Smith+IRV//Approval
I've been thinking a bit why the Condorcet has so little popular
traction, why some quite intelligent
are wary of it and prefer IRV.
Suppose we are talking about electing members of a parliament (or
legislature) in single-member seats.
Typically the two largest parties, say one centre-left and and one
centre-right, will between them win nearly
all the seats and with luck the one that is preferred by more voters
than the other will get more seats
(and so in a Parliamentary system will form a government with its leader
becoming the Prime Minister).
So in this limited sense the result is very very roughly
"proportional". Assuming the small wing parties'
supporters are normally spread out in lots of different districts, they
will get no seats.
But suppose in a lot of the seats the contest looks like this:
47 A>>>C>B
43 B>>>C>A
10 C>A>>B
If this is IRV or FPP then A easily wins, but the CW is C.
But A is clearly the highest "social utility" candidate, and assuming
that voting is voluntary and at
least somewhat inconvenient or costly, then C has only been voted the CW
because both A and B
are on the ballot. If one of those candidates wasn't, then most of his
or her supporters would stay
home and allow the other to easily beat C.
And if something similar (electing a weak centrist that most of the
voters don't like) happens in enough
seats it could result in the "weak centrist party" being grossly
over-represented in the legislature.
So to allay these fears I suggest this compromise with IRV:
Smith+IRV//Approval:
*Voters strictly rank from the top however many or few candidates they
wish. Default approval is only
for the top-ranked candidate, but voters can extend approval to one or
more other candidates by marking
the lowest-ranked candidate they approve.
Elect the most approved candidate that is either in the Smith set or is
the IRV winner.*
Allowing above-bottom equal-preferences (at least without a lot of extra
complexity) makes Push-over strategising
easier.
So in the type of example I just discussed the IRV winner would normally
have a much higher approval score
than the CW, but the supporters of the IRV runner-up could change that
if they like by extending their approval
to the CW (who then might win, especially if the CW's supporters refrain
from extending their approval to the IRV winner).
Chris B.
Chris - as I understand it, there's no reason to expect Condorcet voting
to produce satisfactory results if applied seat-by-seat to
representative assemblies. Some voting theory texts have a disclaimer
near the beginning: "We here discuss the election of a single
office-holder (eg. a president); election of individual members to an
assembly brings in additional considerations" (which are never discussed).
At any rate, if a country is governed by a parliamentary assembly,
then the primary the aim of an election should be to produce an
effective government whose policies are as close as possible to the
consensus view of the electorate. This will not usually be achieved by
giving each constituency a representative who is close to its local
consensus.
I made a proposal of my own a couple of years ago:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2021-October/003113.html
My main concern was to avoid the minority governments which
generally arise when FPTP is replaced by less crude methods. As for
traction... I'm still its sole supporter.
Colin
On 17/09/2023 17:52, C.Benham wrote:
I've been thinking a bit why the Condorcet has so little popular
traction, why some quite intelligent
are wary of it and prefer IRV.
Suppose we are talking about electing members of a parliament (or
legislature) in single-member seats.
Typically the two largest parties, say one centre-left and and one
centre-right, will between them win nearly
all the seats and with luck the one that is preferred by more voters
than the other will get more seats
(and so in a Parliamentary system will form a government with its
leader becoming the Prime Minister).
So in this limited sense the result is very very roughly
"proportional". Assuming the small wing parties'
supporters are normally spread out in lots of different districts,
they will get no seats.
But suppose in a lot of the seats the contest looks like this:
47 A>>>C>B
43 B>>>C>A
10 C>A>>B
If this is IRV or FPP then A easily wins, but the CW is C.
But A is clearly the highest "social utility" candidate, and assuming
that voting is voluntary and at
least somewhat inconvenient or costly, then C has only been voted the
CW because both A and B
are on the ballot. If one of those candidates wasn't, then most of his
or her supporters would stay
home and allow the other to easily beat C.
And if something similar (electing a weak centrist that most of the
voters don't like) happens in enough
seats it could result in the "weak centrist party" being grossly
over-represented in the legislature.
