[EM] A few papers on election science I'd like to point out to y'all

[Arthur Wist]

Hello,

Sorry in advanced for the huge load of information all at once, but I think
you'll highly likely find the following quite interesting:

On how people misunderstood the Duggan-Schwartz theorem:
https://arxiv.org/abs/1611.07105 - Two statements of the Duggan-Schwartz
theorem
https://arxiv.org/abs/1611.07102 - Manipulability of consular election
rules

EVERYTHING here:
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate

Some key highlights from that last link above:

https://arxiv.org/abs/1708.07580 - Achieving Proportional Representation
via Voting [ On which a blog post exists:
https://medium.com/@haris.aziz/achieving-proportional-representation-2d741871e78.
Better than STV and STV derivatives in all criteria? You decide! ]

http://materials.dagstuhl.de/files/17/17261/17261.HarisAziz.Slides.pdf -
Proportional Representation in Approval-based Voting and Beyond. [This is a
presentation - and it's outdated by now, albeit it's only from Summer last
year.]

https://arxiv.org/abs/1703.10415 - A polynomial-time algorithm to achieve
extended justified representation

https://arxiv.org/abs/1711.06030 - Sub-committee Approval Voting and
Generalised Justified Representation Axiom [This generalizes large parts of
the mathematics of voting theory!]

And on the topic of committees, not quite from election science, but
relevant nonetheless:

https://arxiv.org/abs/0804.2202 - To how many politicians should
government be left? [With a p-value of =<10^-6. And no, that's NOT a typo.]
https://arxiv.org/abs/0808.1684 - Parkinson's Law Quantified: Three
Investigations on Bureaucratic Inefficiency

The above two papers got a bit of news & blog coverage back in the day:

http://old.themoscowtimes.com/article/business-in-brief/article/austrians-suggest-small-is-better/article/austrians-suggest-small-is-better/362667.html

http://physicsworld.com/cws/article/news/2008/apr/27/physicists-quantify-the-coefficient-of-inefficiency

https://www.nature.com/news/2008/080822/full/news.2008.1050.html

http://www.telegraph.co.uk/news/science/4221839/Eight-people-on-committee-leads-to-decision-deadlock-scientists-say.html

https://www.thetimes.co.uk/article/numbers-up-for-unlucky-eight-nnt5js8jdvm

https://www.newscientist.com/article/mg20126902.200-editorial-parkinsons-law-is-alive-and-well/

https://www.newscientist.com/article/mg20126901.300-explaining-the-curse-of-work/?full=true


Kind regards,

[Jameson Quinn]

Thanks a lot! More of us should post stuff like this.

Post by Arthur Wist
Hello,
Sorry in advanced for the huge load of information all at once, but I
https://arxiv.org/abs/1611.07105 - Two statements of the Duggan-Schwartz
theorem
https://arxiv.org/abs/1611.07102 - Manipulability of consular election
rules
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate
https://arxiv.org/abs/1708.07580 - Achieving Proportional Representation
aziz/achieving-proportional-representation-2d741871e78. Better than STV
and STV derivatives in all criteria? You decide! ]
http://materials.dagstuhl.de/files/17/17261/17261.HarisAziz.Slides.pdf -
Proportional Representation in Approval-based Voting and Beyond. [This is a
presentation - and it's outdated by now, albeit it's only from Summer last
year.]
https://arxiv.org/abs/1703.10415 - A polynomial-time algorithm to achieve
extended justified representation
https://arxiv.org/abs/1711.06030 - Sub-committee Approval Voting and
Generalised Justified Representation Axiom [This generalizes large parts of
the mathematics of voting theory!]
And on the topic of committees, not quite from election science, but
https://arxiv.org/abs/0804.2202 - To how many politicians should
government be left? [With a p-value of =<10^-6. And no, that's NOT a typo.]
https://arxiv.org/abs/0808.1684 - Parkinson's Law Quantified: Three
Investigations on Bureaucratic Inefficiency
http://old.themoscowtimes.com/article/business-in-brief/
article/austrians-suggest-small-is-better/article/
austrians-suggest-small-is-better/362667.html
http://physicsworld.com/cws/article/news/2008/apr/27/
physicists-quantify-the-coefficient-of-inefficiency
https://www.nature.com/news/2008/080822/full/news.2008.1050.html
http://www.telegraph.co.uk/news/science/4221839/Eight-
people-on-committee-leads-to-decision-deadlock-scientists-say.html
https://www.thetimes.co.uk/article/numbers-up-for-
unlucky-eight-nnt5js8jdvm
https://www.newscientist.com/article/mg20126902.200-
editorial-parkinsons-law-is-alive-and-well/
https://www.newscientist.com/article/mg20126901.300-
explaining-the-curse-of-work/?full=true
Kind regards,
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Arthur Wist]

