Third Parties and Kristofer
Subject: [EM]Third Parties.
To: Kristofer Munsterhjelm and others. (km-elmet@munsterhjelm.no)
FROM: Stephen Bosworth (stevebosworth@hotmail.commailto:stevebosworth@hotmail.com)
I want fully to understand the relevant new ideas you offered in your 7/30/2024 4:06 PM post. These ideas were especially prompted for me by your words and phrases extracted and copied immediately below the next paragraph.
Currently, the intuitions or possibilities your words suggest to me, once fully understood, might require either a rejection or a confirmation of the proportional voting method published in 2020 by my co-authors and myself [https://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v3/].
That article offers a full account of evaluative-proportional representation (EPR), including the algorithm for counting such an election. Additionaly and in the last section of this post, I’ve added a complementary and much shorter introduction to EPR . It explains, for example, how electing a seven-member city council using EPR ensures that every voter is most likely to see one of the elected candidates as representing them accurately. Every party, voter, minority, and majority of voters would be proportionally represented in the council exactly.
Of course, I look forward to receiving as much feedback as possible from you and from other EM contributors. In particular, I want to understand why your “VSE-like proportionality measure” either falsifies or supports my above paragraph’s last two sentences?
Below: Key phrases extracted from: Kristofer’s Post Sent: Wednesday, July 31, 2024 1:02 PM
Subject: Election-Methods Digest, Vol 240, Issue 25 (Third Parties)
- Re: Third parties (Kristofer Munsterhjelm)
- A VSE-like proportionality measure, or the start of one (Kristofer Munsterhjelm)
…. because otherwise you could have a candidate who has an
opinion none of the voters happen to have….
…. perfect proportionality.
…. it would jumble together voters not ranking/rating
candidates in order, and disproportionality of the method itself….
…. the "zero opinion" problem is still real…
Empirically speaking, maybe one could get around this by smoothing the
voter opinion distribution. But perhaps there's a better theoretically
founded way to do it…. - maybe I should look more into them.
…. augment this measure to include….descriptive representation.
In any case, this could be useful to evaluate PR methods'
proportionality, and to check how much proportionality we lose by having
small districts instead of one large district with something like STV.
Ranking a thousand candidates may be impractical for real voters, but
not for computer simulated ones :-)
….proportional (not at all) as electing one….full of candidates at x=0.9. This
seems wrong. It can be dealt with by
dividing voter space into a number of regions and then counting over
each "bin", … a kernel density-like solution? [Is this another way of refering to “ideological districts” or constituencies?]
I don't know it if there is.
…. because there's always some support and it's always decreasing away
from where the voter opinions are concentrated….
….any straightforward proportionality measure, can also
be criticized as quantifying the wrong thing: as Steve Eppley said in
2008, (paraphrased) "why should I be interested if they have the same
opinions as me, if they don't legislate the way I would?". In a similar
way, it doesn't take into account coalition effects or kingmaker
problems with low threshold PR methods, either.
-km
Steve’s following brief explanation and illustration of how evaluative-proportion representation (EPR) works assumes that you, the reader, are voting on the following sample ballot. This ballot is followed by more explanation:
EPR Sample Paper Ballot
City Number 30
Directions: Please grade at least one candidate’s suitability for office by putting an X in either the Excellent, Very Good, Good, or Acceptable box next to each of the candidates you want to grade. You may give the same grade to more than one candidate. You may use Poor or Reject to grade candidates you do not find fit for office. Any candidates who you do not explicitly grade will be automatically counted as if you marked them as ‘Reject/unknown’. You are assured that your one vote of Acceptable or better for a candidate will increase the voting power in the legislative body of the winner you helped to elect directly or indirectly.
Identity Code of the candidate
Candidate
Note: Give only one grade for one or more candidates
by placing an X in the relevant box.
EXCELLENT
VERY GOOD
GOOD
ACCEPTABLE
POOR
REJECT
A
Stephen Collins
X
B
Candice Crosby
X
C
Robin Levy
X
D
Martin Newman
X
E
June Glover
X
F
Frank Field
If none of the candidates you graded as at least Acceptable is elected, your ballot becomes a proxy vote. This proxy vote will be added to the running total of votes received by the winning candidate publicly judged most suitable for office by the candidate to whom you gave your highest grade. However, if you do not want this to happen, circle NO at the end of this sentence:
YES --- N0
More explanation:
The first round counts all voters’ completed ballots. Each ballot provisionally adds one to the total number of votes received by one or other of the candidates. As a result, each candidate will have received a different total number of votes but composed of different numbers of each grade.