So to allay these fears I suggest this compromise with IRV:
Smith+IRV//Approval:
*Voters strictly rank from the top however many or few candidates they
wish. Default approval is only
for the top-ranked candidate, but voters can extend approval to one or
more other candidates by marking
the lowest-ranked candidate they approve.
Elect the most approved candidate that is either in the Smith set or
is the IRV winner.*
Allowing above-bottom equal-preferences (at least without a lot of
extra complexity) makes Push-over strategising
easier.
So in the type of example I just discussed the IRV winner would
normally have a much higher approval score
than the CW, but the supporters of the IRV runner-up could change that
if they like by extending their approval
to the CW (who then might win, especially if the CW's supporters
refrain from extending their approval to the IRV winner).
Chris B.
Some "quite intelligent" people were wary of Condorcet pairing over two centuries ago, namely Pierre-Simon Laplace because Condorcet pairing treats different orders of preference as of equal value.
Laplace, by the way, was rated one of historys half-dozen greatest mathematicians. He offers what JFS Ross called a rather "elliptical" proof for his belief.
He was inclined to say that was too obvious for a proof. When his American translator of Mechanique Celeste, saw that remark, he said he knew he was in for a hard nights work.
An order of choice recognises some choices have priority over others. Condorcet pairing does not, which is reason to be wary of it.
Order (in the vote) and proportion (in the count) are prerequisites of mathematics and of civilization in general, tho politicians demur.
Richard Lung.
On 17 Sep 2023, at 4:52 pm, C.Benham cbenham@adam.com.au wrote:
I've been thinking a bit why the Condorcet has so little popular traction, why some quite intelligent
are wary of it and prefer IRV.
Suppose we are talking about electing members of a parliament (or legislature) in single-member seats.
Typically the two largest parties, say one centre-left and and one centre-right, will between them win nearly
all the seats and with luck the one that is preferred by more voters than the other will get more seats
(and so in a Parliamentary system will form a government with its leader becoming the Prime Minister).
So in this limited sense the result is very very roughly "proportional". Assuming the small wing parties'
supporters are normally spread out in lots of different districts, they will get no seats.
But suppose in a lot of the seats the contest looks like this:
47 A>>>C>B
43 B>>>C>A
10 C>A>>B
If this is IRV or FPP then A easily wins, but the CW is C.
But A is clearly the highest "social utility" candidate, and assuming that voting is voluntary and at
least somewhat inconvenient or costly, then C has only been voted the CW because both A and B
are on the ballot. If one of those candidates wasn't, then most of his or her supporters would stay
home and allow the other to easily beat C.
And if something similar (electing a weak centrist that most of the voters don't like) happens in enough
seats it could result in the "weak centrist party" being grossly over-represented in the legislature.
So to allay these fears I suggest this compromise with IRV: Smith+IRV//Approval:
*Voters strictly rank from the top however many or few candidates they wish. Default approval is only
for the top-ranked candidate, but voters can extend approval to one or more other candidates by marking
the lowest-ranked candidate they approve.
Elect the most approved candidate that is either in the Smith set or is the IRV winner.*
Allowing above-bottom equal-preferences (at least without a lot of extra complexity) makes Push-over strategising
easier.
So in the type of example I just discussed the IRV winner would normally have a much higher approval score
than the CW, but the supporters of the IRV runner-up could change that if they like by extending their approval
to the CW (who then might win, especially if the CW's supporters refrain from extending their approval to the IRV winner).
Chris B.
Election-Methods mailing list - see https://electorama.com/em for list info
On 2023-09-17 18:14, Colin Champion wrote:
Chris - as I understand it, there's no reason to expect Condorcet voting
to produce satisfactory results if applied seat-by-seat to
representative assemblies. Some voting theory texts have a disclaimer
near the beginning: "We here discuss the election of a single
office-holder (eg. a president); election of individual members to an
assembly brings in additional considerations" (which are never discussed).