Post by Jameson Quinn
Thanks a lot!

Glad to help! :)

Post by Jameson Quinn
More of us should post stuff like this.

Well, in the meantime, have a new preprint, on the same topics, published
to aRxiv on Monday:
https://arxiv.org/abs/1801.09346 - "Representing the Insincere:
Strategically Robust Proportional Representation"

Kind regards,

Post by Jameson Quinn
Thanks a lot! More of us should post stuff like this.

Post by Arthur Wist
Hello,
Sorry in advanced for the huge load of information all at once, but I
https://arxiv.org/abs/1611.07105 - Two statements of the Duggan-Schwartz
theorem
https://arxiv.org/abs/1611.07102 - Manipulability of consular election
rules
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate
https://arxiv.org/abs/1708.07580 - Achieving Proportional Representation
/achieving-proportional-representation-2d741871e78. Better than STV and
STV derivatives in all criteria? You decide! ]
http://materials.dagstuhl.de/files/17/17261/17261.HarisAziz.Slides.pdf -
Proportional Representation in Approval-based Voting and Beyond. [This is a
presentation - and it's outdated by now, albeit it's only from Summer last
year.]
https://arxiv.org/abs/1703.10415 - A polynomial-time algorithm to
achieve extended justified representation
https://arxiv.org/abs/1711.06030 - Sub-committee Approval Voting and
Generalised Justified Representation Axiom [This generalizes large parts of
the mathematics of voting theory!]
And on the topic of committees, not quite from election science, but
https://arxiv.org/abs/0804.2202 - To how many politicians should
government be left? [With a p-value of =<10^-6. And no, that's NOT a typo.]
https://arxiv.org/abs/0808.1684 - Parkinson's Law Quantified: Three
Investigations on Bureaucratic Inefficiency
http://old.themoscowtimes.com/article/business-in-brief/arti
cle/austrians-suggest-small-is-better/article/austrians-
suggest-small-is-better/362667.html
http://physicsworld.com/cws/article/news/2008/apr/27/physici
sts-quantify-the-coefficient-of-inefficiency
https://www.nature.com/news/2008/080822/full/news.2008.1050.html
http://www.telegraph.co.uk/news/science/4221839/Eight-people
-on-committee-leads-to-decision-deadlock-scientists-say.html
https://www.thetimes.co.uk/article/numbers-up-for-unlucky-
eight-nnt5js8jdvm
https://www.newscientist.com/article/mg20126902.200-editoria
l-parkinsons-law-is-alive-and-well/
https://www.newscientist.com/article/mg20126901.300-explaini
ng-the-curse-of-work/?full=true
Kind regards,
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Kristofer Munsterhjelm]

Post by Arthur Wist
Hello,
Sorry in advanced for the huge load of information all at once, but I
https://arxiv.org/abs/1611.07105 - Two statements of the Duggan-Schwartz
theorem
https://arxiv.org/abs/1611.07102 -  Manipulability of consular election
rules
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate
https://arxiv.org/abs/1708.07580 - Achieving Proportional Representation
Better than STV and STV derivatives in all criteria? You decide! ]

From a cursory look at the latter, that looks like Bucklin with a
STV-style elect-and-reweight system. I wrote some posts about a
vote-management resistant version of Bucklin at
http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-December/001234.html
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html,
and found out that the simplest way of breaking a tie when more than one
candidate exceeds a Droop quota is nonmonotonic.

