Vidar Wahlberg | 31 Oct 22:52 2014
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Preferential Party-List Proportional Representation (PPLPR)

Some of you may remember that I once brought up the topic of a
party-list voting system with preferential votes. Unfortunately I've not
found much information about such systems, so on a couple occasions I've
tried creating such a system myself. Last time I wrote about it on this
list my attempts at creating a such system did not lead to anything
useful, but a couple weeks ago I thought of another approach to the
problem. This lead to a system I've called "Preferential Party-List
Proportional Representation" (or PPLPR for short). Now I'd like you to
take a look at the system, and point out flaws and weaknesses.

I have implemented the system in JavaScript so you can easily test it
out. There may be bugs in the implementation, there are rounding errors
as well as floating points issues (minor impact), and there are limits
on how many parties it can handle (execution time increase drastically
relative to amount of parties, you'll get an warning at 10 or more
parties in the election). You can find it here:
http://exent.net/~canidae/valg/pplpr/
Note that the vote parser is fairly simplistic, each line must start
with amount of votes, followed by space, and then the preference order
separated with ">". No equal ranking allowed (it isn't implemented in
the voting system either, although I believe it should be possible).

I find it easier to explain by example, so I'll start with simple
examples and progress to some more complex ones. In the examples I'll
have a total of 100 votes for simplicity.
I've created a spreadsheet with these examples which calculates the
steps, it may aid understanding this textual explanation:
https://docs.google.com/spreadsheets/d/1a2O1i7S2-8VUgBGpjShbGeec0pnMtzE3Jv8ErePHrxY

Example 1, three parties, L and R voters with C as 2nd preference:
(Continue reading)

steve bosworth | 31 Oct 10:48 2014
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Questions about Election-Methods Digest, Vol 124, Issue 28

To the 'Owner'
From: Steve (Stephen Bosworth)
                 
Please tell me exactly how I should submit contributions to the 'List'.
 
Several days ago, I discovered that part of my dialogue with Richard Fobes was on the List.  In response, I sent all the elements of my draft article to you believing this would also help other contributors to participate more efficiently. However, I then received an email from you informing me that these were too long (i.e. longer than your 200KB limit).  I then sent you an email on your special form suggesting that I  only the 52KB draft article, not the illustrative 2 flow charts and 3 tables.
 
As I have not received a reply to that 'form email', I will now attach that draft article alone to my 1st reply to this email.
 
In my next email, I will respond to Richards Fobes's comments below.
 
I look forward to receiving your advice.
 
