Using Schulze Election Method to elect a flexible amount of winners
Dear election enthusiasts,
First of all I would like to congratulate you on the great wealth of works
and ideas you brought into the world of voting/election methods. Even
though it may be out of the scope of your focus, I have a consideration I
would like to consult you on. If I came to the wrong place, let me know.
In my organisation we are implementing the Schulze method to all situations
where a single winner or sorted list of winners has to be chosen from more
than two options. We basically did a straight implementation from the
wikipedia pseudocode into our own online voting system.
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. We used to make this
decision by conducting an approval vote with a certain threshold for
winners. I was not happy about this slightly arbitrary choice of threshold.
Now some colleagues wish to again see some value by which the quantity of
support for all the candidates can be understood.
I propose to use the Schulze method and add an option of "no further
winner" to the list of candidates, which is comparable to what is defined
as the "status quo" as mr Schulze described in his paper in the section
super-majorities. I.e. the status quo is 'no winners', and each candidate
has to beat the option of 'no winners' in order to qualify.
Would you think this is an adequate procedure to make this decision on both
the choice of winners and the amount of winners? I am aware there is a risk
of electing no candidates, or all candidates. But at least it is less
artificial than a fixed percentage of votes as was done before.
Best regards,
Paul L. Smits
On 10/3/2016 7:29 AM, Paul Smits wrote:
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. ...
Single-winner methods, such as the Condorcet-Schulze method and the
Condorcet-Kemeny method, cannot be used to elect a second winner. Why?
The voters who favor the most popular choice need to have their
influence reduced in order to correctly identify the second winner.
As explained here,
http://www.votefair.org/calculation_details_representation.html
"Without this adjustment the same voters who are well-represented by the
most popular choice could also determine the second-place winner."
To understand this concept, imagine a group of participants who vote in
order to choose two events that will happen at the same time. The
single-winner method can easily identify the most popular activity. But
if the single-winner method is also used to identify the "second-most
popular" activity, then the second activity will not be well-attended
because most of the participants will attend the most popular activity.
In the meantime, the remaining participants, who were outvoted, will
not be interested in the second activity, and they will be frustrated
that their preferred activity was not chosen as the second event.
I created VoteFair representation ranking to handle such situations.
Later, Markus Schulze created what he calls Schulze-STV to serve this
purpose.
The link above explains how VoteFair representation ranking works. My
ebook "Ending The Hidden Unfairness In U.S. Elections" (which also
applies to other nations as explained near the end of the book) also
explains this concept. It is available for most ebook readers, and I
priced it as low as allowed (which mostly just covers the download fee).
BTW, what many people overlook is the fact that "second-most popular"
has multiple possible interpretations.
If you have more questions, please ask. And thank you for learning
about election-method reform!
Richard Fobes
On 10/3/2016 7:29 AM, Paul Smits wrote:
Dear election enthusiasts,
First of all I would like to congratulate you on the great wealth of
works and ideas you brought into the world of voting/election methods.
Even though it may be out of the scope of your focus, I have a
consideration I would like to consult you on. If I came to the wrong
place, let me know.
In my organisation we are implementing the Schulze method to all
situations where a single winner or sorted list of winners has to be
chosen from more than two options. We basically did a straight
implementation from the wikipedia pseudocode into our own online voting
system.
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. We used to make this
decision by conducting an approval vote with a certain threshold for
winners. I was not happy about this slightly arbitrary choice of
threshold. Now some colleagues wish to again see some value by which the
quantity of support for all the candidates can be understood.
I propose to use the Schulze method and add an option of "no further
winner" to the list of candidates, which is comparable to what is
defined as the "status quo" as mr Schulze described in his paper in the
section super-majorities. I.e. the status quo is 'no winners', and each
candidate has to beat the option of 'no winners' in order to qualify.
Would you think this is an adequate procedure to make this decision on
both the choice of winners and the amount of winners? I am aware there
is a risk of electing no candidates, or all candidates. But at least it
is less artificial than a fixed percentage of votes as was done before.
Best regards,
Paul L. Smits
Election-Methods mailing list - see http://electorama.com/em for list info
�
it seems to me that any Condorcet-compliant method (Schulze, MinMax, Ranked-Pairs) can be extended from single-winner to multi-winner.
why not just run the procedure multiple times, each time removing from the list the candidate that was elected from the single-winner
procedure and, at the same time, reducing the number of office seats available by one? �why can't we do that? �what is wrong with that?
seems to me that it would work.
r b-j
---------------------------- Original Message ----------------------------
Subject: Re: [EM] Using Schulze Election Method to elect a flexible amount of winners
From: "VoteFair" ElectionMethods@VoteFair.org
Date: Tue, October 4, 2016 8:23 pm
To: "election-methods@lists.electorama.com" election-methods@lists.electorama.com
On 10/3/2016 7:29 AM, Paul Smits wrote:
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. ...