The simplest tiebreak is that when there are multiple candidates with
more than a quota's worth of votes (up to the rank you're considering),
you elect the one with the most votes. This can be nonmonotone in th
following way:

Suppose in the base scenario, A wins by tiebreak, and B has one vote
less at the rank q, so A is elected instead of B. In a later round, say,
q+1, E wins. Then suppose a few voters who used to rank A>E decides to
push E higher.

Then B wins at rank q. If now most of the B voters vote E at rank q+1,
it may happen that the deweighting done to these voters (since they got
what they wanted with B being elected instead of A) could keep the
method from electing E.

E.g. A could be a left-wing candidate, B be a right-wing candidate, and
E a center-right candidate. In the base scenario, A wins and then the B
voters get compensated by having the center-right candidate win. But
when someone raises E, the method can't detect the left wing support and
so the right-wing candidate wins instead. Afterwards, the right-wing has
drawn weight away from E (due to E not being a perfect centrist, but
instead being center-right), and so E doesn't win.

Achieving monotonicity in multiwinner rules is rather hard; it's not
obvious how a method could get around the scenario above without
considering later ranks.

I'm not sure if rank-maximality solves the problem above. If it doesn't,
then the above is an example of CM failure but not RRCM failure.

See also
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/094876.html
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-February/095188.html
for another Bucklin PR method that seemed to be monotone.

It's also unknown whether Schulze STV is monotone, though it seems to do
much better than IRV-type STV in this respect. And I'd add that there's
yet another (very strong) type of monotonicity not mentioned in the
paper as far as I could see. Call it "all-winners monotonicity" -
raising a winner on some ballot should not replace any of the candidates
on the elected council with anyone ranked lower on that ballot.

(There's a result by Woodall that you can't have all of LNHelp, LNHarm,
mutual majority and monotonicity. Perhaps, due to the difficulty of
stopping the monotonicity failure scenario above, the equivalent for
multiwinner would turn out to be "you can't have either LNHelp or
LNHarm, and both Droop proportionality and monotonicity"...)
----
Election-Methods mailing list - see http://electoram

[Jameson Quinn]

Yes, I believe that many of these references refer to what is essentially
BTV, which has been known on this list for some time now as a superior
option to STV. I'm happy that it's now in the literature, and don't really
care about naming/precedence.

It's my experience that many prop-rep voting methods can be expressed in
terms of an STV backend. PLACE, Dual Member Proportional, many MMP
variants, etc. can all be seen as just adding options (such as overlapping
seats for MMP and DMP, biproportionality for DMP and PLACE, and partial
delegation for PLACE) on top of STV. You could therefore create new
versions of all of the above by replacing STV with BTV. I think this would
be a small step up — but not worth the additional difficulty of
explanation, in a world that's more used to STV.

Post by Kristofer Munsterhjelm

Post by Arthur Wist
Hello,
Sorry in advanced for the huge load of information all at once, but I
https://arxiv.org/abs/1611.07105 - Two statements of the Duggan-Schwartz
theorem
https://arxiv.org/abs/1611.07102 - Manipulability of consular election
rules
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate
https://arxiv.org/abs/1708.07580 - Achieving Proportional Representation
/achieving-proportional-representation-2d741871e78. Better than STV and
STV derivatives in all criteria? You decide! ]

