems to go against the spirit of
the criterion. About the only response I can think of is that if there's
a cycle, it's impossible to satisfy the criterion (because everyone has
someone else beating him), thus the criterion is suspended entirely for
such elections.
The hard mode interpretation would be that the constraint implies Smith.
But the problem then is that there are so few ways to make a method
that's both Smith and simple to express in natural language. There are
two relatively easy approaches, each with drawbacks: Copeland -- or
elimination (e.g. Benham); and with elimination you lose monotonicity
and (usually) summability[1], whereas Copeland seems to in some sense
always be vulnerable to strategy, no matter what you combine it with.
That's why it's hard mode :-)
-km
[1] Some uncommon exceptions include Nanson, Baldwin, and Raynaud.
Funnily, it seems that combining Copeland and Borda to Copeland//Borda
produces something both summable and monotone.
One thing I'm uncomfortable with is the notion of "unranked" candidates. If there are 4 candidates - A, B, C and D - and one ballot has A>B>C>D and another just A>B>C, they should be treated as the same. Unranked is just (possibly joint) last and I don't see it as having special status.
Toby
On Monday, 20 February 2023 at 01:28:18 GMT, Forest Simmons forest.simmons21@gmail.com wrote:
I have learned a lot from the "hay guys" thread that spontaneously upgraded into this "hey guys" thread.
Colin Champion made some very helpful points and pointers about the psychology of what we are involved in. Many similar practical considerations contributed by all participants.
Several suggestions have been made about how to complete this sentence:
"Lacking a candidate that defeats every other candidate in pairwise head-to-head comparisons, elect the candidate that ..."
I can live with most of those suggestions ... which is neither here nor there in the grand scheme of things ... but I hope haven't offended anybody or discouraged anybody's contributions to these explorations.
Several people have said, "Why not just ...?"
And I thought, "Why didn't I think of that?"
The most promising idea I am currently thinking along these lines goes like this:
Elect the pairwise undefeated champion ... or lacking such a champion, elect the winner of the strongest pairwise defeat ... meaning the pairwise contest with the greatest sum of winner approval and loser disapproval ... winner approval measured by winning votes ... the number of ballots on which the winner outranks the loser... loser disapproval measured by loser abstentions ... the number of ballots on which the pairwise loser is unranked.
So winning votes plus loser abstentions is my proposal for defeat strength ... not to be used in Rsnked Pairs ... but just in the first and strongest step of RP ... and then only in the absence of a Condorcet Winner.
For now it's just an idea needing an experimental shake down beyond my meager manual tests.
But who knows?
-Forest
On Sun, Feb 19, 2023, 10:47 AM Colin Champion colin.champion@routemaster.app wrote:
I asked Kristofer whether Condorcet+FPTP complied with the Condorcet Loser criterion. He replied "probably not" with a sketch proof, and then gave the following example.
<quote> [preliminary election]40: L>C>R
42: R>C>L
10: C>L>R
R is the Condorcet loser and Plurality winner. (L is the IRV winner.)
Now clone C, the CW:
40: L>Ca>Cb>Cc>R
42: R>Cb>Cc>Ca>L
10: Cc>Ca>Cb>L>R
There's no CW, so Plurality elects R, the Condorcet loser. (Incidentally, R ties for first in minmax.)
Seems OK. Verified with https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html.
</quote>
I'd wondered whether Robert didn't have any intellectual commitent to the criterion, but had used it in argument against IRV and therefore found his options limited.
CJC
On 19/02/2023 17:31, Kristofer Munsterhjelm wrote:
On 2/19/23 16:36, Colin Champion wrote:
"Politicians and the voting public would not accept anything more complicated than X" is my own favourite line of argument - but I substitute my own value for X(minimax). I know that my judgement is coloured by my preferences. There's a surprising degree of dissent over which methods are simpler than which, and where the boundary should be drawn. People who deal directly with politicians and the voting public can no doubt get closer to the truth than people whose interest is predominantly theoretical, but I wish there was an authoritative and objective source of information. If only some behavioural psychologist was funded to investigate the question...
To be finicky, the issue isn't exactly one of simplicity but rather one of psychological acceptability, which includes the notions of whether a method "makes sense" to the average onlooker, and whether it is seen as conferring legitimacy on its winner rather than being an unmotivated piece of jiggery pokery.
Notwithstanding all this... you and Robert may well be right.
FWIW, I suspect the complexity people are willing to accept depends on their trust in the political process in general. For instance, some local New Zealand elections use Meek's method, which is complex however you put it.[1] And I wouldn't be prepared to explain the pretty messy greedy algorithm used to allocate party list top-up seats here (in Norway), but people seem to accept it.[2]
I don't think Robert could use minmax because the criterion he's using is "if more people prefer X to Y than vice versa, then Y is not elected". That seems to imply at least Condorcet loser. I'm not sure, though -- if you're particularly critical, you could even say it implies Smith, but I don't think Robert had that in mind.
-km
[1] I wonder what the legal language for that is... it's basically impossible to do by hand.
[2] IMHO, biproportional apportionment is much simpler. I suspect what's keeping it from being changed is mostl inertia.
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
Hi Kristofer,
Le lundi 20 février 2023 à 05:08:01 UTC−6, Kristofer Munsterhjelm km_elmet@t-online.de a écrit :
I don't quite follow that since IRV satisfies Condorcet Loser.
I think the point is this: Robert says that if X beats Y pairwise, then
Y shouldn't be elected. This requires the Condorcet winner criterion to
be satisfied, because otherwise X = the CW, Y = anybody else violates it.
But suppose that a method didn't pass Condorcet loser. Then X = someone
who's not the Condorcet loser, Y = the Condorcet loser would violate the
criterion.
So this leads to a problem when proposing Condorcet,Plurality because if
a Condorcet loser is elected, then it seems to go against the spirit of
the criterion.
If I play devil's advocate, the argument says the winner shouldn't lose pairwise, not that
they should win pairwise. Adding a junk candidate for the FPP winner to defeat, so that the
FPP winner is no longer Condorcet Loser, doesn't seem like it would improve the FPP
winner's electability under the argument.
About the only response I can think of is that if there's
a cycle, it's impossible to satisfy the criterion (because everyone has
someone else beating him), thus the criterion is suspended entirely for
such elections.
It's plausible. "MDD" methods work on this idea, that if every candidate had a full
majority against them then the filter just does nothing instead.
Ideally you'd want an argument that can't disqualify everyone.