Single-winner methods, such as the Condorcet-Schulze method and the
Condorcet-Kemeny method, cannot be used to elect a second winner. Why?
The voters who favor the most popular choice need to have their
influence reduced in order to correctly identify the second winner.
As explained here,
"Without this adjustment the same voters who are well-represented by the
most popular choice could also determine the second-place winner."
To understand this concept, imagine a group of participants who vote in
order to choose two events that will happen at the same time. The
single-winner method can easily identify the most popular activity. But
if the single-winner method is also used to identify the "second-most
popular" activity, then the second activity will not be well-attended
because most of the participants will attend the most popular activity.
In the meantime, the remaining participants, who were outvoted, will
not be interested in the second activity, and they will be frustrated
that their preferred activity was not chosen as the second event.
I created VoteFair representation ranking to handle such situations.
Later, Markus Schulze created what he calls Schulze-STV to serve this
purpose.
The link above explains how VoteFair representation ranking works. My
ebook "Ending The Hidden Unfairness In U.S. Elections" (which also
applies to other nations as explained near the end of the book) also
explains this concept. It is available for most ebook readers, and I
priced it as low as allowed (which mostly just covers the download fee).
BTW, what many people overlook is the fact that "second-most popular"
has multiple possible interpretations.
If you have more questions, please ask. And thank you for learning
about election-method reform!
Richard Fobes
On 10/3/2016 7:29 AM, Paul Smits wrote:
Dear election enthusiasts,
First of all I would like to congratulate you on the great wealth of
works and ideas you brought into the world of voting/election methods.
Even though it may be out of the scope of your focus, I have a
consideration I would like to consult you on. If I came to the wrong
place, let me know.
In my organisation we are implementing the Schulze method to all
situations where a single winner or sorted list of winners has to be
chosen from more than two options. We basically did a straight
implementation from the wikipedia pseudocode into our own online voting
system.
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. We used to make this
decision by conducting an approval vote with a certain threshold for
winners. I was not happy about this slightly arbitrary choice of
threshold. Now some colleagues wish to again see some value by which the
quantity of support for all the candidates can be understood.
I propose to use the Schulze method and add an option of "no further
winner" to the list of candidates, which is comparable to what is
defined as the "status quo" as mr Schulze described in his paper in the
section super-majorities. I.e. the status quo is 'no winners', and each
candidate has to beat the option of 'no winners' in order to qualify.
Would you think this is an adequate procedure to make this decision on
both the choice of winners and the amount of winners? I am aware there
is a risk of electing no candidates, or all candidates. But at least it
is less artificial than a fixed percentage of votes as was done before.
Best regards,
Paul L. Smits
Election-Methods mailing list - see http://electorama.com/em for list info
Election-Methods mailing list - see http://electorama.com/em for list info
--
�
r b-j � � � � � � � � �rbj@audioimagination.com
�
"Imagination is more important than knowledge."
On 10/05/2016 06:39 AM, robert bristow-johnson wrote:
it seems to me that any Condorcet-compliant method (Schulze, MinMax,
Ranked-Pairs) can be extended from single-winner to multi-winner.
why not just run the procedure multiple times, each time removing from
the list the candidate that was elected from the single-winner procedure
and, at the same time, reducing the number of office seats available by
one? why can't we do that? what is wrong with that?
seems to me that it would work.
I think I've mentioned this before, but suppose there are 51% Democrats
and 49% Republicans in district X, and everybody ranks their party's
candidates first. Then (assuming each party fields enough candidates),
any cloneproof Condorcet method will rank all the Democrats first, so
your assembly will be composed entirely of Democrats.
This doesn't seem entirely fair, so I'm not in favor of such an
extension of Condorcet methods. If your assembly is entirely
nonpartisan, it might work, but you're going to get an
overrepresentation of candidates near the median voter. This is what you
want for single-winner, but it does decrease variety (and thus the
benefit of debate) when you have multiple winners.
On 10/03/2016 04:29 PM, Paul Smits wrote:
Dear election enthusiasts,
First of all I would like to congratulate you on the great wealth of
works and ideas you brought into the world of voting/election methods.
Even though it may be out of the scope of your focus, I have a
consideration I would like to consult you on. If I came to the wrong
place, let me know.