If, for example, you awarded the same highest grade to more than one candidate, that grade is exclusively added to the running total of the candidate who will have the larger total as a result. This is justified by the democratic assumption that a candidate who gets more votes is probably better.
The target number of candidates are elected by their having received one of the seven largest totals of votes of at least Acceptable. When finalized, each of these winner’s totals quantifies their voting power in the legislative assembly – their “weighted vote.” Thus, each citizen’s ballot (vote) equally adds to the weighted vote of the elected candidate they are most likely to favor.
Next, in order to ensure that every citizen’s vote continues to count equally and effectively as one in the legislative body, all the ballots (votes) currently held by candidates not elected are now transferred to the running total of one or other of the winners. This is automatically possible for each such ballot that also contains a remaining “highest-available grade” for one of the winners.
The “highest-available grade” on such a ballot is determined at any given point in the count by the rules that govern the count. For example, if a voter’s ballot awarded an “Excellent” to a candidate who could not be elected because they had not received a large enough number of votes from all voters, this ballot would automatically be transferred to the running total of the winner who this ballot awarded its remaining “highest-available grade” – Very Good, Good, or Acceptable.
However, if this ballot does not award any winner in this way, it automatically becomes a “proxy vote.” If the relevant voter has given their permission at the bottom of their ballot bu circling “NO”, their proxy vote is transferred to the weighted vote of the already elected candidate publicly judged most suitable for office by the candidate on their ballot who received this voter’s highest grade.
Consequently, unlike all available alternative voting systems, EPR ensures that every citizen’s vote (ballot) equally adds to the voting power in the legislative assembly of the elected candidate who finally received each voter’s “highest-available grade.” In each case, this grade is either the ballot's highest grade, remaining highest grade, or proxy vote. Thus, EPR guarantees that every ballot will equally increase the weighted vote of one of the elected members by one – the member they are most likely to see as accurately representing their concerns and hopes. Therefore, 100% of the voters have every appropriate reason to be satisfied with the results of an EPR election.
Your above vote:
Again, the first rounds of EPR’s count determine to which candidate’s running total your highest grade (vote) is provisionally given. For the count of your vote already indicated in the ballot, your Excellent must be provisionally added either to the running total of Collins or Levy. It must go to the one who has received the largest number of Excellents from all the ballots cast.
For this illustration, we are assuming that Levy received more such votes (grades) than any other such candidate, including Collins. Therefore, your current “highest-available grade” of “Excellent” is exclusively but provisionally added to Levy’s running total of votes, not to Collins’s. Again, this is justified by the democratic assumption that the candidate who has more votes is probably better.
Therefore, say your Excellent goes to Levy, and for brevity of explanation also assume that this election aims to elect all seven members of a city council. Levy will be elected if she has separately received one of the seven largest numbers of “highest-available grades” from all voters.
Each candidate’s total is composed of different numbers of Excellent, Very Good, Good, and Acceptable received separately from a number of all the ballots cast. One such grade from every citizen’s ballot is added to the total of one of the candidates. When each voter’s ballot has been provisionally added to one of the candidates running total of votes in this way, the seven elected candidates are identified. Each has received one of the seven largest totals. Levy would be elected if her total is one of these seven.
However, if Levy’s final total is not one of these winning seven, your ballot’s “highest-available grade” of Excellent is instead transferred to Collins, but only if Collins would have one of the seven largest totals as a result. If not, your ballot would be transferred to Cosby, but again, only if Cosby would receive one of the largest seven totals as a result. Given this condition, your vote might instead have to be transferred to Newman or Glover.
However, if none of these candidates could receive one of the largest seven totals with the help of your vote (ballot), your ballot automatically becomes your proxy vote as described above. This is to say that if you had not circled the “NO” at the bottom of your above ballot paper, you have given permission for your proxy vote to be finally added to the weighted vote of the winner that is publicly judged to be most fit for office by Levy.
In this way, you and every other citizen is assured that they will be equally represented in the assembly as accurately as possible.
What do you think?
End of Election-Methods Digest, Vol 240, Issue 25
From: steve bosworth stevebosworth@hotmail.com
Sent: Sunday, August 18, 2024 9:58 PM
To: election-methods@lists.electorama.com election-methods@lists.electorama.com
Cc: km-elmet@munsterhjelm.no km-elmet@munsterhjelm.no
Subject: Third Parties and Kristofer
Subject: [EM]Third Parties.