The hard mode interpretation would be that the constraint implies Smith.
But the problem then is that there are so few ways to make a method
that's both Smith and simple to express in natural language. There are
two relatively easy approaches, each with drawbacks: Copeland -- or
elimination (e.g. Benham); and with elimination you lose monotonicity
and (usually) summability[1], whereas Copeland seems to in some sense
always be vulnerable to strategy, no matter what you combine it with.
That's why it's hard mode :-)
Additionally I don't find this satisfying. The reasonableness of Smith isn't obvious enough
to be a mere footnote on this argument. I think it needs its own arguments.
Barely relevant, but there's a property I use privately called "conservative reform." It
says that the winner must either defeat the FPP winner pairwise, or else be the FPP
winner. It brings to my mind the possible sentiment that the FPP winner is special, and can
always be elected if we don't know what else to do.
(This property is probably more conservative than needed, considering that IRV doesn't
satisfy it. However, I do wonder if people would protest if it happened in some IRV
election that the method winner is pairwise defeated by the first-round winner.)
Kevin
votingmethods.net
Toby,
Thanks for you thoughtful critique!
Do you think it's worth the extra verbiage of conflating truncation and
bottom rank?
Many times I have conflated them by saying D has "Ballot Bottom Status"
because it outranks no candidate.
But imho leaving the distinction intact is both simpler and totally
harmless ... it just gives voters an optional lever to pull if they want to.
Also in the present context it confers ISDA compliance. Elimination of
Smith dominated candidates does not change the unranked/abstention count of
any remaining candidate, but it may well change the Ballot Bottom Status of
some of them.
One can take the point of view that
the ordinal information is the same on both ballots, but the implicit
approval is different. The truncation boundary can be considered as an
implicit approval cutoff ... awkward, but better than anything possible
under strict Universal Domain constraints.
With regard to clone dependence ... doesn't it satisfy clone-winner, unlike
any of the other suggestions in this thread?
Doesn't Approval, including implicit approval, satisfy a version of clone
independence? It does under the assumption that true clones are not
interrupted by the virtual approval cutoff candidate (truncation boundary
in this case) any more than they are by other candidates.
Our defeat strength gauge is winning pairwise support plus losing
truncations.
If you replace the defeat winner with a precise clone set ... each member
of the clone set will have the same pairwise support against the loser, so
they will be tied for the strongest victory over the same loser. In
practice, the clone sets are not precise ... but if they were the tie could
easily be broken by applying the method recursively to the tied set ... if
no simpler method existed ... like choosing the tied candidate with the
greatest equal-first count ... another helpful expedient that exists
outside of the strict UD rules.
Another option that makes hardly any difference to the method except to
make its description more wordy, is to gauge defeat strength by winner
implicit approval plus loser implicit disapproval.
Implicit disapproval is already the number of truncations.
And every ballot that pairwise supports the winner over the loser already
contributes to the winner's implicit approval .... so the implicit approval
count will be an increase over the pairwise support.
But is it worth the extra wordiness required ... talking about implicit
approval? We studiously avoided that talk by using "winning votes" a
familiar notion in the context of defeat strength as a proxy for implicit
approval.
Ultimately, if it turns out to make any difference, we should go with the
one that works best .... even if it takes more verbiage.
-Forest
On Mon, Feb 20, 2023, 3:14 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
One thing I'm uncomfortable with is the notion of "unranked" candidates.
If there are 4 candidates - A, B, C and D - and one ballot has A>B>C>D and
another just A>B>C, they should be treated as the same. Unranked is just
(possibly joint) last and I don't see it as having special status.
Toby
On Monday, 20 February 2023 at 01:28:18 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
I have learned a lot from the "hay guys" thread that spontaneously
upgraded into this "hey guys" thread.
Colin Champion made some very helpful points and pointers about the
psychology of what we are involved in. Many similar practical
considerations contributed by all participants.
Several suggestions have been made about how to complete this sentence:
"Lacking a candidate that defeats every other candidate in pairwise
head-to-head comparisons, elect the candidate that ..."
I can live with most of those suggestions ... which is neither here nor
there in the grand scheme of things ... but I hope haven't offended anybody
or discouraged anybody's contributions to these explorations.
Several people have said, "Why not just ...?"
And I thought, "Why didn't I think of that?"
The most promising idea I am currently thinking along these lines goes
like this:
Elect the pairwise undefeated champion ... or lacking such a champion,
elect the winner of the strongest pairwise defeat ... meaning the pairwise
contest with the greatest sum of winner approval and loser disapproval ...
winner approval measured by winning votes ... the number of ballots on
which the winner outranks the loser... loser disapproval measured by loser
abstentions ... the number of ballots on which the pairwise loser is
unranked.
So winning votes plus loser abstentions is my proposal for defeat strength
... not to be used in Rsnked Pairs ... but just in the first and strongest
step of RP ... and then only in the absence of a Condorcet Winner.
For now it's just an idea needing an experimental shake down beyond my
meager manual tests.
But who knows?
-Forest
On Sun, Feb 19, 2023, 10:47 AM Colin Champion <
colin.champion@routemaster.app> wrote:
I asked Kristofer whether Condorcet+FPTP complied with the Condorcet Loser
criterion. He replied "probably not" with a sketch proof, and then gave the
following example.
40: L>C>R
42: R>C>L
10: C>L>R
R is the Condorcet loser and Plurality winner. (L is the IRV winner.)
Now clone C, the CW:
40: L>Ca>Cb>Cc>R
42: R>Cb>Cc>Ca>L
10: Cc>Ca>Cb>L>R
There's no CW, so Plurality elects R, the Condorcet loser. (Incidentally,
R ties for first in minmax.)
Seems OK. Verified with
https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html.
I'd wondered whether Robert didn't have any intellectual commitent to the
criterion, but had used it in argument against IRV and therefore found his
options limited.
CJC
On 19/02/2023 17:31, Kristofer Munsterhjelm wrote:
On 2/19/23 16:36, Colin Champion wrote:
"Politicians and the voting public would not accept anything more
complicated than X" is my own favourite line of argument - but I substitute
my own value for X(minimax). I know that my judgement is coloured by my
preferences. There's a surprising degree of dissent over which methods are
simpler than which, and where the boundary should be drawn. People who deal
directly with politicians and the voting public can no doubt get closer to
the truth than people whose interest is predominantly theoretical, but I
wish there was an authoritative and objective source of information. If
only some behavioural psychologist was funded to investigate the
question...