Steve
++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
> From: election-methods-request <at> lists.electorama.com
> Subject: Election-Methods Digest, Vol 124, Issue 28
> To: election-methods <at> lists.electorama.com
> Date: Thu, 30 Oct 2014 12:02:36 -0700
>
> Send Election-Methods mailing list submissions to
> election-methods <at> lists.electorama.com
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> Today's Topics:
>
> 1. Re: Associational Proportional Representation (APR)
> (Richard Fobes)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Wed, 29 Oct 2014 13:23:38 -0700
> From: Richard Fobes <ElectionMethods <at> VoteFair.org>
> To: election-methods <at> lists.electorama.com
> Subject: Re: [EM] Associational Proportional Representation (APR)
> Message-ID: <54514CCA.9060701 <at> VoteFair.org>
> Content-Type: text/plain; charset=windows-1252; format=flowed
>
> On 10/27/2014 9:12 AM, steve bosworth wrote:
> > Hi Richard,
> > ...
> > I have attached PDF versions of all the attachments you wished not to
> > open because of anti-virus reason.
> >
> > I look forward to our continued dialogue.
>
> Steve, the following comments are based on reading the PDF file that
> describes your method. (Thank you for sending a PDF version.)
>
> Yes, you are correct in saying that improved primary elections would
> yield more-representative candidates for the general election.
>
> The simplest way to improve primary elections is to use approval voting.
> This means just changing the instructions to allow more than one
> candidate's name to be marked. (I don't support the use of approval
> voting in general elections, but I would be happy to see it used in U.S.
> primary elections.)
>
> Your suggested ballot is way too complicated! Also, the marked ballots
> would not be machine-readable. I can see ways to overcome these
> barriers, and still collect the information you want. (The
> cross-district votes can be handled like write-in options within a
> fill-in-the-oval 1-2-3 ballot; you don't need a separate section for
> "bullet" voting [for just one choice].)
>
> Yet the counting method you recommend has serious shortcomings.
>
> Your counting method definitely has the focus-on-the-current-top-choice
> "blinder" approach that I've already described.
>
> The reason you didn't understand my reference to "rounding" is that I
> chose an analogy that was not different enough from the topic. So,
> please ignore my "rounding" analogy.
>
> You offer a definition of a "wasted vote" and then claim that your
> method is the best way to eliminate wasted votes. This tactic -- of
> defining a term and then claiming your method maximizes or minimizes the
> defined term -- is often used in election-method discussions, yet it's
> pointless because advocates of competing methods simply do not accept
> the definition you offer, and instead offer a competing definition.
>
> Finally, yet most importantly, I'll point out a serious issue that you
> seem to have overlooked.
>
> After your counting method is used, the number of voters who support
> each winning candidate becomes public knowledge ? because it determines
> the "weighting" of each legislator's vote. This knowledge, combined
> with the ability to vote for legislators in other districts, makes it
> financially profitable for "consultants" and thugs to bribe voters to
> vote for the legislators whose "backers" provide the most money.
>
> Perhaps you think this kind of bribery is easy to detect and deter.
> It's not.
>
> For several years, while I was writing my creative-problem-solving book,
> I lived in a low-income part of a university town and learned a lot
> about what goes on in a neighborhood that gets lots of police attention.
> The police (and fire) events are just the tip of the iceberg. The
> selling of votes would easily become commonplace in places where people
> are desperate, vulnerable, illiterate, poor, abused (without exceeding
> the legal limit), etc.
>
> If my reactions seem to be excessively critical, and not supportive,
> consider that the best voting methods are the ones with the fewest
> flaws. There is no such thing as a voting method with no flaws!
>
> Regarding this issue, if you are not familiar with the table in the
> Wikipedia article titled "voting systems," then please become familiar
> with it, because it portrays the most common "fairness criteria" [my
> term] that I and others here refer to.
>
> In your article you claim that your method is better than plurality
> voting. I agree with that claim. But that's not saying much. Every
> method promoted here can make that claim.
>
> You claim that your method is not vulnerable to gerrymandering. I do
> not disagree with that claim. Yet I'll point out that there are a
> variety of ways to eliminate gerrymandering. In other words, your
> suggested approach is not the only way.
>
> I understand why you like the method you propose. It has some nice
> counting characteristics. Yet a voting method has to be workable, and
> that involves issues such as machine-readability, incorruptibility,
> ballot simplicity, invulnerability to strategic voting, etc.
>
> That's all I have time for now. If you have further questions, or you
> don't understand what I've said here, just ask.
>
> Most importantly, thank you for taking the time to learn about the many
> subtle issues that affect voting methods.
>
> Richard Fobes
>
>
> On 10/27/2014 9:12 AM, steve bosworth wrote:
> >
> > Hi Richard,
> >
> >
> > Thank you for your additional comments and observations below.I will
> > insert my responses into your text using *bold print*.
> >
> > I have attached PDF versions of all the attachment you wished not to
> > open because of anti-virus reason.
> >
> > I look forward to our continued dialogue.
> >
> >
> > Regards,
> >
> >
> > Steve
> >
> >
> >> Date: Sat, 25 Oct 2014 22:01:14 -0700
> >> From: ElectionMethods <at> VoteFair.org
> >> To: election-methods <at> lists.electorama.com
> >> Subject: Associational Proportional Representation (APR)
> >>
> >> I'm responding (via Bcc) to Steve Bosworth's earlier reply to my
> >> responses, which he repeated in a direct message that is copied below.
> >> I no longer have a copy of the forum message, so please pardon the
> >> creation of a new thread about a conversation in progress. For context,
> >> see below.
> >>
> >> Steve, I only had time to quickly look at your two flowcharts (which
> >> were in PDF format, in contrast to your ".doc" documents which I don't
> >> open for antivirus reasons), but ...
> > *S:Please see the new PDF attachments.*>
> >> I saw that your Associational Proportional Representation (APR) method
> >> involves eliminating a candidate based on having the fewest number of
> >> votes (after possible transfers of votes).
> > *S:The first candidate eliminated could not have received any transfer
> > votes because all elected candidate keep all the votes they have
> > received.These determine the weighted vote each rep will have in the
> > assembly.*
> >> I favor methods that look deeper than each voter's currently top
> >> remaining choice. I don't like methods that only look at one voter's
> >> currently "top choice" at a time. Why? They have the same weaknesses
> >> as plurality voting and instant-runoff voting (IRV), which look at
> which
> >> candidate gets the most, or fewest (respectively) "votes."
> >> *S:In the context of APR, I do not understand why looking at each
> > elector?s ?top choice? as the first step in the count would be weakness.*
> >
> >
> > ***APR allows each elector to guarantee that his vote will be added to
> > the voting power of the rep in the assembly either that he had directly
> > ranked or that his first choice but eliminated candidate had ranked (a
> > special use of Asset Voting) ? every vote can be positive, no vote need
> > be wasted.Do you see any scientific basis for anyone to say that an APR
> > assembly would not be as representative as possible of all citizens?*
> >
> >
> >> Methods that involve the transfer of each voter's vote are open to
> >> strategic manipulations. You asked for more specifics. As a partial
> >> answer, the election results are vulnerable to strategies that control
> >> which candidates are nominated.Usually this manipulation involves
> >> campaign contributions (with the real source of funds for "spoiler"
> >> candidates being hidden).
> >
> > *S:Perhaps you will see that APR provides no incentive to vote
> > strategically, e.g. APR?s special ?primary? election would greatly
> > reduce or eliminate the ?manipulation? you have in mind.In this primary,
> > each citizen could choose the ?electoral association? through which,
> > several months later, he will record his rankings of as many general
> > election candidates in the country as he may wish. Each would try to
> > become such a voting member of the association believes is most likely
> > to field the most attractive candidates.*
> >
> >
> > *This seems to remove any incentive to fund any ?spoiler candidates?.*
> >
> >
> >> All voting methods fail some fairness criteria, so yours does too.
> >> Which ones? I don't know. That requires time-consuming analysis.
> >> Although your method is not instant-runoff voting, it is similar enough
> >> that I suspect it would fail many of the same fairness criteria
> that IRV
> >> fails.
> >
> >
> > *S:Perhaps you will find that a careful reading of the attachments
> > alleys your suspicions in this regard.*
> >>
> >> Of course you can correctly claim that there are no fairness criteria
> >> for proportional methods,
> >
> >
> > *S:I see APR as satisfying the following ?fairness criteria? entirely:*
> >
> >
> > *1)**Each citizen has the same range of options both during the
> > ?primary? and the general election.*
> >
> >
> > *2)**One of these is to guarantee that his vote will be added to the
> > ?weighted vote? of the rep he most trusts, or which his first choice but
> > eliminated candidate most trusts.*
> >
> >
> > *3)**The voting power of each party in the assembly would be exactly
> > proportional to its support by electors because this power would result
> > from combining all the weighted votes of its members.*
> >
> >
> > yet I believe your method involves underlying
> >> algorithms that can be applied to a single-winner method, and that
> >> related single-winner method has to fail some fairness criteria.
> >
> >
> > *S: I would very much appreciate you explaining this because it seems to
> > me that its counting method is clear -- contains no ?underlying
> > algorithm? that would not be fair.*
> >>
> >> As for the method's proportional aspects, the use of sub-groups --
> >> called "associations" in this case -- introduces what can be thought of
> >> as similar to the mathematics of "rounding" numbers too early (instead
> >> of waiting until all the calculations are done, and then rounding).
> >
> >
> > *S: Again, perhaps you will find that the ?associations? only help to
> > expand the number of attractive candidates from the points of view of
> > citizens voting in APR ?primary?.Also, APR never needs or wants to
> > ?round? it numbers.*
> >>
> >> Expressed another way, both the Republican and Democratic parties
> in the
> >> U.S. are heavily controlled by the same relatively few people, and the
> >> result is that voters do not control either political party.
> >
> >
> > *S: The fact that APR citizens will elect all the reps in a given party
> > would seem to mean that they also have a good chance of largely
> > ?controlling? each political party.*
> >
> >
> > I believe
> >> that in Canada each party nominates a candidate using voting at a
> >> convention, but admission to the convention requires paying a fee, so
> >> that too prevents a majority of voters from controlling any political
> > party.
> >>
> >> Looking into the _distant_ future, voting methods will handle
> >> calculations deeply in ways that do not involve any extra layer of
> >> subgroups or rounding, and possibly without involving political
> parties.
> >> In the meantime we are stuck with subgroups such as the "electoral
> >> college" for U.S. Presidential elections, and parliaments/Congress/etc.
> >> that add an extra voting layer (compared to the future when voters
> >> eventually will directly vote on issues of concern). Why not begin now
> >> to get rid of the need for subgroups?
> >
> >
> > *S: Perhaps you will reconsider some of these hopes in the light of
> > Endnote 6 to the attached draft article.*
> >>
> >> I am not saying that your voting method is bad. It might be quite good
> >> for some voting situations!
> >>
> >> I'm just saying -- since you specifically asked me -- that my
> preference
> >> is to skip over slight improvements and jump ahead to advanced voting
> >> methods that look deeply into ballot preferences (beyond one current
> >> "top" choice at a time) and that avoid the need to segment voters into
> >> subgroups.
> >>
> >> For further context I'll say that years ago a group of people within a
> >> local food co-op came up with a very carefully designed way of electing
> >> a group of "representatives" for the purpose of having them make
> >> decisions instead of letting all the members vote on important
> >> decisions. In spite of how well-designed and "fair" (neutral) the
> >> process was, neither the people who wanted the co-op to sell a few meat
> >> items nor the people who wanted absolutely no meat in the store were
> >> willing to let such a group make a decision about that issue. The point
> >> of this example is that each layer of decision-making -- even if it
> gets
> >> adjusted at every election based on the ballots -- does not truly
> >> provide proportional representation. As for what a truly proportional
> >> solution to that "meat" conflict would have been, I'm not sure. Selling
> >> fewer meat items than what a majority of voters wanted would still fail
> >> to represent the members who didn't want any meat sold. (It was not
> >> clear who was in the majority, and probably a middle third of the
> >> members would have been OK with certain meat choices but not other meat
> >> choices.)
> >>
> >> Ultimately voters don't care about the process. That's why so few
> >> citizens "do the math" to discover why they are not represented by the
> >> people "they" elect. This same dilemma applies to all the voting
> >> methods discussed here. Here we are not only "doing the math," but we
> >> are developing "the math" relating to voting methods. Let's eliminate
> >> extra layers and stop using "start-at-the-top" blinders as we look at
> >> each ballot.
> >>
> >> Thank you for your interest in my opinion. I hope this helps, either to
> >> refine your ideas or to refine ways to "sell" whatever method you like
> >> best. (All of us here are learning how to "sell" our favorite
> method(s).)
> >>
> >> BTW, thank you for creating the flowcharts. They do help clarify your
> >> method. (Alas, graphics on websites seem to be the only way to make
> >> flowcharts easy to view, so they are not suitable here in this forum.)
> >>
> >> Richard Fobes
> >>
> >>
> >> On 10/22/2014 6:54 AM, steve bosworth wrote:
> >> > Hi Richard,
> >> >
> >> > Sorry for the late reply. I've been travelling.
> >> > Thank you for your several criticisms, comments and suggestions.
> >> >
> >> > I've *injected my responses within the text of your email bellow,
> using
> >> > bold print*.
> >> >
> >> > I hope you will see that some of the problems you mentioned are
> solved
> >> > within the full explanation of my proposed system (Associatonal
> >> > Proportional Representation (*APR*)) that I have fully described
> in the
> >> > attached article with its illustrative 2 flow charts and 3 tables.
> >> >
> >> > In the light of the more complete information provided, I very
> much hope
> >> > you will be able to find the time to respond to the additional
> > explanations.
> >> >
> >> > Thank you,
> >> > Steve
> >> >
> >> > > Date: Tue, 2 Sep 2014 09:10:10 -0700
> >> > > From: ElectionMethods <at> VoteFair.org
> >> > > To: stevebosworth <at> hotmail.com
> >> > > Subject: Re: (2) "Severity" of failing
> >> > >
> >> > > Steve Bosworth ~
> >> > >
> >> > > Thank you for your interest in my opinion.
> >> > >
> >> > > Getting to the point of your question, your election method
> combines
> >> > > single-winner voting concepts
> >> > *S: No, in effect, APR**is entirely a multi-winner system, e.g.
> to elect
> >> > the 435 members of the US House of Representatives or the UK House of
> >> > Commons. *
> >> > with proportional representation concepts,
> >> > *S: APR's giving different 'weighted votes' to each rep depending
> on how
> >> > many citizens had ranked them would provide complete individual
> >> > representative and party proportionality.*
> >> > > which means that the well-known fairness criteria do not apply.
> >> >
> >> > *S: I know of no such criteria which APR would not satisfy.*
> >> > > Your idea sounds intriguing. Yet it would encounter time-related
> >> > > issues,
> >> > *S: Please explain.*
> >> > especially strategy issues,
> >> > *S: Please explain.*
> >> > if it were converted into an actual
> >> > > election method -- that involves ballots.
> >> > *S: Perhaps you will see that these issues have been solved by the
> >> > detailed presentation of the 'actual method' and the paper
> 'ballots' to
> >> > be used by APR, and explained by the attachments.*
> >> > >
> >> > > The single-winner aspects basically match instant-runoff voting,
> > so the
> >> > > same fairness-criteria failures would apply.
> >> > *S: No, because it is not an IRV system.*
> >> > >
> >> > > As for the proportional part, your method would tend to elect a few
> >> > > celebrity representatives who are supported by "the media"
> >> > *S: Given APR's 'electoral associations' as selected by citizens
> months
> >> > before the general election through APR's special 'primary election',
> >> > the relative influence of 'celebrity' and the 'media' might be much
> >> > reduced. In any case, the article stipulates that any very
> popular rep
> >> > who receives more than 10% of all the votes in the country would be
> >> > required to publish exactly how he will pass on all of his 'extra
> votes'
> >> > to his trusted fellow reps.*
> >> > and the
> >> > > other representatives would tend to be "fringe" types who are
> > supported
> >> > > by fewer voters. Note that this is a tendency, and would be
> reduced to
> >> > > the extent that it's noticed, which means that most voters
> would not
> >> > > notice this tendency.
> >> > >
> >> > > Alas, my time is limited, so I can't offer more feedback at
> this time.
> >> > *S: Thank you again for your time.*
> >> > > I hope this is helpful.
> >> > >
> >> > > If you want more opinions, I suggest that you present the idea
> on the
> >> > > Election Methods forum.
> >> > *S: I keep trying to find out how to do this but have so far
> failed. Can
> >> > you please explain how one contributes to this forum?*
> >> > >
> >> > > Richard Fobes
>
>
>
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>
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Attachment (14Oct-Positive Voting Guaranteed.docx): application/vnd.openxmlformats-officedocument.wordprocessingml.document, 69 KiB
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Forest Simmons | 31 Oct 03:35 2014