Plurality can be used as a rough semiproportional method that's
proportional under strategy (SNTV). But bloc Condorcet isn't. I suspect
that Condorcet failing to be at-large proportional when used for single
member districts is related to this quirk in Plurality. In a way,
Condorcet is too majoritarian.
At any rate, if a country is governed by a parliamentary assembly,
then the primary the aim of an election should be to produce an
effective government whose policies are as close as possible to the
consensus view of the electorate. This will not usually be achieved by
giving each constituency a representative who is close to its local
consensus.
I made a proposal of my own a couple of years ago:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2021-October/003113.html
My main concern was to avoid the minority governments which
generally arise when FPTP is replaced by less crude methods. As for
traction... I'm still its sole supporter.
I think a ranked party list method with a centrist-favoring bias would
work relatively well: to be what something like D'Hondt should have
been, and favor consensus/centrist kingmakers instead of random minor
parties or whatever party happens to get the most Plurality votes.
But I might be coming from a different perspective: in Norway, minority
governments are more common than not, and the legislature-executive
balance of power is much more in favor of the legislature than is common
elsewhere, but things generally work out. Using ranking and a
centrist/consensus bias would reduce the need for thresholds and ad-hoc
tweaks to Sainte-Laguë[1]; they wouldn't eliminate minority governments
unless the bias were much harsher than I have in mind.
-km
[1]
https://en.wikipedia.org/wiki/Sainte-Lagu%C3%AB_method#Modified_Sainte-Lagu%C3%AB_method
How about simply restricting Approval to the candidates with short
beatpaths to the IRV winner (including the IRV winner itself)?
The main advantage of this version is that it doesn't require any
explanation of Smith.
fws
On Sun, Sep 17, 2023, 8:52 AM C.Benham cbenham@adam.com.au wrote:
I've been thinking a bit why the Condorcet has so little popular
traction, why some quite intelligent
are wary of it and prefer IRV.
Suppose we are talking about electing members of a parliament (or
legislature) in single-member seats.
Typically the two largest parties, say one centre-left and and one
centre-right, will between them win nearly
all the seats and with luck the one that is preferred by more voters
than the other will get more seats
(and so in a Parliamentary system will form a government with its leader
becoming the Prime Minister).
So in this limited sense the result is very very roughly
"proportional". Assuming the small wing parties'
supporters are normally spread out in lots of different districts, they
will get no seats.
But suppose in a lot of the seats the contest looks like this:
47 A>>>C>B
43 B>>>C>A
10 C>A>>B
If this is IRV or FPP then A easily wins, but the CW is C.
But A is clearly the highest "social utility" candidate, and assuming
that voting is voluntary and at
least somewhat inconvenient or costly, then C has only been voted the CW
because both A and B
are on the ballot. If one of those candidates wasn't, then most of his
or her supporters would stay
home and allow the other to easily beat C.
And if something similar (electing a weak centrist that most of the
voters don't like) happens in enough
seats it could result in the "weak centrist party" being grossly
over-represented in the legislature.
So to allay these fears I suggest this compromise with IRV:
Smith+IRV//Approval:
*Voters strictly rank from the top however many or few candidates they
wish. Default approval is only
for the top-ranked candidate, but voters can extend approval to one or
more other candidates by marking
the lowest-ranked candidate they approve.
Elect the most approved candidate that is either in the Smith set or is
the IRV winner.*
Allowing above-bottom equal-preferences (at least without a lot of extra
complexity) makes Push-over strategising
easier.
So in the type of example I just discussed the IRV winner would normally
have a much higher approval score
than the CW, but the supporters of the IRV runner-up could change that
if they like by extending their approval
to the CW (who then might win, especially if the CW's supporters refrain
from extending their approval to the IRV winner).
Chris B.
On Sun, Sep 17, 2023, 11:12 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 2023-09-17 18:14, Colin Champion wrote:
Chris - as I understand it, there's no reason to expect Condorcet voting
to produce satisfactory results if applied seat-by-seat to
representative assemblies. Some voting theory texts have a disclaimer
near the beginning: "We here discuss the election of a single
office-holder (eg. a president); election of individual members to an
assembly brings in additional considerations" (which are never
discussed).