To be finicky, the issue isn't exactly one of simplicity but rather one of
psychological acceptability, which includes the notions of whether a method
"makes sense" to the average onlooker, and whether it is seen as conferring
legitimacy on its winner rather than being an unmotivated piece of jiggery
pokery.
Notwithstanding all this... you and Robert may well be right.
FWIW, I suspect the complexity people are willing to accept depends on
their trust in the political process in general. For instance, some local
New Zealand elections use Meek's method, which is complex however you put
it.[1] And I wouldn't be prepared to explain the pretty messy greedy
algorithm used to allocate party list top-up seats here (in Norway), but
people seem to accept it.[2]
I don't think Robert could use minmax because the criterion he's using is
"if more people prefer X to Y than vice versa, then Y is not elected". That
seems to imply at least Condorcet loser. I'm not sure, though -- if you're
particularly critical, you could even say it implies Smith, but I don't
think Robert had that in mind.
-km
[1] I wonder what the legal language for that is... it's basically
impossible to do by hand.
[2] IMHO, biproportional apportionment is much simpler. I suspect what's
keeping it from being changed is mostl inertia.
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
I disagree with Toby here, at least under some circumstances. But I'm
speaking as a voter, not as a student of social choice theory. To me as
a voter, there can be a huge difference between ranking a candidate last
and leaving that candidate unranked. To put it simply, under some
voting rules there will always be candidates that I am unwilling to vote
for, even in last place.
This depends on the voting rule. If the rule makes it impossible for my
last place ranking to ever help the candidate(s) I oppose, and if I can
rank multiple candidates equal bottom, then I am willing to assign a
rank to every candidate when truncation is not allowed. But if the rule
leaves open the possibility that my last place ranking will end up
helping a candidate I oppose get elected, then I would be obligated, as
a matter of conscience, to abstain from voting at all. This can happen,
for example, in IRV when truncation is not allowed.
If I were Australian, I would end up paying the fine for not voting
after every election.
--Bob Richard
------ Original Message ------
From "Toby Pereira" tdp201b@yahoo.co.uk
To "Colin Champion" colin.champion@routemaster.app; "Forest Simmons"
forest.simmons21@gmail.com
Cc "EM" election-methods@lists.electorama.com
Date 2/20/2023 3:14:01 AM
Subject Re: [EM] Hey guys, look at this...
One thing I'm uncomfortable with is the notion of "unranked"
candidates. If there are 4 candidates - A, B, C and D - and one ballot
has A>B>C>D and another just A>B>C, they should be treated as the same.
Unranked is just (possibly joint) last and I don't see it as having
special status.
Toby
Well I think a problem with ranking = implicit approval is that a voter might have a preference between two candidates they hate just as much as between two candidates they like, and they would have to implicitly approve one of these candidates to make the distinction.
I sometimes think that Condorcet with cardinal ballots would work better. You have scores or grades, but don't use the values themselves for anything, just the ordinal positions. This way you can easily equal rank at the top, bottom, or somewhere in the middle, not just at the end by not ranking the candidates you hate.
I also think it could alleviate some of the problems of burial. Burial isn't necessarily just a problem because of deliberate strategising. If there are two main candidates, one that a voter likes (A), and one that a voter dislikes (B), and couple of relative unknowns (C and D), there seems to be a prevailing view that because A and B are the "strongest" candidates, an honest vote would be something like A>B>C>D, people would only bottom rank B as some sort of burial strategy, which must be overcome by the method. But I don't think that's the case. Most voters would probably bottom rank B anyway in this case, and do something like A>C>D>B or just A>C>B. But with cardinal ballots, they would be more likely to simply give a zero score to all the candidates they dislike and non-entities. B would therefore be less likely to be buried under other candidates.
As for the clone thing, I'm not entirely sure what all the different clone definitions are - e.g. I can't easily find a definition of clone winner.
Toby
On Monday, 20 February 2023 at 19:22:13 GMT, Forest Simmons forest.simmons21@gmail.com wrote:
Toby,
Thanks for you thoughtful critique!
Do you think it's worth the extra verbiage of conflating truncation and bottom rank?
Many times I have conflated them by saying D has "Ballot Bottom Status" because it outranks no candidate.
But imho leaving the distinction intact is both simpler and totally harmless ... it just gives voters an optional lever to pull if they want to.
Also in the present context it confers ISDA compliance. Elimination of Smith dominated candidates does not change the unranked/abstention count of any remaining candidate, but it may well change the Ballot Bottom Status of some of them.
One can take the point of view thatthe ordinal information is the same on both ballots, but the implicit approval is different. The truncation boundary can be considered as an implicit approval cutoff ... awkward, but better than anything possible under strict Universal Domain constraints.
With regard to clone dependence ... doesn't it satisfy clone-winner, unlike any of the other suggestions in this thread?
Doesn't Approval, including implicit approval, satisfy a version of clone independence? It does under the assumption that true clones are not interrupted by the virtual approval cutoff candidate (truncation boundary in this case) any more than they are by other candidates.
Our defeat strength gauge is winning pairwise support plus losing truncations.
If you replace the defeat winner with a precise clone set ... each member of the clone set will have the same pairwise support against the loser, so they will be tied for the strongest victory over the same loser. In practice, the clone sets are not precise ... but if they were the tie could easily be broken by applying the method recursively to the tied set ... if no simpler method existed ... like choosing the tied candidate with the greatest equal-first count ... another helpful expedient that exists outside of the strict UD rules.
Another option that makes hardly any difference to the method except to make its description more wordy, is to gauge defeat strength by winner implicit approval plus loser implicit disapproval.
Implicit disapproval is already the number of truncations.
And every ballot that pairwise supports the winner over the loser already contributes to the winner's implicit approval .... so the implicit approval count will be an increase over the pairwise support.
But is it worth the extra wordiness required ... talking about implicit approval? We studiously avoided that talk by using "winning votes" a familiar notion in the context of defeat strength as a proxy for implicit approval.
Ultimately, if it turns out to make any difference, we should go with the one that works best .... even if it takes more verbiage.
-Forest
On Mon, Feb 20, 2023, 3:14 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
One thing I'm uncomfortable with is the notion of "unranked" candidates. If there are 4 candidates - A, B, C and D - and one ballot has A>B>C>D and another just A>B>C, they should be treated as the same. Unranked is just (possibly joint) last and I don't see it as having special status.
Toby
On Monday, 20 February 2023 at 01:28:18 GMT, Forest Simmons forest.simmons21@gmail.com wrote:
I have learned a lot from the "hay guys" thread that spontaneously upgraded into this "hey guys" thread.