Sincere Range and Approval

I have written before about how to convert sincere ratings into sincere approval ballots.  This time I want to step back and explain a way to compute sincere ratings: when the meanings of the sincere ratings are more evident, then the sincere approvals take on additional meaning, too.


Suppose that by examining the voting record of candidate X you see that on a random issue of interest to you there is a probability p that she would vote the same way you would vote if you had the opportunity to vote in the representative body, i.e. there is a probability p that she would correctly represent your wishes if she were your representative.


I will now explain why I consider this probability p to be a natural choice for your sincere rating of candidate X.


In fact, if every voter V rated candidate X according to the voter’s  subjective (if not calculated) probability of X correctly representing V on a random issue of interest, then the sum of these ratings would be the expected number of voters that would be correctly represented by X on a random issue of interest.

So with this definition of sincere ratings, the candidate with the highest sum of ratings is by definition the candidate expected to correctly represent the greatest number of voters on a random issue of interest:  i.e. the Range Winner maximizes the expected number of correctly represented voters (as long as ratings are sincere).


One of the most interesting things about this point of view is that from it follows a simple definition of sincere approval voting.  We will get to that definition in two conceptual steps:


(1) An approval voter trying to stochastically mimic her sincere rating p of candidate X could spin a spinner with fraction p of the circle shaded green.  If the spinner arrow lands in the green, then the voter approves X.  If all approval voters were to use this strategy, then the expected sum of approvals for candidate X would be the same as the expected sum of ratings: i.e. Approval Voting would be statistically equivalent to Range Voting were all voters to use this spinner strategy.  Both estimate the number of correctly represented voters.  The main difference is that compared to the Range Voting estimate, the Approval estimate would have a larger variance (although both variances would be inversely proportional to the number of voters).  To significantly reduce this variance in the case of Approval Voting is the purpose of the second conceptual step.


(2)  The expected number of candidates approved by voter V using the spinner method is the sum of voter V’s ratings of the candidates.  So instead of using a spinner for each candidate, voter V should simply approve her top k candidates and use a q-shaded spinner to decide whether or not to approve the candidate she ranks (k+1) from the top, where k is the integer part of the sum of V’s candidate ratings and q is the fractional part of that sum. This procedure defines what I call “Sincere Approval.”


One slight change is to allow an affine transformation of the probabilities to adjust the extremes to zero and one, even if the voter V sincerely neither completely disagrees nor completely agrees with any candidate.


Another tweak is to allow the voter V to use strategy instead of a spinner for deciding whether or not to approve the candidate Y that she ranks (k+1).  One such strategy is to approve Y only if voter V’s ballot is more likely to be pivotal between Y and some candidate that V considers inferior to Y than some candidate that V likes better than Y.


I will finish by observing that it is well known that a strategically sophisticated Range Voter can achieve optimal results while using only the extreme ratings: i.e. Range and Approval are strategically equivalent.  What I have shown above is that Range and Approval are also statistically equivalent in the case of sincere voting.  These two facts taken together suggest that Approval, with its simpler ballots, is an adequate substitute for Range.  However, we must remember that it is very likely that psychological considerations outweigh both strategical and statistical considerations.


Forest

 

 



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Richard Fobes | 29 Oct 21:23 2014

Re: Associational Proportional Representation (APR)

On 10/27/2014 9:12 AM, steve bosworth wrote:
 > Hi Richard,
 > ...
 > I have attached PDF versions of all the attachments you wished not to
 > open because of anti-virus reason.
 >
 > I look forward to our continued dialogue.