To: Kristofer Munsterhjelm and others. (km-elmet@munsterhjelm.no)
FROM: Stephen Bosworth (stevebosworth@hotmail.commailto:stevebosworth@hotmail.com)
I want fully to understand the relevant new ideas you offered in your 7/30/2024 4:06 PM post. These ideas were especially prompted for me by your words and phrases extracted and copied immediately below the next paragraph.
Currently, the intuitions or possibilities your words suggest to me, once fully understood, might require either a rejection or a confirmation of the proportional voting method published in 2020 by my co-authors and myself [https://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v3/].
That article offers a full account of evaluative-proportional representation (EPR), including the algorithm for counting such an election. Additionaly and in the last section of this post, I’ve added a complementary and much shorter introduction to EPR . It explains, for example, how electing a seven-member city council using EPR ensures that every voter is most likely to see one of the elected candidates as representing them accurately. Every party, voter, minority, and majority of voters would be proportionally represented in the council exactly.
Of course, I look forward to receiving as much feedback as possible from you and from other EM contributors. In particular, I want to understand why your “VSE-like proportionality measure” either falsifies or supports my above paragraph’s last two sentences?
Below: Key phrases extracted from: Kristofer’s Post Sent: Wednesday, July 31, 2024 1:02 PM
Subject: Election-Methods Digest, Vol 240, Issue 25 (Third Parties)
- Re: Third parties (Kristofer Munsterhjelm)
- A VSE-like proportionality measure, or the start of one (Kristofer Munsterhjelm)
…. because otherwise you could have a candidate who has an
opinion none of the voters happen to have….
…. perfect proportionality.
…. it would jumble together voters not ranking/rating
candidates in order, and disproportionality of the method itself….
…. the "zero opinion" problem is still real…
Empirically speaking, maybe one could get around this by smoothing the
voter opinion distribution. But perhaps there's a better theoretically
founded way to do it…. - maybe I should look more into them.
…. augment this measure to include….descriptive representation.
In any case, this could be useful to evaluate PR methods'
proportionality, and to check how much proportionality we lose by having
small districts instead of one large district with something like STV.
Ranking a thousand candidates may be impractical for real voters, but
not for computer simulated ones :-)
….proportional (not at all) as electing one….full of candidates at x=0.9. This
seems wrong. It can be dealt with by
dividing voter space into a number of regions and then counting over
each "bin", … a kernel density-like solution? [Is this another way of refering to “ideological districts” or constituencies?]
I don't know it if there is.
…. because there's always some support and it's always decreasing away
from where the voter opinions are concentrated….
….any straightforward proportionality measure, can also
be criticized as quantifying the wrong thing: as Steve Eppley said in
2008, (paraphrased) "why should I be interested if they have the same
opinions as me, if they don't legislate the way I would?". In a similar
way, it doesn't take into account coalition effects or kingmaker
problems with low threshold PR methods, either.
-km
Steve’s following brief explanation and illustration of how evaluative-proportion representation (EPR) works assumes that you, the reader, are voting on the following sample ballot. This ballot is followed by more explanation:
EPR Sample Paper Ballot
City Number 30
Directions: Please grade at least one candidate’s suitability for office by putting an X in either the Excellent, Very Good, Good, or Acceptable box next to each of the candidates you want to grade. You may give the same grade to more than one candidate. You may use Poor or Reject to grade candidates you do not find fit for office. Any candidates who you do not explicitly grade will be automatically counted as if you marked them as ‘Reject/unknown’. You are assured that your one vote of Acceptable or better for a candidate will increase the voting power in the legislative body of the winner you helped to elect directly or indirectly.
Identity Code of the candidate
Candidate
Note: Give only one grade for one or more candidates
by placing an X in the relevant box.
EXCELLENT
VERY GOOD
GOOD
ACCEPTABLE
POOR
REJECT
A
Stephen Collins
X
B
Candice Crosby
X
C
Robin Levy
X
D
Martin Newman
X
E
June Glover
X
F
Frank Field
If none of the candidates you graded as at least Acceptable is elected, your ballot becomes a proxy vote. This proxy vote will be added to the running total of votes received by the winning candidate publicly judged most suitable for office by the candidate to whom you gave your highest grade. However, if you do not want this to happen, circle NO at the end of this sentence:
YES --- N0
More explanation:
The first round counts all voters’ completed ballots. Each ballot provisionally adds one to the total number of votes received by one or other of the candidates. As a result, each candidate will have received a different total number of votes but composed of different numbers of each grade.
If, for example, you awarded the same highest grade to more than one candidate, that grade is exclusively added to the running total of the candidate who will have the larger total as a result. This is justified by the democratic assumption that a candidate who gets more votes is probably better.