Colin Champion made some very helpful points and pointers about the psychology of what we are involved in. Many similar practical considerations contributed by all participants.
Several suggestions have been made about how to complete this sentence:
"Lacking a candidate that defeats every other candidate in pairwise head-to-head comparisons, elect the candidate that ..."
I can live with most of those suggestions ... which is neither here nor there in the grand scheme of things ... but I hope haven't offended anybody or discouraged anybody's contributions to these explorations.
Several people have said, "Why not just ...?"
And I thought, "Why didn't I think of that?"
The most promising idea I am currently thinking along these lines goes like this:
Elect the pairwise undefeated champion ... or lacking such a champion, elect the winner of the strongest pairwise defeat ... meaning the pairwise contest with the greatest sum of winner approval and loser disapproval ... winner approval measured by winning votes ... the number of ballots on which the winner outranks the loser... loser disapproval measured by loser abstentions ... the number of ballots on which the pairwise loser is unranked.
So winning votes plus loser abstentions is my proposal for defeat strength ... not to be used in Rsnked Pairs ... but just in the first and strongest step of RP ... and then only in the absence of a Condorcet Winner.
For now it's just an idea needing an experimental shake down beyond my meager manual tests.
But who knows?
-Forest
On Sun, Feb 19, 2023, 10:47 AM Colin Champion colin.champion@routemaster.app wrote:
I asked Kristofer whether Condorcet+FPTP complied with the Condorcet Loser criterion. He replied "probably not" with a sketch proof, and then gave the following example.
<quote> [preliminary election]40: L>C>R
42: R>C>L
10: C>L>R
R is the Condorcet loser and Plurality winner. (L is the IRV winner.)
Now clone C, the CW:
40: L>Ca>Cb>Cc>R
42: R>Cb>Cc>Ca>L
10: Cc>Ca>Cb>L>R
There's no CW, so Plurality elects R, the Condorcet loser. (Incidentally, R ties for first in minmax.)
Seems OK. Verified with https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html.
</quote>
I'd wondered whether Robert didn't have any intellectual commitent to the criterion, but had used it in argument against IRV and therefore found his options limited.
CJC
On 19/02/2023 17:31, Kristofer Munsterhjelm wrote:
On 2/19/23 16:36, Colin Champion wrote:
"Politicians and the voting public would not accept anything more complicated than X" is my own favourite line of argument - but I substitute my own value for X(minimax). I know that my judgement is coloured by my preferences. There's a surprising degree of dissent over which methods are simpler than which, and where the boundary should be drawn. People who deal directly with politicians and the voting public can no doubt get closer to the truth than people whose interest is predominantly theoretical, but I wish there was an authoritative and objective source of information. If only some behavioural psychologist was funded to investigate the question...
To be finicky, the issue isn't exactly one of simplicity but rather one of psychological acceptability, which includes the notions of whether a method "makes sense" to the average onlooker, and whether it is seen as conferring legitimacy on its winner rather than being an unmotivated piece of jiggery pokery.
Notwithstanding all this... you and Robert may well be right.
FWIW, I suspect the complexity people are willing to accept depends on their trust in the political process in general. For instance, some local New Zealand elections use Meek's method, which is complex however you put it.[1] And I wouldn't be prepared to explain the pretty messy greedy algorithm used to allocate party list top-up seats here (in Norway), but people seem to accept it.[2]
I don't think Robert could use minmax because the criterion he's using is "if more people prefer X to Y than vice versa, then Y is not elected". That seems to imply at least Condorcet loser. I'm not sure, though -- if you're particularly critical, you could even say it implies Smith, but I don't think Robert had that in mind.
-km
[1] I wonder what the legal language for that is... it's basically impossible to do by hand.
[2] IMHO, biproportional apportionment is much simpler. I suspect what's keeping it from being changed is mostl inertia.
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
On 2/21/23 12:18, Toby Pereira wrote:
As for the clone thing, I'm not entirely sure what all the different
clone definitions are - e.g. I can't easily find a definition of clone
winner.
What I know of cloning definitions is:
A clone set is a group of candidates between which no voter ranks any
other candidate. That is, every voter ranks them consecutively in some
order.
Then the clone failure types are[1]:
Teaming: Replacing a candidate A with a clone set makes one of the
clones win.
Vote-splitting: Replacing a candidate A with a clone set makes the
clones lose.
Crowding: Replacing a candidate A with a clone set changes the winner
from B to C.
Woodall defines the clone criteria like this
(https://www.rangevoting.org/WoodallP5.html)
Clone-no-help: No vote-splitting.
Clone-no-harm: No teaming.
Clone-in: For multiwinner elections, reducing the size of a clone set
should not increase the number of winners elected from it.
I think clone-winner is "no vote-splitting" and clone-loser is "no
teaming":
https://en.wikipedia.org/wiki/Talk%3AIndependence_of_clones_criterion#Woodall's_terminology
Apparently this terminology is also from Woodall, though I can't find
any papers using them.
-km
[1] Strictly speaking, they're also defined for ties and methods with
chance: teaming happens when the total probability of electing from the
clone set is higher than the probability of electing the candidate who
was cloned, etc.
Toby,
Good points!
Many of us wish we had the advantages of score ballots.
Score Sorted Margins is one of the best Condorcet methods that shows what
you can do with score ballots. Without score ballots or explicit approval
cutoffs the best you can do in this vein is implicit approval sorted
margins.
How about Borda Sorted Margins?
Clone dependent.
Thus the infestation of clone dependent Condorcet completion methods ...
Black, Nanson, Kemeny-Young, Baldwin, not to mention all of Quick and Dirty
kluges that have been resorted to.
Clone Winner says that if the method winner is replaced by a clone set, the
new winner should be from the clone set ... preferably the member of the
clone set that would be elected if the method were restricted to the clone
set.
Thanks for bringing out these important points!
-Forest
On Tue, Feb 21, 2023, 3:19 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
Well I think a problem with ranking = implicit approval is that a voter
might have a preference between two candidates they hate just as much as
between two candidates they like, and they would have to implicitly approve
one of these candidates to make the distinction.
I sometimes think that Condorcet with cardinal ballots would work better.
You have scores or grades, but don't use the values themselves for
anything, just the ordinal positions. This way you can easily equal rank at
the top, bottom, or somewhere in the middle, not just at the end by not
ranking the candidates you hate.