Plurality can be used as a rough semiproportional method that's
proportional under strategy (SNTV).
Plurality elects the candidate with the highest likelihood of being random
plurality ballot favorite.
So how about electing the candidate with the greatest likelihood of being
the random approval ballot winner RABW.
The probabilities can be found analytically by exponentiating Markov
Transition Matrices ... or approximately by MonteCarlo.
The Random Approval Ballot Favorite probability distribution is
democratically proportional like the random plurality favorite probability
distribution ... but with less entropy ... i.e. greater expected consenus.
But bloc Condorcet isn't. I suspect
that Condorcet failing to be at-large proportional when used for single
member districts is related to this quirk in Plurality. In a way,
Condorcet is too majoritarian.
At any rate, if a country is governed by a parliamentary assembly,
then the primary the aim of an election should be to produce an
effective government whose policies are as close as possible to the
consensus view of the electorate. This will not usually be achieved by
giving each constituency a representative who is close to its local
consensus.
I made a proposal of my own a couple of years ago:
My main concern was to avoid the minority governments which
generally arise when FPTP is replaced by less crude methods. As for
traction... I'm still its sole supporter.
I think a ranked party list method with a centrist-favoring bias would
work relatively well: to be what something like D'Hondt should have
been, and favor consensus/centrist kingmakers instead of random minor
parties or whatever party happens to get the most Plurality votes.
But I might be coming from a different perspective: in Norway, minority
governments are more common than not, and the legislature-executive
balance of power is much more in favor of the legislature than is common
elsewhere, but things generally work out. Using ranking and a
centrist/consensus bias would reduce the need for thresholds and ad-hoc
tweaks to Sainte-Laguë[1]; they wouldn't eliminate minority governments
unless the bias were much harsher than I have in mind.
-km
[1]
https://en.wikipedia.org/wiki/Sainte-Lagu%C3%AB_method#Modified_Sainte-Lagu%C3%AB_method
Election-Methods mailing list - see https://electorama.com/em for list
info
It had crossed my mind that it might be possible to construct a
(probably) complicated and implausible example where
the IRV winner wins but there is a more approved candidate that pairwise
beats the IRV winner but is not in the Smith set.
That would be a very embarrassing failure of Double Defeat.
Your suggestion avoids that problem, but on the other hand to me it
sounds a bit more arbitrary.
Why only "short" beatpaths? Why not any beatpath?
Chris
On 19/09/2023 7:57 am, Forest Simmons wrote:
How about simply restricting Approval to the candidates with short
beatpaths to the IRV winner (including the IRV winner itself)?
The main advantage of this version is that it doesn't require any
explanation of Smith.
fws
On Sun, Sep 17, 2023, 8:52 AM C.Benham cbenham@adam.com.au wrote:
I've been thinking a bit why the Condorcet has so little popular
traction, why some quite intelligent people
are wary of it and prefer IRV.
Suppose we are talking about electing members of a parliament (or
legislature) in single-member seats.
Typically the two largest parties, say one centre-left and and one
centre-right, will between them win nearly
all the seats and with luck the one that is preferred by more voters
than the other will get more seats
(and so in a Parliamentary system will form a government with its
leader
becoming the Prime Minister).
So in this limited sense the result is very very roughly
"proportional". Assuming the small wing parties'
supporters are normally spread out in lots of different districts,
they
will get no seats.
But suppose in a lot of the seats the contest looks like this:
47 A>>>C>B
43 B>>>C>A
10 C>A>>B
If this is IRV or FPP then A easily wins, but the CW is C.
But A is clearly the highest "social utility" candidate, and assuming
that voting is voluntary and at
least somewhat inconvenient or costly, then C has only been voted
the CW
because both A and B
are on the ballot. If one of those candidates wasn't, then most of
his
or her supporters would stay
home and allow the other to easily beat C.