Steve, the following comments are based on reading the PDF file that 
describes your method.  (Thank you for sending a PDF version.)

Yes, you are correct in saying that improved primary elections would 
yield more-representative candidates for the general election.

The simplest way to improve primary elections is to use approval voting. 
  This means just changing the instructions to allow more than one 
candidate's name to be marked.  (I don't support the use of approval 
voting in general elections, but I would be happy to see it used in U.S. 
primary elections.)

Your suggested ballot is way too complicated!  Also, the marked ballots 
would not be machine-readable.  I can see ways to overcome these 
barriers, and still collect the information you want.  (The 
cross-district votes can be handled like write-in options within a 
fill-in-the-oval 1-2-3 ballot; you don't need a separate section for 
"bullet" voting [for just one choice].)

Yet the counting method you recommend has serious shortcomings.

Your counting method definitely has the focus-on-the-current-top-choice 
"blinder" approach that I've already described.

The reason you didn't understand my reference to "rounding" is that I 
chose an analogy that was not different enough from the topic.  So, 
please ignore my "rounding" analogy.

You offer a definition of a "wasted vote" and then claim that your 
method is the best way to eliminate wasted votes.  This tactic -- of 
defining a term and then claiming your method maximizes or minimizes the 
defined term -- is often used in election-method discussions, yet it's 
pointless because advocates of competing methods simply do not accept 
the definition you offer, and instead offer a competing definition.

Finally, yet most importantly, I'll point out a serious issue that you 
seem to have overlooked.

After your counting method is used, the number of voters who support 
each winning candidate becomes public knowledge – because it determines 
the "weighting" of each legislator's vote.  This knowledge, combined 
with the ability to vote for legislators in other districts, makes it 
financially profitable for "consultants" and thugs to bribe voters to 
vote for the legislators whose "backers" provide the most money.

Perhaps you think this kind of bribery is easy to detect and deter. 
It's not.

For several years, while I was writing my creative-problem-solving book, 
I lived in a low-income part of a university town and learned a lot 
about what goes on in a neighborhood that gets lots of police attention. 
  The police (and fire) events are just the tip of the iceberg.  The 
selling of votes would easily become commonplace in places where people 
are desperate, vulnerable, illiterate, poor, abused (without exceeding 
the legal limit), etc.

If my reactions seem to be excessively critical, and not supportive, 
consider that the best voting methods are the ones with the fewest 
flaws.  There is no such thing as a voting method with no flaws!

Regarding this issue, if you are not familiar with the table in the 
Wikipedia article titled "voting systems," then please become familiar 
with it, because it portrays the most common "fairness criteria" [my 
term] that I and others here refer to.

In your article you claim that your method is better than plurality 
voting.  I agree with that claim.  But that's not saying much.  Every 
method promoted here can make that claim.

You claim that your method is not vulnerable to gerrymandering.  I do 
not disagree with that claim.  Yet I'll point out that there are a 
variety of ways to eliminate gerrymandering.  In other words, your 
suggested approach is not the only way.

I understand why you like the method you propose.  It has some nice 
counting characteristics.  Yet a voting method has to be workable, and 
that involves issues such as machine-readability, incorruptibility, 
ballot simplicity, invulnerability to strategic voting, etc.

That's all I have time for now.  If you have further questions, or you 
don't understand what I've said here, just ask.

Most importantly, thank you for taking the time to learn about the many 
subtle issues that affect voting methods.