The target number of candidates are elected by their having received one of the seven largest totals of votes of at least Acceptable. When finalized, each of these winner’s totals quantifies their voting power in the legislative assembly – their “weighted vote.” Thus, each citizen’s ballot (vote) equally adds to the weighted vote of the elected candidate they are most likely to favor.
Next, in order to ensure that every citizen’s vote continues to count equally and effectively as one in the legislative body, all the ballots (votes) currently held by candidates not elected are now transferred to the running total of one or other of the winners. This is automatically possible for each such ballot that also contains a remaining “highest-available grade” for one of the winners.
The “highest-available grade” on such a ballot is determined at any given point in the count by the rules that govern the count. For example, if a voter’s ballot awarded an “Excellent” to a candidate who could not be elected because they had not received a large enough number of votes from all voters, this ballot would automatically be transferred to the running total of the winner who this ballot awarded its remaining “highest-available grade” – Very Good, Good, or Acceptable.
However, if this ballot does not award any winner in this way, it automatically becomes a “proxy vote.” If the relevant voter has given their permission at the bottom of their ballot bu circling “NO”, their proxy vote is transferred to the weighted vote of the already elected candidate publicly judged most suitable for office by the candidate on their ballot who received this voter’s highest grade.
Consequently, unlike all available alternative voting systems, EPR ensures that every citizen’s vote (ballot) equally adds to the voting power in the legislative assembly of the elected candidate who finally received each voter’s “highest-available grade.” In each case, this grade is either the ballot's highest grade, remaining highest grade, or proxy vote. Thus, EPR guarantees that every ballot will equally increase the weighted vote of one of the elected members by one – the member they are most likely to see as accurately representing their concerns and hopes. Therefore, 100% of the voters have every appropriate reason to be satisfied with the results of an EPR election.
Your above vote:
Again, the first rounds of EPR’s count determine to which candidate’s running total your highest grade (vote) is provisionally given. For the count of your vote already indicated in the ballot, your Excellent must be provisionally added either to the running total of Collins or Levy. It must go to the one who has received the largest number of Excellents from all the ballots cast.
For this illustration, we are assuming that Levy received more such votes (grades) than any other such candidate, including Collins. Therefore, your current “highest-available grade” of “Excellent” is exclusively but provisionally added to Levy’s running total of votes, not to Collins’s. Again, this is justified by the democratic assumption that the candidate who has more votes is probably better.
Therefore, say your Excellent goes to Levy, and for brevity of explanation also assume that this election aims to elect all seven members of a city council. Levy will be elected if she has separately received one of the seven largest numbers of “highest-available grades” from all voters.
Each candidate’s total is composed of different numbers of Excellent, Very Good, Good, and Acceptable received separately from a number of all the ballots cast. One such grade from every citizen’s ballot is added to the total of one of the candidates. When each voter’s ballot has been provisionally added to one of the candidates running total of votes in this way, the seven elected candidates are identified. Each has received one of the seven largest totals. Levy would be elected if her total is one of these seven.
However, if Levy’s final total is not one of these winning seven, your ballot’s “highest-available grade” of Excellent is instead transferred to Collins, but only if Collins would have one of the seven largest totals as a result. If not, your ballot would be transferred to Cosby, but again, only if Cosby would receive one of the largest seven totals as a result. Given this condition, your vote might instead have to be transferred to Newman or Glover.
However, if none of these candidates could receive one of the largest seven totals with the help of your vote (ballot), your ballot automatically becomes your proxy vote as described above. This is to say that if you had not circled the “NO” at the bottom of your above ballot paper, you have given permission for your proxy vote to be finally added to the weighted vote of the winner that is publicly judged to be most fit for office by Levy.
In this way, you and every other citizen is assured that they will be equally represented in the assembly as accurately as possible.
What do you think?
End of Election-Methods Digest, Vol 240, Issue 25
On 2024-08-19 06:58, steve bosworth wrote:
Subject: [EM]Third Parties.
To: Kristofer Munsterhjelm and others. (km-elmet@munsterhjelm.no)
FROM: Stephen Bosworth (stevebosworth@hotmail.com
mailto:stevebosworth@hotmail.com)
I want fully to understand the relevant new ideas you offered in your
7/30/2024 4:06 PM post. These ideas were especially prompted for me by
your words and phrases extracted and copied immediately below the next
paragraph.
Currently, the intuitions or possibilities your words suggest to me,
once fully understood, might require either a rejection or a
confirmation of the proportional voting method published in 2020 by my
co-authors and myself
[/https://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v3/ https://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v3//].