In my organisation we are implementing the Schulze method to all
situations where a single winner or sorted list of winners has to be
chosen from more than two options. We basically did a straight
implementation from the wikipedia pseudocode into our own online voting
system.
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. We used to make this
decision by conducting an approval vote with a certain threshold for
winners. I was not happy about this slightly arbitrary choice of
threshold. Now some colleagues wish to again see some value by which the
quantity of support for all the candidates can be understood.
The way I'm reading this is that you're wondering how you might extend a
Condorcet method to a situation where you want "how many winners to
elect" to also be up to vote, and not just to a situation where you know
the number of winners to elect. If it's just an ordinary multiwinner
situation (you know the assembly will be, say, 12 seats), see below.
If your scenario can handle repeated balloting, I would suggest
something like this:
Produce a list by the Schulze proportional ranking
(http://m-schulze.9mail.de/schulze2.pdf).
Then, starting with one winner, repeatedly hold a majority vote of
whether the assembly size should be increased to two seats, three seats,
etc. When the motion fails, the assembly size is set.
If you can't do repeated balloting, something like this should work:
On the ballot, have two questions. The first asks for the voter's
ranking of the candidates, and the second asks for how large an assembly
he wants to have.
Once you have the ballots, determine the median value of the second
question: this is the value where just as many voters want a larger
assembly as a smaller one, so in a sense there's a balance there.
Then use either a proportional ranking method (like the Schulze
proportional ranking) or an STV method (like Schulze STV) to elect that
many candidates.
The greatest problem with these proposals, I think, is that both Schulze
STV and the Schulze proportional ranking are very complex systems. You
might have a problem getting them accepted to begin with.
One interesting question is, if you want proportional representation, should you use the proportional ranking approach. The simplest example in maybe the following one.
40: A>B>C
10: B>A>C
10: B>C>A
40: C>B>A
B is the Condorcet winner, so it would be a good choice if we will elect one winner. But if we elect two winners, then electing A and C could be a good choice. B would not be elected although B was elected if the number of elected candidates was one lower.
One thus needs to decide if one wants to have an ordering of the candidates (e.g. if one picks them one by one without possibility to change the already elected candidates), or if one wants the proportionality to be accurate (in the way described above). One can not have both.
Juho
On 05 Oct 2016, at 12:16, Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 10/03/2016 04:29 PM, Paul Smits wrote:
Dear election enthusiasts,
First of all I would like to congratulate you on the great wealth of
works and ideas you brought into the world of voting/election methods.
Even though it may be out of the scope of your focus, I have a
consideration I would like to consult you on. If I came to the wrong
place, let me know.
In my organisation we are implementing the Schulze method to all
situations where a single winner or sorted list of winners has to be
chosen from more than two options. We basically did a straight
implementation from the wikipedia pseudocode into our own online voting
system.
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. We used to make this
decision by conducting an approval vote with a certain threshold for
winners. I was not happy about this slightly arbitrary choice of
threshold. Now some colleagues wish to again see some value by which the
quantity of support for all the candidates can be understood.
The way I'm reading this is that you're wondering how you might extend a
Condorcet method to a situation where you want "how many winners to
elect" to also be up to vote, and not just to a situation where you know
the number of winners to elect. If it's just an ordinary multiwinner
situation (you know the assembly will be, say, 12 seats), see below.
If your scenario can handle repeated balloting, I would suggest
something like this:
Produce a list by the Schulze proportional ranking
(http://m-schulze.9mail.de/schulze2.pdf).
Then, starting with one winner, repeatedly hold a majority vote of
whether the assembly size should be increased to two seats, three seats,
etc. When the motion fails, the assembly size is set.
If you can't do repeated balloting, something like this should work:
On the ballot, have two questions. The first asks for the voter's
ranking of the candidates, and the second asks for how large an assembly
he wants to have.
Once you have the ballots, determine the median value of the second
question: this is the value where just as many voters want a larger
assembly as a smaller one, so in a sense there's a balance there.
Then use either a proportional ranking method (like the Schulze
proportional ranking) or an STV method (like Schulze STV) to elect that
many candidates.
The greatest problem with these proposals, I think, is that both Schulze
STV and the Schulze proportional ranking are very complex systems. You
might have a problem getting them accepted to begin with.
Election-Methods mailing list - see http://electorama.com/em for list info
"Now some colleagues wish to again see some value by which the
quantity of support for all the candidates can be understood."
My method of Binomial STV should do that, by giving every candidate a
keep value. In extension from Meek STV which just gives quota-surplus
keep values, Ive introduced quota-deficit keep values.