From a cursory look at the latter, that looks like Bucklin with a
STV-style elect-and-reweight system. I wrote some posts about a
vote-management resistant version of Bucklin at
http://lists.electorama.com/pipermail/election-methods-elect
orama.com/2016-December/001234.html and http://lists.electorama.com/pi
permail/election-methods-electorama.com/2017-September/001584.html, and
found out that the simplest way of breaking a tie when more than one
candidate exceeds a Droop quota is nonmonotonic.
The simplest tiebreak is that when there are multiple candidates with more
than a quota's worth of votes (up to the rank you're considering), you
elect the one with the most votes. This can be nonmonotone in th following
Suppose in the base scenario, A wins by tiebreak, and B has one vote less
at the rank q, so A is elected instead of B. In a later round, say, q+1, E
wins. Then suppose a few voters who used to rank A>E decides to push E
higher.
Then B wins at rank q. If now most of the B voters vote E at rank q+1, it
may happen that the deweighting done to these voters (since they got what
they wanted with B being elected instead of A) could keep the method from
electing E.
E.g. A could be a left-wing candidate, B be a right-wing candidate, and E
a center-right candidate. In the base scenario, A wins and then the B
voters get compensated by having the center-right candidate win. But when
someone raises E, the method can't detect the left wing support and so the
right-wing candidate wins instead. Afterwards, the right-wing has drawn
weight away from E (due to E not being a perfect centrist, but instead
being center-right), and so E doesn't win.
Achieving monotonicity in multiwinner rules is rather hard; it's not
obvious how a method could get around the scenario above without
considering later ranks.
I'm not sure if rank-maximality solves the problem above. If it doesn't,
then the above is an example of CM failure but not RRCM failure.
See also http://lists.electorama.com/pipermail/election-methods-elect
orama.com/2012-January/094876.html and http://lists.electorama.com/pi
permail/election-methods-electorama.com/2012-February/095188.html for
another Bucklin PR method that seemed to be monotone.
It's also unknown whether Schulze STV is monotone, though it seems to do
much better than IRV-type STV in this respect. And I'd add that there's yet
another (very strong) type of monotonicity not mentioned in the paper as
far as I could see. Call it "all-winners monotonicity" - raising a winner
on some ballot should not replace any of the candidates on the elected
council with anyone ranked lower on that ballot.
(There's a result by Woodall that you can't have all of LNHelp, LNHarm,
mutual majority and monotonicity. Perhaps, due to the difficulty of
stopping the monotonicity failure scenario above, the equivalent for
multiwinner would turn out to be "you can't have either LNHelp or LNHarm,
and both Droop proportionality and monotonicity"...)
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Richard Lung]

BTV "known on this list for some time now as a superior option to STV."
Other systems, including BTV are not so regarded by organisations, like
the PRSA and Electoral Reform Society for well over a century. Not to
mention Fair Votes USA.

Richard Lung.

Post by Jameson Quinn
Yes, I believe that many of these references refer to what is
essentially BTV, which has been known on this list for some time now
as a superior option to STV. I'm happy that it's now in the
literature, and don't really care about naming/precedence.
It's my experience that many prop-rep voting methods can be expressed
in terms of an STV backend. PLACE, Dual Member Proportional, many MMP
variants, etc. can all be seen as just adding options (such as
overlapping seats for MMP and DMP, biproportionality for DMP and
PLACE, and partial delegation for PLACE) on top of STV. You could
therefore create new versions of all of the above by replacing STV
with BTV. I think this would be a small step up — but not worth the
additional difficulty of explanation, in a world that's more used to STV.
2018-02-04 12:22 GMT-05:00 Kristofer Munsterhjelm
Hello,
Sorry in advanced for the huge load of information all at
once, but I think you'll highly likely find the following
https://arxiv.org/abs/1611.07105
<https://arxiv.org/abs/1611.07105> - Two statements of the
Duggan-Schwartz theorem
https://arxiv.org/abs/1611.07102
<https://arxiv.org/abs/1611.07102> -  Manipulability of
consular election rules
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate
<https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate>
https://arxiv.org/abs/1708.07580
<https://arxiv.org/abs/1708.07580> - Achieving Proportional
Better than STV and STV derivatives in all criteria? You decide! ]

Post by Kristofer Munsterhjelm
From a cursory look at the latter, that looks like Bucklin with a