And if something similar (electing a weak centrist that most of the
voters don't like) happens in enough
seats it could result in the "weak centrist party" being grossly
over-represented in the legislature.
So to allay these fears I suggest this compromise with IRV:
Smith+IRV//Approval:
*Voters strictly rank from the top however many or few candidates
they
wish. Default approval is only
for the top-ranked candidate, but voters can extend approval to
one or
more other candidates by marking
the lowest-ranked candidate they approve.
Elect the most approved candidate that is either in the Smith set
or is
the IRV winner.*
Allowing above-bottom equal-preferences (at least without a lot of
extra
complexity) makes Push-over strategising
easier.
So in the type of example I just discussed the IRV winner would
normally
have a much higher approval score
than the CW, but the supporters of the IRV runner-up could change
that
if they like by extending their approval
to the CW (who then might win, especially if the CW's supporters
refrain
from extending their approval to the IRV winner).
Chris B.
No difference in practice, because when Smith has only three members, all
three have short beatpaths to every candidate.
Simpler to omit the word "short" and not worry anybody about it.
So whichever is easier to
On Mon, Sep 18, 2023, 8:12 PM C.Benham cbenham@adam.com.au wrote:
It had crossed my mind that it might be possible to construct a (probably)
complicated and implausible example where
the IRV winner wins but there is a more approved candidate that pairwise
beats the IRV winner but is not in the Smith set.
That would be a very embarrassing failure of Double Defeat.
Your suggestion avoids that problem, but on the other hand to me it sounds
a bit more arbitrary.
Why only "short" beatpaths? Why not any beatpath?
Chris
On 19/09/2023 7:57 am, Forest Simmons wrote:
How about simply restricting Approval to the candidates with short
beatpaths to the IRV winner (including the IRV winner itself)?
The main advantage of this version is that it doesn't require any
explanation of Smith.
fws
On Sun, Sep 17, 2023, 8:52 AM C.Benham cbenham@adam.com.au wrote:
I've been thinking a bit why the Condorcet has so little popular
traction, why some quite intelligent people
are wary of it and prefer IRV.
Suppose we are talking about electing members of a parliament (or
legislature) in single-member seats.
Typically the two largest parties, say one centre-left and and one
centre-right, will between them win nearly
all the seats and with luck the one that is preferred by more voters
than the other will get more seats
(and so in a Parliamentary system will form a government with its leader
becoming the Prime Minister).
So in this limited sense the result is very very roughly
"proportional". Assuming the small wing parties'
supporters are normally spread out in lots of different districts, they
will get no seats.
But suppose in a lot of the seats the contest looks like this:
47 A>>>C>B
43 B>>>C>A
10 C>A>>B
If this is IRV or FPP then A easily wins, but the CW is C.
But A is clearly the highest "social utility" candidate, and assuming
that voting is voluntary and at
least somewhat inconvenient or costly, then C has only been voted the CW
because both A and B
are on the ballot. If one of those candidates wasn't, then most of his
or her supporters would stay
home and allow the other to easily beat C.
And if something similar (electing a weak centrist that most of the
voters don't like) happens in enough
seats it could result in the "weak centrist party" being grossly
over-represented in the legislature.
So to allay these fears I suggest this compromise with IRV:
Smith+IRV//Approval:
*Voters strictly rank from the top however many or few candidates they
wish. Default approval is only
for the top-ranked candidate, but voters can extend approval to one or
more other candidates by marking
the lowest-ranked candidate they approve.
Elect the most approved candidate that is either in the Smith set or is
the IRV winner.*
Allowing above-bottom equal-preferences (at least without a lot of extra
complexity) makes Push-over strategising
easier.
So in the type of example I just discussed the IRV winner would normally
have a much higher approval score
than the CW, but the supporters of the IRV runner-up could change that
if they like by extending their approval
to the CW (who then might win, especially if the CW's supporters refrain
from extending their approval to the IRV winner).
Chris B.