I also think it could alleviate some of the problems of burial. Burial
isn't necessarily just a problem because of deliberate strategising. If
there are two main candidates, one that a voter likes (A), and one that a
voter dislikes (B), and couple of relative unknowns (C and D), there seems
to be a prevailing view that because A and B are the "strongest"
candidates, an honest vote would be something like A>B>C>D, people would
only bottom rank B as some sort of burial strategy, which must be overcome
by the method. But I don't think that's the case. Most voters would
probably bottom rank B anyway in this case, and do something like A>C>D>B
or just A>C>B. But with cardinal ballots, they would be more likely to
simply give a zero score to all the candidates they dislike and
non-entities. B would therefore be less likely to be buried under other
candidates.
As for the clone thing, I'm not entirely sure what all the different clone
definitions are - e.g. I can't easily find a definition of clone winner.
Toby
On Monday, 20 February 2023 at 19:22:13 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
Toby,
Thanks for you thoughtful critique!
Do you think it's worth the extra verbiage of conflating truncation and
bottom rank?
Many times I have conflated them by saying D has "Ballot Bottom Status"
because it outranks no candidate.
But imho leaving the distinction intact is both simpler and totally
harmless ... it just gives voters an optional lever to pull if they want to.
Also in the present context it confers ISDA compliance. Elimination of
Smith dominated candidates does not change the unranked/abstention count of
any remaining candidate, but it may well change the Ballot Bottom Status of
some of them.
One can take the point of view that
the ordinal information is the same on both ballots, but the implicit
approval is different. The truncation boundary can be considered as an
implicit approval cutoff ... awkward, but better than anything possible
under strict Universal Domain constraints.
With regard to clone dependence ... doesn't it satisfy clone-winner,
unlike any of the other suggestions in this thread?
Doesn't Approval, including implicit approval, satisfy a version of clone
independence? It does under the assumption that true clones are not
interrupted by the virtual approval cutoff candidate (truncation boundary
in this case) any more than they are by other candidates.
Our defeat strength gauge is winning pairwise support plus losing
truncations.
If you replace the defeat winner with a precise clone set ... each member
of the clone set will have the same pairwise support against the loser, so
they will be tied for the strongest victory over the same loser. In
practice, the clone sets are not precise ... but if they were the tie could
easily be broken by applying the method recursively to the tied set ... if
no simpler method existed ... like choosing the tied candidate with the
greatest equal-first count ... another helpful expedient that exists
outside of the strict UD rules.
Another option that makes hardly any difference to the method except to
make its description more wordy, is to gauge defeat strength by winner
implicit approval plus loser implicit disapproval.
Implicit disapproval is already the number of truncations.
And every ballot that pairwise supports the winner over the loser already
contributes to the winner's implicit approval .... so the implicit approval
count will be an increase over the pairwise support.
But is it worth the extra wordiness required ... talking about implicit
approval? We studiously avoided that talk by using "winning votes" a
familiar notion in the context of defeat strength as a proxy for implicit
approval.
Ultimately, if it turns out to make any difference, we should go with the
one that works best .... even if it takes more verbiage.
-Forest
On Mon, Feb 20, 2023, 3:14 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
One thing I'm uncomfortable with is the notion of "unranked" candidates.
If there are 4 candidates - A, B, C and D - and one ballot has A>B>C>D and
another just A>B>C, they should be treated as the same. Unranked is just
(possibly joint) last and I don't see it as having special status.
Toby
On Monday, 20 February 2023 at 01:28:18 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
I have learned a lot from the "hay guys" thread that spontaneously
upgraded into this "hey guys" thread.
Colin Champion made some very helpful points and pointers about the
psychology of what we are involved in. Many similar practical
considerations contributed by all participants.
Several suggestions have been made about how to complete this sentence:
"Lacking a candidate that defeats every other candidate in pairwise
head-to-head comparisons, elect the candidate that ..."
I can live with most of those suggestions ... which is neither here nor
there in the grand scheme of things ... but I hope haven't offended anybody
or discouraged anybody's contributions to these explorations.
Several people have said, "Why not just ...?"
And I thought, "Why didn't I think of that?"
The most promising idea I am currently thinking along these lines goes
like this:
Elect the pairwise undefeated champion ... or lacking such a champion,
elect the winner of the strongest pairwise defeat ... meaning the pairwise
contest with the greatest sum of winner approval and loser disapproval ...
winner approval measured by winning votes ... the number of ballots on
which the winner outranks the loser... loser disapproval measured by loser
abstentions ... the number of ballots on which the pairwise loser is
unranked.
So winning votes plus loser abstentions is my proposal for defeat strength
... not to be used in Rsnked Pairs ... but just in the first and strongest
step of RP ... and then only in the absence of a Condorcet Winner.
For now it's just an idea needing an experimental shake down beyond my
meager manual tests.
But who knows?
-Forest
On Sun, Feb 19, 2023, 10:47 AM Colin Champion <
colin.champion@routemaster.app> wrote:
I asked Kristofer whether Condorcet+FPTP complied with the Condorcet Loser
criterion. He replied "probably not" with a sketch proof, and then gave the
following example.
40: L>C>R
42: R>C>L
10: C>L>R
R is the Condorcet loser and Plurality winner. (L is the IRV winner.)
Now clone C, the CW:
40: L>Ca>Cb>Cc>R
42: R>Cb>Cc>Ca>L
10: Cc>Ca>Cb>L>R
There's no CW, so Plurality elects R, the Condorcet loser. (Incidentally,
R ties for first in minmax.)
Seems OK. Verified with
https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html.
I'd wondered whether Robert didn't have any intellectual commitent to the
criterion, but had used it in argument against IRV and therefore found his
options limited.
CJC
On 19/02/2023 17:31, Kristofer Munsterhjelm wrote:
On 2/19/23 16:36, Colin Champion wrote:
"Politicians and the voting public would not accept anything more
complicated than X" is my own favourite line of argument - but I substitute
my own value for X(minimax). I know that my judgement is coloured by my
preferences. There's a surprising degree of dissent over which methods are
simpler than which, and where the boundary should be drawn. People who deal
directly with politicians and the voting public can no doubt get closer to
the truth than people whose interest is predominantly theoretical, but I
wish there was an authoritative and objective source of information. If
only some behavioural psychologist was funded to investigate the
question...
To be finicky, the issue isn't exactly one of simplicity but rather one of
psychological acceptability, which includes the notions of whether a method
"makes sense" to the average onlooker, and whether it is seen as conferring
legitimacy on its winner rather than being an unmotivated piece of jiggery
pokery.