Richard Fobes

On 10/27/2014 9:12 AM, steve bosworth wrote:
 >
 > Hi Richard,
 >
 >
 > Thank you for your additional comments and observations below.I will
 > insert my responses into your text using *bold print*.
 >
 > I have attached PDF versions of all the attachment you wished not to
 > open because of anti-virus reason.
 >
 > I look forward to our continued dialogue.
 >
 >
 > Regards,
 >
 >
 > Steve
 >
 >
 >>  Date: Sat, 25 Oct 2014 22:01:14 -0700
 >>  From: ElectionMethods <at> VoteFair.org
 >>  To: election-methods <at> lists.electorama.com
 >>  Subject: Associational Proportional Representation (APR)
 >>
 >>  I'm responding (via Bcc) to Steve Bosworth's earlier reply to my
 >>  responses, which he repeated in a direct message that is copied below.
 >>  I no longer have a copy of the forum message, so please pardon the
 >>  creation of a new thread about a conversation in progress. For context,
 >>  see below.
 >>
 >>  Steve, I only had time to quickly look at your two flowcharts (which
 >>  were in PDF format, in contrast to your ".doc" documents which I don't
 >>  open for antivirus reasons), but ...
 > *S:Please see the new PDF attachments.*>
 >>  I saw that your Associational Proportional Representation (APR) method
 >>  involves eliminating a candidate based on having the fewest number of
 >>  votes (after possible transfers of votes).
 > *S:The first candidate eliminated could not have received any transfer
 > votes because all elected candidate keep all the votes they have
 > received.These determine the weighted vote each rep will have in the
 > assembly.*
 >>  I favor methods that look deeper than each voter's currently top
 >>  remaining choice. I don't like methods that only look at one voter's
 >>  currently "top choice" at a time. Why? They have the same weaknesses
 >>  as plurality voting and instant-runoff voting (IRV), which look at 
which
 >>  candidate gets the most, or fewest (respectively) "votes."
 >>  *S:In the context of APR, I do not understand why looking at each
 > elector’s ‘top choice’ as the first step in the count would be weakness.*
 >
 >
 > ***APR allows each elector to guarantee that his vote will be added to
 > the voting power of the rep in the assembly either that he had directly
 > ranked or that his first choice but eliminated candidate had ranked (a
 > special use of Asset Voting) – every vote can be positive, no vote need
 > be wasted.Do you see any scientific basis for anyone to say that an APR
 > assembly would not be as representative as possible of all citizens?*
 >
 >
 >>  Methods that involve the transfer of each voter's vote are open to
 >>  strategic manipulations. You asked for more specifics. As a partial
 >>  answer, the election results are vulnerable to strategies that control
 >>  which candidates are nominated.Usually this manipulation involves
 >>  campaign contributions (with the real source of funds for "spoiler"
 >>  candidates being hidden).
 >
 > *S:Perhaps you will see that APR provides no incentive to vote
 > strategically, e.g. APR’s special ‘primary’ election would greatly
 > reduce or eliminate the ‘manipulation’ you have in mind.In this primary,
 > each citizen could choose the ‘electoral association’ through which,
 > several months later, he will record his rankings of as many general
 > election candidates in the country as he may wish. Each would try to
 > become such a voting member of the association believes is most likely
 > to field the most attractive candidates.*
 >
 >
 > *This seems to remove any incentive to fund any ‘spoiler candidates’.*
 >
 >
 >>  All voting methods fail some fairness criteria, so yours does too.
 >>  Which ones? I don't know. That requires time-consuming analysis.
 >>  Although your method is not instant-runoff voting, it is similar enough
 >>  that I suspect it would fail many of the same fairness criteria 
that IRV
 >>  fails.
 >
 >
 > *S:Perhaps you will find that a careful reading of the attachments
 > alleys your suspicions in this regard.*
 >>
 >>  Of course you can correctly claim that there are no fairness criteria
 >>  for proportional methods,
 >
 >
 > *S:I see APR as satisfying the following ‘fairness criteria’ entirely:*
 >
 >
 > *1)**Each citizen has the same range of options both during the
 > ‘primary’ and the general election.*
 >
 >
 > *2)**One of these is to guarantee that his vote will be added to the
 > ‘weighted vote’ of the rep he most trusts, or which his first choice but
 > eliminated candidate most trusts.*
 >
 >
 > *3)**The voting power of each party in the assembly would be exactly
 > proportional to its support by electors because this power would result
 > from combining all the weighted votes of its members.*
 >
 >
 > yet I believe your method involves underlying
 >>  algorithms that can be applied to a single-winner method, and that
 >>  related single-winner method has to fail some fairness criteria.
 >
 >
 > *S: I would very much appreciate you explaining this because it seems to
 > me that its counting method is clear -- contains no ‘underlying
 > algorithm’ that would not be fair.*
 >>
 >>  As for the method's proportional aspects, the use of sub-groups --
 >>  called "associations" in this case -- introduces what can be thought of
 >>  as similar to the mathematics of "rounding" numbers too early (instead
 >>  of waiting until all the calculations are done, and then rounding).
 >
 >
 > *S: Again, perhaps you will find that the ‘associations’ only help to
 > expand the number of attractive candidates from the points of view of
 > citizens voting in APR ‘primary’.Also, APR never needs or wants to
 > ‘round’ it numbers.*
 >>
 >>  Expressed another way, both the Republican and Democratic parties 
in the
 >>  U.S. are heavily controlled by the same relatively few people, and the
 >>  result is that voters do not control either political party.
 >
 >
 > *S: The fact that APR citizens will elect all the reps in a given party
 > would seem to mean that they also have a good chance of largely
 > ‘controlling’ each political party.*
 >
 >
 > I believe
 >>  that in Canada each party nominates a candidate using voting at a
 >>  convention, but admission to the convention requires paying a fee, so
 >>  that too prevents a majority of voters from controlling any political
 > party.
 >>
 >>  Looking into the _distant_ future, voting methods will handle
 >>  calculations deeply in ways that do not involve any extra layer of
 >>  subgroups or rounding, and possibly without involving political 
parties.
 >>  In the meantime we are stuck with subgroups such as the "electoral
 >>  college" for U.S. Presidential elections, and parliaments/Congress/etc.
 >>  that add an extra voting layer (compared to the future when voters
 >>  eventually will directly vote on issues of concern). Why not begin now
 >>  to get rid of the need for subgroups?
 >
 >
 > *S: Perhaps you will reconsider some of these hopes in the light of
 > Endnote 6 to the attached draft article.*
 >>
 >>  I am not saying that your voting method is bad. It might be quite good
 >>  for some voting situations!
 >>
 >>  I'm just saying -- since you specifically asked me -- that my 
preference
 >>  is to skip over slight improvements and jump ahead to advanced voting
 >>  methods that look deeply into ballot preferences (beyond one current
 >>  "top" choice at a time) and that avoid the need to segment voters into
 >>  subgroups.
 >>
 >>  For further context I'll say that years ago a group of people within a
 >>  local food co-op came up with a very carefully designed way of electing
 >>  a group of "representatives" for the purpose of having them make
 >>  decisions instead of letting all the members vote on important
 >>  decisions. In spite of how well-designed and "fair" (neutral) the
 >>  process was, neither the people who wanted the co-op to sell a few meat
 >>  items nor the people who wanted absolutely no meat in the store were
 >>  willing to let such a group make a decision about that issue. The point
 >>  of this example is that each layer of decision-making -- even if it 
gets
 >>  adjusted at every election based on the ballots -- does not truly
 >>  provide proportional representation. As for what a truly proportional
 >>  solution to that "meat" conflict would have been, I'm not sure. Selling
 >>  fewer meat items than what a majority of voters wanted would still fail
 >>  to represent the members who didn't want any meat sold. (It was not
 >>  clear who was in the majority, and probably a middle third of the
 >>  members would have been OK with certain meat choices but not other meat
 >>  choices.)
 >>
 >>  Ultimately voters don't care about the process. That's why so few
 >>  citizens "do the math" to discover why they are not represented by the
 >>  people "they" elect. This same dilemma applies to all the voting
 >>  methods discussed here. Here we are not only "doing the math," but we
 >>  are developing "the math" relating to voting methods. Let's eliminate
 >>  extra layers and stop using "start-at-the-top" blinders as we look at
 >>  each ballot.
 >>
 >>  Thank you for your interest in my opinion. I hope this helps, either to
 >>  refine your ideas or to refine ways to "sell" whatever method you like
 >>  best. (All of us here are learning how to "sell" our favorite 
method(s).)
 >>
 >>  BTW, thank you for creating the flowcharts. They do help clarify your
 >>  method. (Alas, graphics on websites seem to be the only way to make
 >>  flowcharts easy to view, so they are not suitable here in this forum.)
 >>
 >>  Richard Fobes
 >>
 >>
 >>  On 10/22/2014 6:54 AM, steve bosworth wrote:
 >>  > Hi Richard,
 >>  >
 >>  > Sorry for the late reply. I've been travelling.
 >>  > Thank you for your several criticisms, comments and suggestions.
 >>  >
 >>  > I've *injected my responses within the text of your email bellow, 
using
 >>  > bold print*.
 >>  >
 >>  > I hope you will see that some of the problems you mentioned are 
solved
 >>  > within the full explanation of my proposed system (Associatonal
 >>  > Proportional Representation (*APR*)) that I have fully described 
in the
 >>  > attached article with its illustrative 2 flow charts and 3 tables.
 >>  >
 >>  > In the light of the more complete information provided, I very 
much hope
 >>  > you will be able to find the time to respond to the additional
 > explanations.
 >>  >
 >>  > Thank you,
 >>  > Steve
 >>  >
 >>  > > Date: Tue, 2 Sep 2014 09:10:10 -0700
 >>  > > From: ElectionMethods <at> VoteFair.org
 >>  > > To: stevebosworth <at> hotmail.com
 >>  > > Subject: Re: (2) "Severity" of failing
 >>  > >
 >>  > > Steve Bosworth ~
 >>  > >
 >>  > > Thank you for your interest in my opinion.
 >>  > >
 >>  > > Getting to the point of your question, your election method 
combines
 >>  > > single-winner voting concepts
 >>  > *S: No, in effect, APR**is entirely a multi-winner system, e.g. 
to elect
 >>  > the 435 members of the US House of Representatives or the UK House of
 >>  > Commons. *
 >>  > with proportional representation concepts,
 >>  > *S: APR's giving different 'weighted votes' to each rep depending 
on how
 >>  > many citizens had ranked them would provide complete individual
 >>  > representative and party proportionality.*
 >>  > > which means that the well-known fairness criteria do not apply.
 >>  >
 >>  > *S: I know of no such criteria which APR would not satisfy.*
 >>  > > Your idea sounds intriguing. Yet it would encounter time-related
 >>  > > issues,
 >>  > *S: Please explain.*
 >>  > especially strategy issues,
 >>  > *S: Please explain.*
 >>  > if it were converted into an actual
 >>  > > election method -- that involves ballots.
 >>  > *S: Perhaps you will see that these issues have been solved by the
 >>  > detailed presentation of the 'actual method' and the paper 
'ballots' to
 >>  > be used by APR, and explained by the attachments.*
 >>  > >
 >>  > > The single-winner aspects basically match instant-runoff voting,
 > so the
 >>  > > same fairness-criteria failures would apply.
 >>  > *S: No, because it is not an IRV system.*
 >>  > >
 >>  > > As for the proportional part, your method would tend to elect a few
 >>  > > celebrity representatives who are supported by "the media"
 >>  > *S: Given APR's 'electoral associations' as selected by citizens 
months
 >>  > before the general election through APR's special 'primary election',
 >>  > the relative influence of 'celebrity' and the 'media' might be much
 >>  > reduced. In any case, the article stipulates that any very 
popular rep
 >>  > who receives more than 10% of all the votes in the country would be
 >>  > required to publish exactly how he will pass on all of his 'extra 
votes'
 >>  > to his trusted fellow reps.*
 >>  > and the
 >>  > > other representatives would tend to be "fringe" types who are
 > supported
 >>  > > by fewer voters. Note that this is a tendency, and would be 
reduced to
 >>  > > the extent that it's noticed, which means that most voters 
would not
 >>  > > notice this tendency.
 >>  > >
 >>  > > Alas, my time is limited, so I can't offer more feedback at 
this time.
 >>  > *S: Thank you again for your time.*
 >>  > > I hope this is helpful.
 >>  > >
 >>  > > If you want more opinions, I suggest that you present the idea 
on the
 >>  > > Election Methods forum.
 >>  > *S: I keep trying to find out how to do this but have so far 
failed. Can
 >>  > you please explain how one contributes to this forum?*
 >>  > >
 >>  > > Richard Fobes