Binomial STV could be codified following on from the Meek STV computer
count.
from Richard Lung.
On 10/03/2016 04:29 PM, Paul Smits wrote:
Dear election enthusiasts,
First of all I would like to congratulate you on the great wealth of
works and ideas you brought into the world of voting/election methods.
Even though it may be out of the scope of your focus, I have a
consideration I would like to consult you on. If I came to the wrong
place, let me know.
In my organisation we are implementing the Schulze method to all
situations where a single winner or sorted list of winners has to be
chosen from more than two options. We basically did a straight
implementation from the wikipedia pseudocode into our own online voting
system.
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. We used to make this
decision by conducting an approval vote with a certain threshold for
winners. I was not happy about this slightly arbitrary choice of
threshold. Now some colleagues wish to again see some value by which the
quantity of support for all the candidates can be understood.
The way I'm reading this is that you're wondering how you might extend a
Condorcet method to a situation where you want "how many winners to
elect" to also be up to vote, and not just to a situation where you know
the number of winners to elect. If it's just an ordinary multiwinner
situation (you know the assembly will be, say, 12 seats), see below.
If your scenario can handle repeated balloting, I would suggest
something like this:
Produce a list by the Schulze proportional ranking
(http://m-schulze.9mail.de/schulze2.pdf).
Then, starting with one winner, repeatedly hold a majority vote of
whether the assembly size should be increased to two seats, three seats,
etc. When the motion fails, the assembly size is set.
If you can't do repeated balloting, something like this should work:
On the ballot, have two questions. The first asks for the voter's
ranking of the candidates, and the second asks for how large an assembly
he wants to have.
Once you have the ballots, determine the median value of the second
question: this is the value where just as many voters want a larger
assembly as a smaller one, so in a sense there's a balance there.
Then use either a proportional ranking method (like the Schulze
proportional ranking) or an STV method (like Schulze STV) to elect that
many candidates.
The greatest problem with these proposals, I think, is that both Schulze
STV and the Schulze proportional ranking are very complex systems. You
might have a problem getting them accepted to begin with.
Election-Methods mailing list - see http://electorama.com/em for list info
On 10/05/2016 06:00 PM, Juho Laatu wrote:
One interesting question is, if you want proportional representation,
should you use the proportional ranking approach. The simplest
example in maybe the following one.
40: A>B>C
10: B>A>C
10: B>C>A
40: C>B>A
B is the Condorcet winner, so it would be a good choice if we will
elect one winner. But if we elect two winners, then electing A and C
could be a good choice. B would not be elected although B was elected
if the number of elected candidates was one lower.
One thus needs to decide if one wants to have an ordering of the
candidates (e.g. if one picks them one by one without possibility to
change the already elected candidates), or if one wants the
proportionality to be accurate (in the way described above). One can
not have both.
The example I usually trot out is LCR (exact numbers vary):
20: L>C>R
18: R>C>L
3: C>R>L
For a single-winner election, C should win. For two winners, the set
should be L and R, otherwise the outcome will be biased in favor of
whoever the not-centrist ends up being.
LCR is also a center-squeeze scenario. Plurality elects L and IRV elects R.
You're right that you can't have both. Imperfect symmetry is the price
you pay for "house monotonicity" (that n-1 of the n winners in an n-seat
election are the winners of the n-1 seat election). I seem to recall
reading somewhere (while investigating approximation methods to the
k-median and facility location problems) about how close you can get to
the optimum while being house monotone. However, I don't recall what the
bounds were, other than that I was surprised they weren't worse.
I guess those mentioned examples are about the worst ones. If the number of elected representatives is high, the symmetry/proportionality errors may easily get lost in the overall noise. The described problem is still there. There could be a need e.g. to change the n-1'th candidate when electing the n'th candidate, just as in the original examples. But since we are now talking about the last allocated seats, maybe nobody cares. The errors probably get smaller if counted as % of error, but may stay about at the same level if counted as number of representatives that should have been changed.
I don't have any exact numbers or proper estimates though. Maybe your calculations showed that the frequency of errors gets lower, or that the amount of distortion per error (as %) gets lower.
Juho
P.S. This is also related to the highest averages vs. largest remainder question.
On 05 Oct 2016, at 23:57, Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 10/05/2016 06:00 PM, Juho Laatu wrote:
One interesting question is, if you want proportional representation,
should you use the proportional ranking approach. The simplest
example in maybe the following one.