Notwithstanding all this... you and Robert may well be right.
FWIW, I suspect the complexity people are willing to accept depends on
their trust in the political process in general. For instance, some local
New Zealand elections use Meek's method, which is complex however you put
it.[1] And I wouldn't be prepared to explain the pretty messy greedy
algorithm used to allocate party list top-up seats here (in Norway), but
people seem to accept it.[2]
I don't think Robert could use minmax because the criterion he's using is
"if more people prefer X to Y than vice versa, then Y is not elected". That
seems to imply at least Condorcet loser. I'm not sure, though -- if you're
particularly critical, you could even say it implies Smith, but I don't
think Robert had that in mind.
-km
[1] I wonder what the legal language for that is... it's basically
impossible to do by hand.
[2] IMHO, biproportional apportionment is much simpler. I suspect what's
keeping it from being changed is mostl inertia.
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
I get the feeling that you consider score ballots to be a non-starter in electoral reform. Do you think this the case?
Toby
On Tuesday, 21 February 2023 at 18:56:52 GMT, Forest Simmons forest.simmons21@gmail.com wrote:
Toby,
Good points!
Many of us wish we had the advantages of score ballots.
Score Sorted Margins is one of the best Condorcet methods that shows what you can do with score ballots. Without score ballots or explicit approval cutoffs the best you can do in this vein is implicit approval sorted margins.
How about Borda Sorted Margins?
Clone dependent.
Thus the infestation of clone dependent Condorcet completion methods ... Black, Nanson, Kemeny-Young, Baldwin, not to mention all of Quick and Dirty kluges that have been resorted to.
Clone Winner says that if the method winner is replaced by a clone set, the new winner should be from the clone set ... preferably the member of the clone set that would be elected if the method were restricted to the clone set.
Thanks for bringing out these important points!
-Forest
On Tue, Feb 21, 2023, 3:19 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
Well I think a problem with ranking = implicit approval is that a voter might have a preference between two candidates they hate just as much as between two candidates they like, and they would have to implicitly approve one of these candidates to make the distinction.
I sometimes think that Condorcet with cardinal ballots would work better. You have scores or grades, but don't use the values themselves for anything, just the ordinal positions. This way you can easily equal rank at the top, bottom, or somewhere in the middle, not just at the end by not ranking the candidates you hate.
I also think it could alleviate some of the problems of burial. Burial isn't necessarily just a problem because of deliberate strategising. If there are two main candidates, one that a voter likes (A), and one that a voter dislikes (B), and couple of relative unknowns (C and D), there seems to be a prevailing view that because A and B are the "strongest" candidates, an honest vote would be something like A>B>C>D, people would only bottom rank B as some sort of burial strategy, which must be overcome by the method. But I don't think that's the case. Most voters would probably bottom rank B anyway in this case, and do something like A>C>D>B or just A>C>B. But with cardinal ballots, they would be more likely to simply give a zero score to all the candidates they dislike and non-entities. B would therefore be less likely to be buried under other candidates.
As for the clone thing, I'm not entirely sure what all the different clone definitions are - e.g. I can't easily find a definition of clone winner.
Toby
On Monday, 20 February 2023 at 19:22:13 GMT, Forest Simmons forest.simmons21@gmail.com wrote:
Toby,
Thanks for you thoughtful critique!
Do you think it's worth the extra verbiage of conflating truncation and bottom rank?
Many times I have conflated them by saying D has "Ballot Bottom Status" because it outranks no candidate.
But imho leaving the distinction intact is both simpler and totally harmless ... it just gives voters an optional lever to pull if they want to.
Also in the present context it confers ISDA compliance. Elimination of Smith dominated candidates does not change the unranked/abstention count of any remaining candidate, but it may well change the Ballot Bottom Status of some of them.
One can take the point of view thatthe ordinal information is the same on both ballots, but the implicit approval is different. The truncation boundary can be considered as an implicit approval cutoff ... awkward, but better than anything possible under strict Universal Domain constraints.
With regard to clone dependence ... doesn't it satisfy clone-winner, unlike any of the other suggestions in this thread?
Doesn't Approval, including implicit approval, satisfy a version of clone independence? It does under the assumption that true clones are not interrupted by the virtual approval cutoff candidate (truncation boundary in this case) any more than they are by other candidates.
Our defeat strength gauge is winning pairwise support plus losing truncations.
If you replace the defeat winner with a precise clone set ... each member of the clone set will have the same pairwise support against the loser, so they will be tied for the strongest victory over the same loser. In practice, the clone sets are not precise ... but if they were the tie could easily be broken by applying the method recursively to the tied set ... if no simpler method existed ... like choosing the tied candidate with the greatest equal-first count ... another helpful expedient that exists outside of the strict UD rules.
Another option that makes hardly any difference to the method except to make its description more wordy, is to gauge defeat strength by winner implicit approval plus loser implicit disapproval.
Implicit disapproval is already the number of truncations.
And every ballot that pairwise supports the winner over the loser already contributes to the winner's implicit approval .... so the implicit approval count will be an increase over the pairwise support.
But is it worth the extra wordiness required ... talking about implicit approval? We studiously avoided that talk by using "winning votes" a familiar notion in the context of defeat strength as a proxy for implicit approval.
Ultimately, if it turns out to make any difference, we should go with the one that works best .... even if it takes more verbiage.
-Forest
On Mon, Feb 20, 2023, 3:14 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
One thing I'm uncomfortable with is the notion of "unranked" candidates. If there are 4 candidates - A, B, C and D - and one ballot has A>B>C>D and another just A>B>C, they should be treated as the same. Unranked is just (possibly joint) last and I don't see it as having special status.
Toby
On Monday, 20 February 2023 at 01:28:18 GMT, Forest Simmons forest.simmons21@gmail.com wrote:
I have learned a lot from the "hay guys" thread that spontaneously upgraded into this "hey guys" thread.
Colin Champion made some very helpful points and pointers about the psychology of what we are involved in. Many similar practical considerations contributed by all participants.
Several suggestions have been made about how to complete this sentence:
"Lacking a candidate that defeats every other candidate in pairwise head-to-head comparisons, elect the candidate that ..."
I can live with most of those suggestions ... which is neither here nor there in the grand scheme of things ... but I hope haven't offended anybody or discouraged anybody's contributions to these explorations.
Several people have said, "Why not just ...?"
And I thought, "Why didn't I think of that?"