STV-style elect-and-reweight system. I wrote some posts about a
vote-management resistant version of Bucklin at
http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-December/001234.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-December/001234.html>
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html>,
and found out that the simplest way of breaking a tie when more
than one candidate exceeds a Droop quota is nonmonotonic.
The simplest tiebreak is that when there are multiple candidates
with more than a quota's worth of votes (up to the rank you're
considering), you elect the one with the most votes. This can be
Suppose in the base scenario, A wins by tiebreak, and B has one
vote less at the rank q, so A is elected instead of B. In a later
round, say, q+1, E wins. Then suppose a few voters who used to
rank A>E decides to push E higher.
Then B wins at rank q. If now most of the B voters vote E at rank
q+1, it may happen that the deweighting done to these voters
(since they got what they wanted with B being elected instead of
A) could keep the method from electing E.
E.g. A could be a left-wing candidate, B be a right-wing
candidate, and E a center-right candidate. In the base scenario, A
wins and then the B voters get compensated by having the
center-right candidate win. But when someone raises E, the method
can't detect the left wing support and so the right-wing candidate
wins instead. Afterwards, the right-wing has drawn weight away
from E (due to E not being a perfect centrist, but instead being
center-right), and so E doesn't win.
Achieving monotonicity in multiwinner rules is rather hard; it's
not obvious how a method could get around the scenario above
without considering later ranks.
I'm not sure if rank-maximality solves the problem above. If it
doesn't, then the above is an example of CM failure but not RRCM
failure.
See also
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/094876.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/094876.html>
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-February/095188.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-February/095188.html>
for another Bucklin PR method that seemed to be monotone.
It's also unknown whether Schulze STV is monotone, though it seems
to do much better than IRV-type STV in this respect. And I'd add
that there's yet another (very strong) type of monotonicity not
mentioned in the paper as far as I could see. Call it "all-winners
monotonicity" - raising a winner on some ballot should not replace
any of the candidates on the elected council with anyone ranked
lower on that ballot.
(There's a result by Woodall that you can't have all of LNHelp,
LNHarm, mutual majority and monotonicity. Perhaps, due to the
difficulty of stopping the monotonicity failure scenario above,
the equivalent for multiwinner would turn out to be "you can't
have either LNHelp or LNHarm, and both Droop proportionality and
monotonicity"...)
----
Election-Methods mailing list - see http://electorama.com/em for list info
----
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--
Richard Lung.
http://www.voting.ukscientists.com
Democracy Science series 3 free e-books in pdf:
https://plus.google.com/106191200795605365085
E-books in epub format:
https://www.smashwords.com/profile/view/democracyscience



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[Jameson Quinn]

I meant "theoretically superior". I agree that in practice STV is a better
proposal — more well-tested, and the theoretical downsides are relatively
minor.

Post by Richard Lung
BTV "known on this list for some time now as a superior option to STV."
Other systems, including BTV are not so regarded by organisations, like the
PRSA and Electoral Reform Society for well over a century. Not to mention
Fair Votes USA.
Richard Lung.
Yes, I believe that many of these references refer to what is essentially
BTV, which has been known on this list for some time now as a superior
option to STV. I'm happy that it's now in the literature, and don't really
care about naming/precedence.
It's my experience that many prop-rep voting methods can be expressed in
terms of an STV backend. PLACE, Dual Member Proportional, many MMP
variants, etc. can all be seen as just adding options (such as overlapping
seats for MMP and DMP, biproportionality for DMP and PLACE, and partial
delegation for PLACE) on top of STV. You could therefore create new
versions of all of the above by replacing STV with BTV. I think this would
be a small step up — but not worth the additional difficulty of
explanation, in a world that's more used to STV.

Post by Kristofer Munsterhjelm

Post by Arthur Wist
Hello,
Sorry in advanced for the huge load of information all at once, but I
https://arxiv.org/abs/1611.07105 - Two statements of the
Duggan-Schwartz theorem
https://arxiv.org/abs/1611.07102 - Manipulability of consular election
rules
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate
https://arxiv.org/abs/1708.07580 - Achieving Proportional
entation-2d741871e78. Better than STV and STV derivatives in all
criteria? You decide! ]
From a cursory look at the latter, that looks like Bucklin with a