----
Election-Methods mailing list - see http://electorama.com/em for list info

Kristofer Munsterhjelm | 27 Oct 20:14 2014
Picon

Unbiasing Statistical Condorcet

Some time ago, I wrote about a method based on Schulze STV and on 
statistics (more specifically, the relation between the chi-squared 
test, the exact multinomial test, and Sainte-Laguë/Webster). I came up 
with a MLE approach where one maximizes the pmf of the multinomial with 
the "samples" fixed to the council composition and the probability 
parameters adjusted to maximize the pmf subject to certain constraints 
derived from the ballots.

But then I found out that the probability parameters that would maximize 
the pmf in the ideal case (that the ballots permitted it to be fully 
maximized, i.e. that they posed no constraints whatsoever) would lead to 
the D'Hondt allocation, not the Sainte-Laguë allocation. And I know that 
the D'Hondt allocation is biased in favor of large parties, which I 
consider undesirable.

Then I got kinda confused because the relation between the chi-square 
test and the Sainte-Laguë allocation is exact. How could the 
approximation (the chi-square test) be better than the real thing (the 
multinomial pmf)?

But I think I have an idea now. Maximum likelihood estimators can be 
biased for finite samples (in this case, a finite number of seats). MLEs 
are unbiased in the limit, but they may stay quite biased before one 
gets there. For instance, the MLE for the variance of a Gaussian is 
biased for finite n.

Something similar might be the case for the multinomial. If so, the 
imprecision in the chi-square just happens to cancel out the bias in the 
"real thing", which means that we should try to cancel out the bias in 
the exact method in some other way to achieve the same effect.

(Another approach is to just use the chi-squared test right away. That 
would be more pragmatic and we wouldn't need to go through all the 
derivation, but I think an explicit canceling would be more 
well-founded, or at least simpler to generalize.)

-

If the number of parties is k and the number of seats is n, and the 
number of members of party r in the council we're considering is c_r, 
then the uncorrected score function is |v_x| * f(c_1,...,c_k; p_1,...,p_k).

Here v_x is the number of voters that we can marshal in support of this 
council (against the other council that has one candidate that differs), 
and p_1...p_k are the parameters to alter to maximize f, where f is the 
multinomial pmf.

Then, if we hold all values of p constant but one (say it's p_1), the 
optimum value of p_1 should have the property that floor(n * p_1) = c_1. 
This is what causes the D'Hondt reduction. (NOTE: I have not rigorously 
proven this. I only know that when you're free to set all ps, this holds 
in aggregate. An actual proof would probably be based on the multinomial 
pmf's monotonicity.)

What we would like is to have the property that floor(n * (q + p_1)) = 
c_1 instead, where q is chosen to cancel out the bias, which means the 
p_1 we should give to the pmf should instead be p_1' = q + p_1.

If we just want Sainte-Laguë right away, it's pretty easy to start off 
with floor(n * p_1 + 0.5) = c_1, i.e. floor(n * (0.5/n + p_1) = c_1 
which gives an adjustment of p_1' = 1/2n + p_1.

But there's another snag: this might cause a violation of two 
constraints on a probability parameter. First, the sum of all the 
parameters must be one, and second, no single parameter can exceed one. 
So let's find out a better p_i' by making it of the form

p_i' = (1/2n + p_i)/x

where x is chosen to make the sum come out to one. We have:

SUM i=1..k p_i' = 1
SUM i=1..k (1/2nx) + SUM i=1..k (p_i/x) = 1
k/(2nx) + 1/x = 1
x = 1 + k/2n

p_i' = (1/2n + p_i)/(1 + k/2n)     ("1")
or
p_i' = (2n*p_i + 1) / (k + 2n).    ("2")

(If I've got this wrong, do tell me.)

In the limit of n->inf, ("1") becomes: (0 + p_i)/(1 + 0) = p_i. So the 
MLE is asymptotically unbiased as expected.

---

Some might object that I just plucked the Sainte-Laguë divisor out of 
nowhere, so I'll give a quick reasoning for why it is unbiased.

Let X be a random variable (a party's support, in terms of the fraction 
of the total electorate) on 0..1. Then the transformation g is unbiased 
with respect to x if the expected value of g(X) is equal to the expected 
value of X. In other words, if you draw lots of different party 
fractions and run them through the rounding function, you should, on 
average, get the same value as if you did nothing to it.

So let g(X) = floor(n(X + r)) where n is the number of seats and r is 
some adjustment constant to unbias.

Then the expected value of g(X) is the integral from 0 to 1 of g(X). 
Intuitively, this is the same as saying: the mean value is: the 
probability of getting a party fraction that is rounded to 0 seats, 
times 0, plus the probability of getting a party fraction that is 
rounded to 1 seat, times 1, plus... plus the probability of getting a 
party fraction that is rounded to n seats, times n.

Since g(X) gives a result from 0..n, we also have to scale X by n when 
doing the "if you did nothing to it" comparison. So floor(n(x+r)) is 
unbiased if the integral from 0 to 1 of it is equal to the integral from 
0 to 1 of nx dx - which gives the expected value if fractional seats 
were allowed.

The integral from 0 to 1 of nx dx is simply n/2, which is reasonable 
enough: the average number of seats is half of the maximum.
The integral from 0 to 1 of floor(nx) is (n-1)/2, which clearly does not 
equal n/2. So D'Hondt is biased.

Now consider integral from 0 to 1 of floor(n(x+r)) dx. This is clearly 
equal to integral from r to 1+r of floor(nx) dx. If r < 1/n, then we can 
further simplify this to

integral from 0 to 1 of floor(nx) dx + integral from 1 to 1+r of 
floor(nx) dx

which is

(n-1)/2 + integral from 1 to 1+r of floor(nx) dx

but because r < 1/n, floor(nx) is simply n for x on [1 ... 1+r], so

= (n-1)/2 + integral from 1 to 1+r of n dx

= (n-1)/2 + n * (1+r) - n
= (n-1)/2 + nr

Set this equal to n/2 to cancel out bias, and solve for r:

(n-1)/2 + nr = n/2

r = 1/2n = 0.5/n

which is the Sainte-Laguë correction.

It should in theory be possible to apply this to other distributions as 
well. The above implicitly assumes the uniform distribution, but you 
could weight the probability of getting 0 seats, 1 seats etc according 
to any distribution. However, there are two problems with this. First: 
since Statistical Condorcet uses pairwise comparisons, it's far from 
obvious what kind of distribution to use, and even less so when you 
consider that voting patterns might change as a result of using the 
method. Second: it's really easy to get lost in this rabbit hole. I did, 
and it ate a week of my time just like that. Since probabilities can 
only range from 0 to 1, the distribution also has to be somehow divided 
by the number of people that are voting in total, and constructing ratio 
distributions in general is pretty hard.