That article offers a full account of evaluative-proportional
representation (EPR), including the algorithm for counting such an
election. Additionaly and in the last section of this post, I’ve added a
complementary and much shorter introduction to EPR . It explains, for
example, how electing a seven-member city council using EPR ensures that
every voter is most likely to see one of the elected candidates as
representing them accurately. Every party, voter, minority, and majority
of voters would be proportionally represented in the council exactly.
Of course, I look forward to receiving as much feedback as possible from
you and from other EM contributors. In particular, I want to understand
why your “*VSE-like proportionality measure” *either falsifies or
supports my above paragraph’s last two sentences?
Bottom line first: the VSE measure is intended as a way to quantify how
proportional a method is. Thus the only way to know whether it rules EPR
in or out would be to test it. I haven't actually implemented my measure
yet, though, and the parts you quote deal mainly with how the VSE idea
could be extended to creating a proportionality measure for real STV
elections.
However, more generally, you could probably devise an assignment where
EPR doesn't perfectly represent the voters. I'll get back to that at the
bottom, after explaining what my measure was about, and what the idea of
applying it to real elections also was about. See [1].
My idea was that we draw the voters and candidates from an opinion
space. For instance, a 2D opinion space might be like the classical
authoritarian/libertarian and economic left/right of the political
compass[2], and both voters and candidates would have a position on it.
I'm currently only talking about synthetic data, generated by a
computer: not actual voter and candidate positions in opinion space.
Thus the system doesn't need to know what the different dimensions stand
for when evaluating a method.
If a method is proportional, then the distribution of elected candidates
would tend, over a large number of elections, to be like the
distribution of the voters. Suppose say 10% of the voters are quite
socialist and neither authoritarian nor libertarian. Then a proportional
method will elect 10% socialist balanced-authority candidates too,
because the 10% of the voters will express a preference for them.
(It's a bit more complicated because there may not be a candidate at
that position, so it's not just about first preferences. But it should
give you the gist.)
So my VSE measure would use a computer to draw a bunch of voters and a
bunch of candidates according to a normal distribution, and then judge
the method according to whether the elected candidates ended up where
you'd expect them to be based on the voter distribution of opinions. The
"VSE" part is that it normalizes the score so that zero is what you get
if you just picked people at random, and one is the best possible.
It uses the Sainte-Laguë index because Sainte-Laguë (Webster) is usually
considered the best measure of proportionality.
That's the first part. In the second part, I basically say: we might be
able to use this approach to quantify proportionality of an election in
the real world, too.
For context: this is a real problem when using methods like STV. If you
use party list, it's easy to determine proportionality. You just take
ecah party's support and the fraction of seats it got, and use a
standard measure like Euclidean distance or Sainte-Laguë. But for STV
(and EPR, Schulze STV, QPQ, PAV, Phragmen, etc.), you can't do that,
because later preferences matter. So people who report election results
usually use party preference, but that can't easily tell you if the
current election was proportional or not.
My idea would, if it could be implemented, solve that.
Say we ask a bunch of candidates and a bunch of voters a number of issue
questions like, for example, "Farmers are paid too little" or "We need
to give local government more of a say" and record how much they
agree/disagree with them. Now we have a distribution of voter opinions
and we know the opinions of every candidate. (This can be postprocessed
to reduce the number of dimensions, but I won't get into that here.)
After the election is over and some of these candidates are elected, we
could, in principle use the measure from above to determine how
accurately the elected candidates mirror the voters' opinions. And this
would work no matter what method you use for electing them.
Descriptive representation would be easy to add, as well. Just augment
opinion space with additional properties - like class, ethnicity,
gender, etc.
But it's not that simple. The Sainte-Laguë index is very sensitive to
polling errors. For instance, if a libertarian was elected but (by sheer
coincidence) none of the voters polled were libertarian, then the
Sainte-Laguë index would be infinite, just because the polling missed
the few libertarians who got that candidate elected. That's what I meant
by the "zero opinion problem".
So that part is about "how to make real world measures of
proportionality better" in a way that allows one to answer "but how
proportional was the last election". It hasn't got anything to do with
any method in particular.
-km
[1] Suppose, for instance, that a constituency has 10 parties of 10%
support each, and every voter is perfectly partisan and vote their own
party top and every other party bottom. Then you can't fit ten reps into
seven seats and something has to go. It's very unrealistic, but it shows
that having perfect representation all the time is impossible.
[2] Or, for that matter, the kind love/tough love and
pragmatic/ideological axes of
https://web.archive.org/web/20080212053747/http://politics.beasts.org/scripts/eigenvectors