The most promising idea I am currently thinking along these lines goes like this:
Elect the pairwise undefeated champion ... or lacking such a champion, elect the winner of the strongest pairwise defeat ... meaning the pairwise contest with the greatest sum of winner approval and loser disapproval ... winner approval measured by winning votes ... the number of ballots on which the winner outranks the loser... loser disapproval measured by loser abstentions ... the number of ballots on which the pairwise loser is unranked.
So winning votes plus loser abstentions is my proposal for defeat strength ... not to be used in Rsnked Pairs ... but just in the first and strongest step of RP ... and then only in the absence of a Condorcet Winner.
For now it's just an idea needing an experimental shake down beyond my meager manual tests.
But who knows?
-Forest
On Sun, Feb 19, 2023, 10:47 AM Colin Champion colin.champion@routemaster.app wrote:
I asked Kristofer whether Condorcet+FPTP complied with the Condorcet Loser criterion. He replied "probably not" with a sketch proof, and then gave the following example.
<quote> [preliminary election]40: L>C>R
42: R>C>L
10: C>L>R
R is the Condorcet loser and Plurality winner. (L is the IRV winner.)
Now clone C, the CW:
40: L>Ca>Cb>Cc>R
42: R>Cb>Cc>Ca>L
10: Cc>Ca>Cb>L>R
There's no CW, so Plurality elects R, the Condorcet loser. (Incidentally, R ties for first in minmax.)
Seems OK. Verified with https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html.
</quote>
I'd wondered whether Robert didn't have any intellectual commitent to the criterion, but had used it in argument against IRV and therefore found his options limited.
CJC
On 19/02/2023 17:31, Kristofer Munsterhjelm wrote:
On 2/19/23 16:36, Colin Champion wrote:
"Politicians and the voting public would not accept anything more complicated than X" is my own favourite line of argument - but I substitute my own value for X(minimax). I know that my judgement is coloured by my preferences. There's a surprising degree of dissent over which methods are simpler than which, and where the boundary should be drawn. People who deal directly with politicians and the voting public can no doubt get closer to the truth than people whose interest is predominantly theoretical, but I wish there was an authoritative and objective source of information. If only some behavioural psychologist was funded to investigate the question...
To be finicky, the issue isn't exactly one of simplicity but rather one of psychological acceptability, which includes the notions of whether a method "makes sense" to the average onlooker, and whether it is seen as conferring legitimacy on its winner rather than being an unmotivated piece of jiggery pokery.
Notwithstanding all this... you and Robert may well be right.
FWIW, I suspect the complexity people are willing to accept depends on their trust in the political process in general. For instance, some local New Zealand elections use Meek's method, which is complex however you put it.[1] And I wouldn't be prepared to explain the pretty messy greedy algorithm used to allocate party list top-up seats here (in Norway), but people seem to accept it.[2]
I don't think Robert could use minmax because the criterion he's using is "if more people prefer X to Y than vice versa, then Y is not elected". That seems to imply at least Condorcet loser. I'm not sure, though -- if you're particularly critical, you could even say it implies Smith, but I don't think Robert had that in mind.
-km
[1] I wonder what the legal language for that is... it's basically impossible to do by hand.
[2] IMHO, biproportional apportionment is much simpler. I suspect what's keeping it from being changed is mostl inertia.
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
Why have the STAR folks stubbornly dug in their heels with a clone
dependent version when one simple change would make it both Condorcet
efficient and clone-independent?
Instead of just top two score runoff ... extend it to a runoff between the
score winner and the champion from below ... not just the score winner from
below ... but the winner from below determined (recursively) by the same
method .... i.e. Sequential Pairwise Elimination in disguise ... a very
respectable method with a long and hoary tradition behind it in
deliberative assemblies .. Robert'sRules of Order and the like.
The manual version is more laborious than the manual version of full runoff
... so it never got into large public elections.
Ironically, the instant version of SPE is much easier than IRV ...precinct
summable, etc ...but it's hard to break old habits of thought.
-Forest
On Tue, Feb 21, 2023, 3:39 PM Toby Pereira tdp201b@yahoo.co.uk wrote:
I get the feeling that you consider score ballots to be a non-starter in
electoral reform. Do you think this the case?
Toby
On Tuesday, 21 February 2023 at 18:56:52 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
Toby,
Good points!
Many of us wish we had the advantages of score ballots.
Score Sorted Margins is one of the best Condorcet methods that shows what
you can do with score ballots. Without score ballots or explicit approval
cutoffs the best you can do in this vein is implicit approval sorted
margins.
How about Borda Sorted Margins?
Clone dependent.
Thus the infestation of clone dependent Condorcet completion methods ...
Black, Nanson, Kemeny-Young, Baldwin, not to mention all of Quick and Dirty
kluges that have been resorted to.
Clone Winner says that if the method winner is replaced by a clone set,
the new winner should be from the clone set ... preferably the member of
the clone set that would be elected if the method were restricted to the
clone set.
Thanks for bringing out these important points!
-Forest
On Tue, Feb 21, 2023, 3:19 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
Well I think a problem with ranking = implicit approval is that a voter
might have a preference between two candidates they hate just as much as
between two candidates they like, and they would have to implicitly approve
one of these candidates to make the distinction.
I sometimes think that Condorcet with cardinal ballots would work better.
You have scores or grades, but don't use the values themselves for
anything, just the ordinal positions. This way you can easily equal rank at
the top, bottom, or somewhere in the middle, not just at the end by not
ranking the candidates you hate.
I also think it could alleviate some of the problems of burial. Burial
isn't necessarily just a problem because of deliberate strategising. If
there are two main candidates, one that a voter likes (A), and one that a
voter dislikes (B), and couple of relative unknowns (C and D), there seems
to be a prevailing view that because A and B are the "strongest"
candidates, an honest vote would be something like A>B>C>D, people would
only bottom rank B as some sort of burial strategy, which must be overcome
by the method. But I don't think that's the case. Most voters would
probably bottom rank B anyway in this case, and do something like A>C>D>B
or just A>C>B. But with cardinal ballots, they would be more likely to
simply give a zero score to all the candidates they dislike and
non-entities. B would therefore be less likely to be buried under other
candidates.
As for the clone thing, I'm not entirely sure what all the different clone
definitions are - e.g. I can't easily find a definition of clone winner.
Toby
On Monday, 20 February 2023 at 19:22:13 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
Toby,
Thanks for you thoughtful critique!
Do you think it's worth the extra verbiage of conflating truncation and
bottom rank?