I did attempt to do so with a toy distribution with cdf F(r) = x^2, but 
my notes are kind of messy. Let me know if you'd like to see them.
----
Election-Methods mailing list - see http://electorama.com/em for list info
Richard Fobes | 26 Oct 06:01 2014

Associational Proportional Representation (APR)

I'm responding (via Bcc) to Steve Bosworth's earlier reply to my 
responses, which he repeated in a direct message that is copied below. 
I no longer have a copy of the forum message, so please pardon the 
creation of a new thread about a conversation in progress.  For context, 
see below.

Steve, I only had time to quickly look at your two flowcharts (which 
were in PDF format, in contrast to your ".doc" documents which I don't 
open for antivirus reasons), but ...

I saw that your Associational Proportional Representation (APR) method 
involves eliminating a candidate based on having the fewest number of 
votes (after possible transfers of votes).

I favor methods that look deeper than each voter's currently top 
remaining choice.  I don't like methods that only look at one voter's 
currently "top choice" at a time.  Why?  They have the same weaknesses 
as plurality voting and instant-runoff voting (IRV), which look at which 
candidate gets the most, or fewest (respectively) "votes."

Methods that involve the transfer of each voter's vote are open to 
strategic manipulations.  You asked for more specifics.  As a partial 
answer, the election results are vulnerable to strategies that control 
which candidates are nominated.  Usually this manipulation involves 
campaign contributions (with the real source of funds for "spoiler" 
candidates being hidden).

All voting methods fail some fairness criteria, so yours does too. 
Which ones?  I don't know.  That requires time-consuming analysis.
Although your method is not instant-runoff voting, it is similar enough 
that I suspect it would fail many of the same fairness criteria that IRV 
fails.

Of course you can correctly claim that there are no fairness criteria 
for proportional methods, yet I believe your method involves underlying 
algorithms that can be applied to a single-winner method, and that 
related single-winner method has to fail some fairness criteria.

As for the method's proportional aspects, the use of sub-groups -- 
called "associations" in this case -- introduces what can be thought of 
as similar to the mathematics of "rounding" numbers too early (instead 
of waiting until all the calculations are done, and then rounding).

Expressed another way, both the Republican and Democratic parties in the 
U.S. are heavily controlled by the same relatively few people, and the 
result is that voters do not control either political party.  I believe 
that in Canada each party nominates a candidate using voting at a 
convention, but admission to the convention requires paying a fee, so 
that too prevents a majority of voters from controlling any political party.

Looking into the _distant_ future, voting methods will handle 
calculations deeply in ways that do not involve any extra layer of 
subgroups or rounding, and possibly without involving political parties. 
  In the meantime we are stuck with subgroups such as the "electoral 
college" for U.S. Presidential elections, and parliaments/Congress/etc. 
that add an extra voting layer (compared to the future when voters 
eventually will directly vote on issues of concern).  Why not begin now 
to get rid of the need for subgroups?

I am not saying that your voting method is bad.  It might be quite good 
for some voting situations!

I'm just saying -- since you specifically asked me -- that my preference 
is to skip over slight improvements and jump ahead to advanced voting 
methods that look deeply into ballot preferences (beyond one current 
"top" choice at a time) and that avoid the need to segment voters into 
subgroups.

For further context I'll say that years ago a group of people within a 
local food co-op came up with a very carefully designed way of electing 
a group of "representatives" for the purpose of having them make 
decisions instead of letting all the members vote on important 
decisions.  In spite of how well-designed and "fair" (neutral) the 
process was, neither the people who wanted the co-op to sell a few meat 
items nor the people who wanted absolutely no meat in the store were 
willing to let such a group make a decision about that issue.  The point 
of this example is that each layer of decision-making -- even if it gets 
adjusted at every election based on the ballots -- does not truly 
provide proportional representation.  As for what a truly proportional 
solution to that "meat" conflict would have been, I'm not sure.  Selling 
fewer meat items than what a majority of voters wanted would still fail 
to represent the members who didn't want any meat sold.  (It was not 
clear who was in the majority, and probably a middle third of the 
members would have been OK with certain meat choices but not other meat 
choices.)

Ultimately voters don't care about the process.  That's why so few 
citizens "do the math" to discover why they are not represented by the 
people "they" elect.  This same dilemma applies to all the voting 
methods discussed here.  Here we are not only "doing the math," but we 
are developing "the math" relating to voting methods.  Let's eliminate 
extra layers and stop using "start-at-the-top" blinders as we look at 
each ballot.

Thank you for your interest in my opinion.  I hope this helps, either to 
refine your ideas or to refine ways to "sell" whatever method you like 
best.  (All of us here are learning how to "sell" our favorite method(s).)

BTW, thank you for creating the flowcharts.  They do help clarify your 
method.  (Alas, graphics on websites seem to be the only way to make 
flowcharts easy to view, so they are not suitable here in this forum.)

Richard Fobes

On 10/22/2014 6:54 AM, steve bosworth wrote:
> Hi Richard,
>
> Sorry for the late reply. I've been travelling.
> Thank you for your several criticisms, comments and suggestions.
>
> I've *injected my responses within the text of your email bellow, using
> bold print*.
>
> I hope you will see that some of the problems you mentioned are solved
> within the full explanation of my proposed system (Associatonal
> Proportional Representation (*APR*)) that I have fully described in the
> attached article with its illustrative 2 flow charts and 3 tables.
>
> In the light of the more complete information provided, I very much hope
> you will be able to find the time to respond to the additional explanations.
>
> Thank you,
> Steve
>
>  > Date: Tue, 2 Sep 2014 09:10:10 -0700
>  > From: ElectionMethods <at> VoteFair.org
>  > To: stevebosworth <at> hotmail.com
>  > Subject: Re: (2) "Severity" of failing
>  >
>  > Steve Bosworth ~
>  >
>  > Thank you for your interest in my opinion.
>  >
>  > Getting to the point of your question, your election method combines
>  > single-winner voting concepts
> *S: No, in effect, APR**is entirely a multi-winner system, e.g. to elect
> the 435 members of the US House of Representatives or the UK House of
> Commons. *
> with proportional representation concepts,
> *S: APR's giving different 'weighted votes' to each rep depending on how
> many citizens had ranked them would provide complete individual
> representative and party proportionality.*
>  > which means that the well-known fairness criteria do not apply.
>
> *S: I know of no such criteria which APR would not satisfy.*
>  > Your idea sounds intriguing. Yet it would encounter time-related
>  > issues,
> *S: Please explain.*
> especially strategy issues,
> *S: Please explain.*
> if it were converted into an actual
>  > election method -- that involves ballots.
> *S: Perhaps you will see that these issues have been solved by the
> detailed presentation of the 'actual method' and the paper 'ballots' to
> be used by APR, and explained by the attachments.*
>  >
>  > The single-winner aspects basically match instant-runoff voting, so the
>  > same fairness-criteria failures would apply.
> *S: No, because it is not an IRV system.*
>  >
>  > As for the proportional part, your method would tend to elect a few
>  > celebrity representatives who are supported by "the media"
> *S: Given APR's 'electoral associations' as selected by citizens months
> before the general election through APR's special 'primary election',
> the relative influence of 'celebrity' and the 'media' might be much
> reduced. In any case, the article stipulates that any very popular rep
> who receives more than 10% of all the votes in the country would be
> required to publish exactly how he will pass on all of his 'extra votes'
> to his trusted fellow reps.*
> and the
>  > other representatives would tend to be "fringe" types who are supported
>  > by fewer voters. Note that this is a tendency, and would be reduced to
>  > the extent that it's noticed, which means that most voters would not
>  > notice this tendency.
>  >
>  > Alas, my time is limited, so I can't offer more feedback at this time.
> *S: Thank you again for your time.*
>  > I hope this is helpful.
>  >
>  > If you want more opinions, I suggest that you present the idea on the
>  > Election Methods forum.
> *S: I keep trying to find out how to do this but have so far failed. Can
> you please explain how one contributes to this forum?*
>  >
>  > Richard Fobes
>  >
>  >

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Kristofer Munsterhjelm | 19 Oct 14:08 2014
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Party lists and candidate multiwinner elections

Say we have two settings: one is an ordinary multiwinner election with, 
say, 10 seats. The other is a party list PR election to a very large 
assembly (say 500 seats), but where the number of distinct parties has 
been limited to 10. That is, no more than 10 parties may be represented 
in that large council.