STV-style elect-and-reweight system. I wrote some posts about a
vote-management resistant version of Bucklin at
http://lists.electorama.com/pipermail/election-methods-elect
orama.com/2016-December/001234.html and http://lists.electorama.com/pi
permail/election-methods-electorama.com/2017-September/001584.html, and
found out that the simplest way of breaking a tie when more than one
candidate exceeds a Droop quota is nonmonotonic.
The simplest tiebreak is that when there are multiple candidates with
more than a quota's worth of votes (up to the rank you're considering), you
elect the one with the most votes. This can be nonmonotone in th following
Suppose in the base scenario, A wins by tiebreak, and B has one vote less
at the rank q, so A is elected instead of B. In a later round, say, q+1, E
wins. Then suppose a few voters who used to rank A>E decides to push E
higher.
Then B wins at rank q. If now most of the B voters vote E at rank q+1, it
may happen that the deweighting done to these voters (since they got what
they wanted with B being elected instead of A) could keep the method from
electing E.
E.g. A could be a left-wing candidate, B be a right-wing candidate, and E
a center-right candidate. In the base scenario, A wins and then the B
voters get compensated by having the center-right candidate win. But when
someone raises E, the method can't detect the left wing support and so the
right-wing candidate wins instead. Afterwards, the right-wing has drawn
weight away from E (due to E not being a perfect centrist, but instead
being center-right), and so E doesn't win.
Achieving monotonicity in multiwinner rules is rather hard; it's not
obvious how a method could get around the scenario above without
considering later ranks.
I'm not sure if rank-maximality solves the problem above. If it doesn't,
then the above is an example of CM failure but not RRCM failure.
See also http://lists.electorama.com/pipermail/election-methods-elect
orama.com/2012-January/094876.html and http://lists.electorama.com/pi
permail/election-methods-electorama.com/2012-February/095188.html for
another Bucklin PR method that seemed to be monotone.
It's also unknown whether Schulze STV is monotone, though it seems to do
much better than IRV-type STV in this respect. And I'd add that there's yet
another (very strong) type of monotonicity not mentioned in the paper as
far as I could see. Call it "all-winners monotonicity" - raising a winner
on some ballot should not replace any of the candidates on the elected
council with anyone ranked lower on that ballot.
(There's a result by Woodall that you can't have all of LNHelp, LNHarm,
mutual majority and monotonicity. Perhaps, due to the difficulty of
stopping the monotonicity failure scenario above, the equivalent for
multiwinner would turn out to be "you can't have either LNHelp or LNHarm,
and both Droop proportionality and monotonicity"...)
----
Election-Methods mailing list - see http://electorama.com/em for list info

----
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--
Richard Lung.http://www.voting.ukscientists.com
Democracy Science series 3 free e-books in pdf:https://plus.google.com/106191200795605365085
E-books in epub format:https://www.smashwords.com/profile/view/democracyscience
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[Richard Lung]

Have not noticed any theoretcal advantages, tho not familiar with
Bucklin. As mentioned before, Laplace decided in favor of election
counting the relative importance of preferences, which is why he favored
Borda to Condorcet. (It doesn't look like Bucklin does that, beyond
co-opting a Borda count.) Since then Gregory method has improved on
Borda. And actually the Meek method keep value is a further conceptual
improvement. I have an interest to declare there, because have extended
the use of the keep value, in a Binomial STV, and to which I recently
made a couple of up-dates. So it's considerably changed (complexified!)
from the example I did for Kristofer: now it is: Four Averages Binomial
Single Transferable Vote (FAB STV).

Next day (brushing aside the cobwebs): It occurs to me that by
"theoretically superior," you may be refering to Bucklin uniformity of
method for single and multiple vacancies. If so, Binomial STV (STV^) has
that covered, because  it is a progression from Meek method, extending
the use of keep values, to conduct counts for single vacancies the same
way as multiple vacancies, as Gregory method could not, nor indeed Meek
method itself, from where it left off.

For theorists, who seek general explanations, STV^ fulfills the
requirement of a consistent treatment of both single and multiple vacancies.

The scientific significance of this is that STV^ brings a more powerful
scale of measurement to single vacancies. However single vacancies are
(much) less desirable both from a democratic and a mensural view-point,
lacking "Proportional Representation. The key to democracy." (As the
Hoag and Hallett classic is titled.)

Following Google notation for "to the power of", which is the
circumflex, ^, then notation for Binomial STV is: STV^. The binomial
theorem expands by powers, and this expansion is the (non-commutative)
guide for systematic STV recounts.

Traditional (uninomial) STV is STV^0 (zero order STV -- like your
start-up Meccano set 0, which this child never got beyond!).
First order Binomial STV is STV^1. (Basic combination of preference
election count and reverse preference or unpreference exclusion count)
Second order is STV^2, and so on. (Recounts based on systematic
qualifications of the previous order results.)

  from
Richard Lung.