40: A>B>C
10: B>A>C
10: B>C>A
40: C>B>A
B is the Condorcet winner, so it would be a good choice if we will
elect one winner. But if we elect two winners, then electing A and C
could be a good choice. B would not be elected although B was elected
if the number of elected candidates was one lower.
One thus needs to decide if one wants to have an ordering of the
candidates (e.g. if one picks them one by one without possibility to
change the already elected candidates), or if one wants the
proportionality to be accurate (in the way described above). One can
not have both.
The example I usually trot out is LCR (exact numbers vary):
20: L>C>R
18: R>C>L
3: C>R>L
For a single-winner election, C should win. For two winners, the set
should be L and R, otherwise the outcome will be biased in favor of
whoever the not-centrist ends up being.
LCR is also a center-squeeze scenario. Plurality elects L and IRV elects R.
You're right that you can't have both. Imperfect symmetry is the price
you pay for "house monotonicity" (that n-1 of the n winners in an n-seat
election are the winners of the n-1 seat election). I seem to recall
reading somewhere (while investigating approximation methods to the
k-median and facility location problems) about how close you can get to
the optimum while being house monotone. However, I don't recall what the
bounds were, other than that I was surprised they weren't worse.
On 10/5/2016 2:16 AM, Kristofer Munsterhjelm wrote:
On 10/03/2016 04:29 PM, Paul Smits wrote:
...
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate.
...
The way I'm reading this is that you're wondering how you might extend a
Condorcet method to a situation where you want "how many winners to
elect" to also be up to vote, and not just to a situation where you know
the number of winners to elect.
In my previous reply I focused on the importance of using a proportional
method rather than a single-winner method, and I forgot about this part
of the question.
The answer for this part depends on the answers to these questions:
-
What is the range for the number of seats?
-
Is the number voted on at the same time as the candidates are ranked?
Or are there two rounds of voting such that the voters know which
candidates will get elected when they vote on increasing the number of
winners?
As an extreme case, the transition from 1 to 2 seats likely would not
get majority support -- because the majority chooses the first winner,
who gets total control.
A similar but more complex effect can occur going from 2 to 3
candidates, or going from 3 to 4 candidates.
At about 5 candidates the proportionality of the results stabilizes --
if a good proportional method is chosen. At about this number or higher
there is less strategic advantage (mathematically anyway) to support or
oppose an increased number of seats.
Without knowing the answers to the above questions it's difficult to
further answer this question beyond Kristofer's thorough reply.
Richard Fobes
On 10/5/2016 2:16 AM, Kristofer Munsterhjelm wrote:
On 10/03/2016 04:29 PM, Paul Smits wrote:
Dear election enthusiasts,
First of all I would like to congratulate you on the great wealth of
works and ideas you brought into the world of voting/election methods.
Even though it may be out of the scope of your focus, I have a
consideration I would like to consult you on. If I came to the wrong
place, let me know.
In my organisation we are implementing the Schulze method to all
situations where a single winner or sorted list of winners has to be
chosen from more than two options. We basically did a straight
implementation from the wikipedia pseudocode into our own online voting
system.
Now the question arose how we could use the Schulze method in a decision
where the amount of winners is also up for debate. We used to make this
decision by conducting an approval vote with a certain threshold for
winners. I was not happy about this slightly arbitrary choice of
threshold. Now some colleagues wish to again see some value by which the
quantity of support for all the candidates can be understood.
The way I'm reading this is that you're wondering how you might extend a
Condorcet method to a situation where you want "how many winners to
elect" to also be up to vote, and not just to a situation where you know
the number of winners to elect. If it's just an ordinary multiwinner
situation (you know the assembly will be, say, 12 seats), see below.
If your scenario can handle repeated balloting, I would suggest
something like this:
Produce a list by the Schulze proportional ranking
(http://m-schulze.9mail.de/schulze2.pdf).
Then, starting with one winner, repeatedly hold a majority vote of
whether the assembly size should be increased to two seats, three seats,
etc. When the motion fails, the assembly size is set.
If you can't do repeated balloting, something like this should work:
On the ballot, have two questions. The first asks for the voter's
ranking of the candidates, and the second asks for how large an assembly
he wants to have.
Once you have the ballots, determine the median value of the second
question: this is the value where just as many voters want a larger
assembly as a smaller one, so in a sense there's a balance there.
Then use either a proportional ranking method (like the Schulze
proportional ranking) or an STV method (like Schulze STV) to elect that
many candidates.
The greatest problem with these proposals, I think, is that both Schulze
STV and the Schulze proportional ranking are very complex systems. You
might have a problem getting them accepted to begin with.
Election-Methods mailing list - see http://electorama.com/em for list info