Furthermore, assume that the voters' ballots are completely identical in 
the two settings. So if a voter in setting two ranks party A > party B > 
party C, then in setting one he would rank candidate A > candidate B > 
candidate C.

Now, my question is: is there any situation where we would expect the 
candidates elected in setting one to differ from the parties that get at 
least one seat in setting two?

I can't think of any off-hand, but if there are none, what implications 
do the fact that different parties have very different numbers of seats 
in party list PR have for ordinary multiwinner elections? Is it simply 
an artifact of parties being a lot harder to start than to run as an 
independent candidate in ordinary multiwinner PR? Or is it a consequence 
of party list methods being based on Plurality?

Or are there cases where the party composition would differ from the 
candidates elected in an analogous multiwinner election? Perhaps party 
composition should be more like the results of Minmax Approval (i.e. 
should obey Warren's "representativeness" criterion) and one should use 
relative seat counts to even out the power imbalance? What do you think?
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Toby Pereira | 8 Oct 20:50 2014
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Re: General PR question (from Andy Jennings in 2011)

From: Kathy Dopp <kathy.dopp <at> gmail.com>
 
>> My
>> system, for example, uses squared rather than absolute deviation (and uses a
>> different measure of deviation anyway) and it gives the results that I
>> wanted it to when I tested it, including stable results for the largest two
>> factions when the size of the third tiny faction changes, and the three-way
>> tie from the other example. It doesn't work by ignoring or eliminating
>> smaller factions;

>Neither does mine (in case you are implying such)  Some party list
>systems do work that way however.

I wasn't implying that but you suggested in one of your posts that it might be desirable. I was just saying that my system deals with it "naturally" - i.e. without manually taking out factions.

>> And I'm still unsure how to translate your method into approval voting with
>> overlapping factions.

>It works exactly the same way with overlapping candidate support in
>different factions. (i.e. v_i and s_i have exactly the same meanings,
>the number of voters in the group and the number of winning candidates
>each group contributes to electing.

But what I mean is that if a large faction (with say 50% of all voters) is divided into two (say 25% each) because of a single controversial candidate who appears on half of that faction's ballots but not the other half, then if that faction receives half the candidates (and the one controversial candidate is not elected), then it will be measured as unproportional because each faction will have each contributed to 50% of the candidates but will only be 25% of the electorate each.

>What is the logic of using squared rather than absolute deviation? and
>are you also selecting the slate of candidates minimizing your formula?

Squared deviation gave better and more consistent results when I tried it. I always come armed with election scenarios where I have an intended result, and I see if the method being tested gives the intended result. My method with squared deviation gave every result I wanted it to. Absolute deviation didn't.

And yes, in my method the winning set would be the one with the lowest sum of the squared deviations. Well, not necessarily, because if candidates could be elected sequentially, which could give a different result.

Toby



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Toby Pereira | 7 Oct 23:23 2014
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Re: General PR question (from Andy Jennings in 2011)

From: Kathy Dopp <kathy.dopp <at> gmail.com>

>So, perhaps there is an improved alternative over a truly
>proportionate allocation of seats to voters. Perhaps the voting groups
>who cannot win seats should be taken out of the equation as, I
>believe, some party list systems do when calculating winners.

--
>Kathy Dopp


Perhaps there's a more proportional method than a "truly proportionate allocation of seats to voters"! But what I would say is that there are several methods that people might deem to be proportional, and so to say that yours is *the* method would probably cause some disagreement.
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Richard Fobes | 7 Oct 22:42 2014

Re: How choice of voting systems depend on amount of participants

On 10/6/2014 11:47 PM, Kristofer Munsterhjelm wrote:
> ...
> I seem to recall someone mentioning a US region that used majority
> voting: there were rounds of voting until someone got an outright
> majority, and the rounds kept on for as long as needed. I don't recall
> the details, though.

This is how the "electoral college" works when voting for U.S. 
President, or at least the way it was set up to work.  Under current 
conditions, with each state giving all its electoral votes to either the 
Republican candidate or the Democratic candidate (and never any 
electoral votes to a third-party candidate), in recent decades there has 
always a winner on the first round of voting.  If there were not a 
majority winner, then the contest would be (and has been, three or four 
times) transferred to the U.S. House of Representatives, with each state 
getting one vote (but with no indication as to how that one vote (per 
state) is assigned).

Richard Fobes

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Toby Pereira | 28 Sep 01:28 2014
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Re: General PR question (from Andy Jennings in 2011)

I was thinking recently again about Andy Jennings's PR question (below) and available here http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-July/093278.html, which is about the trade of between proportionality and having candidates with strong support. Warren Smith (http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-July/126111.html) gave the extreme example of a 500-member parliament where two candidates each get 50% approval, and the others each get 0.2% approval. Perfect proportionality could be achieved by electing 500 candidates with 0.2% approval, but in many ways this would seem a perverse result.

But the more I think about it, the more I think there isn't a non-arbitrary solution to the problem. What's the exchange rate between proportionality and support? There isn't an obvious answer.

I proposed my own proportional approval and score system a few months ago (http://lists.electorama.com/pipermail/election-methods-electorama.com/2014-May/098049.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2014-June/130772.html), and it purely bases result on proportionality, so would elect CDE in Andy's example but would also elect 500 candidates with 0.2% support in Warren's example. However, this also assumes that every possible winning set of candidates would be looked at and the most proportional one found. In practice, the system might be used sequentially. This would force through the most popular candidate, and then each subsequent candidate would be elected to balance it proportionally. This would elect the two most popular candidates in Warren's example, but would fail to elect CDE in Andy's example. But given that there may be no non-arbitrary solution, electing sequentially may be the simplest and least arbitrary way around the problems we have. It is also a solution that would likely be forced upon us due to limits on computing power when it comes to comparing all possible sets of candidates. Necessity may force the pragmatic solution upon us.

Toby



>Forest and I were discussing PR last week and the following  situation came
>up.  Suppose there are five candidates, A, B, C, D, E.  A and B evenly
>divide the electorate and, in a completely orthogonal way, C, D, and E
>evenly divide the electorate.  That is:

>One-sixth of the electorate approves A and C.
>One-sixth of the electorate approves A and D.
>One-sixth of the electorate approves A and E.
>One-sixth of the electorate approves B and C.
>One-sixth of the electorate approves B and D.
>One-sixth of the electorate approves B and E.

>It is obvious that the best two-winner representative body is A and B.  What
>is the best three-winner representative body?

>CDE seems to be the fairest.  As Forest said, it is "envy-free".

>Some methods would choose ABC, ABD, or ABE, which seem to give more total
>satisfaction.

>Is one unequivocally better than the other?

>I tend to feel that each representative should represent one-third of the
>voters, so CDE is a much better outcome.  Certain methods, like STV, Monroe,
>and AT-TV (I think) can even output a list of which voters are represented
>by each candidate, which I really like.

>I also note that if there was another candidate, F, approved by everybody,
>it is probably true that ABF would be an even better committee than CDE.  Is
>there a method that can choose CDE in the first case and ABF in the second
>case?

>Andy

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Gmane