Post by Jameson Quinn
I meant "theoretically superior". I agree that in practice STV is a
better proposal — more well-tested, and the theoretical downsides are
relatively minor.
BTV "known on this list for some time now as a superior option to
STV." Other systems, including BTV are not so regarded by
organisations, like the PRSA and Electoral Reform Society for well
over a century. Not to mention Fair Votes USA.
Richard Lung.

Post by Jameson Quinn
Yes, I believe that many of these references refer to what is
essentially BTV, which has been known on this list for some time
now as a superior option to STV. I'm happy that it's now in the
literature, and don't really care about naming/precedence.
It's my experience that many prop-rep voting methods can be
expressed in terms of an STV backend. PLACE, Dual Member
Proportional, many MMP variants, etc. can all be seen as just
adding options (such as overlapping seats for MMP and DMP,
biproportionality for DMP and PLACE, and partial delegation for
PLACE) on top of STV. You could therefore create new versions of
all of the above by replacing STV with BTV. I think this would be
a small step up — but not worth the additional difficulty of
explanation, in a world that's more used to STV.
2018-02-04 12:22 GMT-05:00 Kristofer Munsterhjelm
Hello,
Sorry in advanced for the huge load of information all at
once, but I think you'll highly likely find the following
https://arxiv.org/abs/1611.07105
<https://arxiv.org/abs/1611.07105> - Two statements of
the Duggan-Schwartz theorem
https://arxiv.org/abs/1611.07102
<https://arxiv.org/abs/1611.07102> -  Manipulability of
consular election rules
https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate
<https://scholar.google.com/citations?user=ssb0yjUAAAAJ&sortby=pubdate>
https://arxiv.org/abs/1708.07580
<https://arxiv.org/abs/1708.07580> - Achieving
Proportional Representation via Voting [ On which a blog
Better than STV and STV derivatives in all criteria? You
decide! ]

Post by Kristofer Munsterhjelm
From a cursory look at the latter, that looks like Bucklin

with a STV-style elect-and-reweight system. I wrote some
posts about a vote-management resistant version of Bucklin at
http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-December/001234.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-December/001234.html>
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html>,
and found out that the simplest way of breaking a tie when
more than one candidate exceeds a Droop quota is nonmonotonic.
The simplest tiebreak is that when there are multiple
candidates with more than a quota's worth of votes (up to the
rank you're considering), you elect the one with the most
Suppose in the base scenario, A wins by tiebreak, and B has
one vote less at the rank q, so A is elected instead of B. In
a later round, say, q+1, E wins. Then suppose a few voters
who used to rank A>E decides to push E higher.
Then B wins at rank q. If now most of the B voters vote E at
rank q+1, it may happen that the deweighting done to these
voters (since they got what they wanted with B being elected
instead of A) could keep the method from electing E.
E.g. A could be a left-wing candidate, B be a right-wing
candidate, and E a center-right candidate. In the base
scenario, A wins and then the B voters get compensated by
having the center-right candidate win. But when someone
raises E, the method can't detect the left wing support and
so the right-wing candidate wins instead. Afterwards, the
right-wing has drawn weight away from E (due to E not being a
perfect centrist, but instead being center-right), and so E
doesn't win.
Achieving monotonicity in multiwinner rules is rather hard;
it's not obvious how a method could get around the scenario
above without considering later ranks.
I'm not sure if rank-maximality solves the problem above. If
it doesn't, then the above is an example of CM failure but
not RRCM failure.
See also
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/094876.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/094876.html>
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-February/095188.html
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-February/095188.html>
for another Bucklin PR method that seemed to be monotone.
It's also unknown whether Schulze STV is monotone, though it
seems to do much better than IRV-type STV in this respect.
And I'd add that there's yet another (very strong) type of
monotonicity not mentioned in the paper as far as I could
see. Call it "all-winners monotonicity" - raising a winner on
some ballot should not replace any of the candidates on the
elected council with anyone ranked lower on that ballot.
(There's a result by Woodall that you can't have all of
LNHelp, LNHarm, mutual majority and monotonicity. Perhaps,
due to the difficulty of stopping the monotonicity failure
scenario above, the equivalent for multiwinner would turn out
to be "you can't have either LNHelp or LNHarm, and both Droop
proportionality and monotonicity"...)
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