Many times I have conflated them by saying D has "Ballot Bottom Status"
because it outranks no candidate.
But imho leaving the distinction intact is both simpler and totally
harmless ... it just gives voters an optional lever to pull if they want to.
Also in the present context it confers ISDA compliance. Elimination of
Smith dominated candidates does not change the unranked/abstention count of
any remaining candidate, but it may well change the Ballot Bottom Status of
some of them.
One can take the point of view that
the ordinal information is the same on both ballots, but the implicit
approval is different. The truncation boundary can be considered as an
implicit approval cutoff ... awkward, but better than anything possible
under strict Universal Domain constraints.
With regard to clone dependence ... doesn't it satisfy clone-winner,
unlike any of the other suggestions in this thread?
Doesn't Approval, including implicit approval, satisfy a version of clone
independence? It does under the assumption that true clones are not
interrupted by the virtual approval cutoff candidate (truncation boundary
in this case) any more than they are by other candidates.
Our defeat strength gauge is winning pairwise support plus losing
truncations.
If you replace the defeat winner with a precise clone set ... each member
of the clone set will have the same pairwise support against the loser, so
they will be tied for the strongest victory over the same loser. In
practice, the clone sets are not precise ... but if they were the tie could
easily be broken by applying the method recursively to the tied set ... if
no simpler method existed ... like choosing the tied candidate with the
greatest equal-first count ... another helpful expedient that exists
outside of the strict UD rules.
Another option that makes hardly any difference to the method except to
make its description more wordy, is to gauge defeat strength by winner
implicit approval plus loser implicit disapproval.
Implicit disapproval is already the number of truncations.
And every ballot that pairwise supports the winner over the loser already
contributes to the winner's implicit approval .... so the implicit approval
count will be an increase over the pairwise support.
But is it worth the extra wordiness required ... talking about implicit
approval? We studiously avoided that talk by using "winning votes" a
familiar notion in the context of defeat strength as a proxy for implicit
approval.
Ultimately, if it turns out to make any difference, we should go with the
one that works best .... even if it takes more verbiage.
-Forest
On Mon, Feb 20, 2023, 3:14 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
One thing I'm uncomfortable with is the notion of "unranked" candidates.
If there are 4 candidates - A, B, C and D - and one ballot has A>B>C>D and
another just A>B>C, they should be treated as the same. Unranked is just
(possibly joint) last and I don't see it as having special status.
Toby
On Monday, 20 February 2023 at 01:28:18 GMT, Forest Simmons <
forest.simmons21@gmail.com> wrote:
I have learned a lot from the "hay guys" thread that spontaneously
upgraded into this "hey guys" thread.
Colin Champion made some very helpful points and pointers about the
psychology of what we are involved in. Many similar practical
considerations contributed by all participants.
Several suggestions have been made about how to complete this sentence:
"Lacking a candidate that defeats every other candidate in pairwise
head-to-head comparisons, elect the candidate that ..."
I can live with most of those suggestions ... which is neither here nor
there in the grand scheme of things ... but I hope haven't offended anybody
or discouraged anybody's contributions to these explorations.
Several people have said, "Why not just ...?"
And I thought, "Why didn't I think of that?"
The most promising idea I am currently thinking along these lines goes
like this:
Elect the pairwise undefeated champion ... or lacking such a champion,
elect the winner of the strongest pairwise defeat ... meaning the pairwise
contest with the greatest sum of winner approval and loser disapproval ...
winner approval measured by winning votes ... the number of ballots on
which the winner outranks the loser... loser disapproval measured by loser
abstentions ... the number of ballots on which the pairwise loser is
unranked.
So winning votes plus loser abstentions is my proposal for defeat strength
... not to be used in Rsnked Pairs ... but just in the first and strongest
step of RP ... and then only in the absence of a Condorcet Winner.
For now it's just an idea needing an experimental shake down beyond my
meager manual tests.
But who knows?
-Forest
On Sun, Feb 19, 2023, 10:47 AM Colin Champion <
colin.champion@routemaster.app> wrote:
I asked Kristofer whether Condorcet+FPTP complied with the Condorcet Loser
criterion. He replied "probably not" with a sketch proof, and then gave the
following example.
40: L>C>R
42: R>C>L
10: C>L>R
R is the Condorcet loser and Plurality winner. (L is the IRV winner.)
Now clone C, the CW:
40: L>Ca>Cb>Cc>R
42: R>Cb>Cc>Ca>L
10: Cc>Ca>Cb>L>R
There's no CW, so Plurality elects R, the Condorcet loser. (Incidentally,
R ties for first in minmax.)
Seems OK. Verified with
https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html.
I'd wondered whether Robert didn't have any intellectual commitent to the
criterion, but had used it in argument against IRV and therefore found his
options limited.
CJC
On 19/02/2023 17:31, Kristofer Munsterhjelm wrote:
On 2/19/23 16:36, Colin Champion wrote:
"Politicians and the voting public would not accept anything more
complicated than X" is my own favourite line of argument - but I substitute
my own value for X(minimax). I know that my judgement is coloured by my
preferences. There's a surprising degree of dissent over which methods are
simpler than which, and where the boundary should be drawn. People who deal
directly with politicians and the voting public can no doubt get closer to
the truth than people whose interest is predominantly theoretical, but I
wish there was an authoritative and objective source of information. If
only some behavioural psychologist was funded to investigate the
question...
To be finicky, the issue isn't exactly one of simplicity but rather one of
psychological acceptability, which includes the notions of whether a method
"makes sense" to the average onlooker, and whether it is seen as conferring
legitimacy on its winner rather than being an unmotivated piece of jiggery
pokery.
Notwithstanding all this... you and Robert may well be right.
FWIW, I suspect the complexity people are willing to accept depends on
their trust in the political process in general. For instance, some local
New Zealand elections use Meek's method, which is complex however you put
it.[1] And I wouldn't be prepared to explain the pretty messy greedy
algorithm used to allocate party list top-up seats here (in Norway), but
people seem to accept it.[2]
I don't think Robert could use minmax because the criterion he's using is
"if more people prefer X to Y than vice versa, then Y is not elected". That
seems to imply at least Condorcet loser. I'm not sure, though -- if you're
particularly critical, you could even say it implies Smith, but I don't
think Robert had that in mind.
-km
[1] I wonder what the legal language for that is... it's basically
impossible to do by hand.
[2] IMHO, biproportional apportionment is much simpler. I suspect what's
keeping it from being changed is mostl inertia.
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info