[EM] Another approach to geographical proportionality and single-winner districts (was: PR for USA or UK)

[Juho Laatu]

On 30.7.2011, at 19.11, Jameson Quinn wrote:

> I concur that this method does quite well on my stated criteria. Therefore, I heartily support it.
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> I especially like how, without any compromise in the secret ballot, it allows each* voter to know who "their" representative is; a representative who they certainly supported by party, and probably supported directly. (* Of course, there is the inevitable Droop quota of unrepresented or diluted voters.)
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> Here's what I don't like about it:
> 1 and 2 censored on second thought - they were purely aesthetic and personal issues, and I'm sure I could get over them.
> 3. Since the party districts are not known beforehand, it could happen that one of the districts elects a candidate with very few votes.

If some region doesn't have strong candidates, that should attract new candidates. Also parties should nominate numerous good candidates in all areas to attract voters (since the total sum of votes determines the number of seats of the party). In principle the system approximates a system that elects the Condorcet winner of all regions. The winner could be "weak" in the same sense as Condorcet winners can be weak, i.e. having lots of second preference votes and not that many first preference votes.

> Imagine that the party gets 3 seats, and A, B, and C split the party's votes in a nearly geographically-even 40%:30%:20% ratio.

I guess these are fist preference votes (and D will get 10% of the first preference votes).

> However, D gets 30% of the vote in one third of the area — that is, 10% of the overall vote (thus slightly reducing the first three candidate's totals in that region and increasing them in others). The winners will be A, B, and D, even though C had twice the votes of D, and D had only 10%.

That makes sense. In a regionally proportional system any region that has one "quota" of votes should be able to pick their favourite representative. (The same rule applies to political parties in politically proportional systems.)

On the other hand it is quite possible that the winning slate does not contain D. If A, B and C are very strong in some areas, their regions might be complemented by adding one third of "D's region" to each of their regions. The equation is complex, so I can't tell exactly what would happen, but if A, B and C have lots of first preference support, it is quite possible that one can combine very strong regions for them, even if they are not that strong everywhere within "D's region". (I guess I'd need more simulations to understand better how the method finds the best balance.)

> Also, the A and B districts will be arbitrary.

Second and third preferences will tell what regions make sense.

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> Let's consider the party strategy in this system; perhaps by formalizing it, we can improve the results.
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> A party which hopes for N or fewer seats

We can assume that this party will get about N seats with whatever mind of candidates and campaign.

> , should divide the country/state into N regions, and have one "principal" candidate campaign in each region, with a few "backups" campaigning countrywide.

Since the borderlines will be determined dynamically it could be that candidates typically have a campaign that covers an area whose size is at least two regions (unless they are very sure where they can collect their votes). Giving second or third preference votes makes also sense to voters in the nearby regions.

Also for a party that wants to handpick N representatives it could make sense to market them wider than in one guessed region only. Usually already in open list based systems it makes sense to nominate multiple candidates and hope that they will collect all the additional votes they can. In open lists one could nominate multiple candidates from multiple competing smaller districts at one region if one wants to make space for the party favourite. But in this method that strategy will not work as well since this method is at each region "Condorcet winner oriented" instead of "plurality oriented".

> Imperfect results could arise if...:
> 1. ...the party gets more than N seats. the extra candidate will not be the strongest "backup", but the "backup" who is strongest where the "principal" is weakest.

Yes, but that makes sense in regional proportionality. Electing two candidates that are very popular at one region only is a worse outcome than electing candidates that cover the whole country (or two regions in this case).

> 2. ...one of the N principals turns out to be relatively unpopular. It is unlikely that one of the backups would have been concentrating particularly on that unpopular candidate's area, so the weak candidate will still win their area, without really deserving to.

Maybe the weak candidate is anyway the most liked candidate in that region. I think a good strategy would be to allow all candidates to collect votes and campaign in a wider area than one region. If one of the candidates is weak, then the regions of the strong candidates can move to make space for the strongest backup candidate wherever his strongest support is. (Moving regions could help also in the previous point (1.) above.)

> 3. ...one of the backups turns out to be particularly popular. This is, in essence, similar to option 2.

It is good if the voters will decide which candidate is most popular. The regions should be also here flexible enough to allow one good representative to emerge even in an area that is already covered by other strong candidates, but whose regions can move in some direction a bit to make space for this newcomer.

> 4. ...one of the planned N regions turns out to have an unexpected rise or fall in the vote for this party. This will probably result in a situation similar to 2 or 3.

This is one good reason why the party should not guess and fix the regions. Based on earlier elections they may make some guesses, but better provide some overlapping coverage, to be prepared for changing regions.

> 5. The party gets fewer than N seats. Probably what will happen is that the N-m candidates will slice up those m regions (where m is most likely to be just 1), in a basically arbitrary fashion.

The second and third preferences should make the new areas less arbitrary. (And I hope the candidates campaigned on wider areas than one planned region only.)

> 
> I think that this uncertainty can be reduced. Here's an attempt.
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> Each party splits the country into districts (composed of AVAs) based on the number of representatives they currently have in the parliament, and based on the distribution of first-place votes for those representatives. (This is a rough guess of the number of seats they can expect. If a party has split or renamed, the number of current affiliates in the parliament is the best unbiased guess of the prospective vote of each fragment, although of course in this case it could be very wrong).

Yes, results of the previous election are probably a good way to plan the campaigning regions of the old representatives. Also they should campaign in wider areas than in on region since additional votes to them in other areas may increase the overall number of votes of that party. They will also not steal the seat of anyone else if they will be elected anyway (probably in their strongest planned region). A wider campaign area allows also their support area to move slightly from one election to the next.

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> There is also an "official, default" division of the country into N equipopulous districts for any N up to the number of seats. Starting from 1, this is drawn to maximize the "overlap" between N and N+1, except when N mod 3 = 1. These "districts" are used for new parties which had no representation in the prior parliament. 

I just note that the distribution of support of different parties may vary. Some parties might e.g. get their support mainly from large cities, or from north, or from industrial areas.

> 
> Each candidate is listed on the ballot in their home district. The party may use any democratic process to determine the order and number of candidates listed in each district. If participation in that process is lower than x%, the list is open and randomized in order. The more candidates are listed, the smaller the font used for each; this is to discourage parties from listing an excessive number of candidates per district. 

Did you propose that candidates would be allowed to get their names (and numbers) in the ballots of some agreed size geographic (or party support density based) area? That could add votes to local candidates, but that would make the printing process of the ballots complex. I guess people could get the same information also from advertisements or official posters that list e.g. the "local candidates" of each AVA.

The number of candidates could be limited e.g. based on the number of representatives that each party has, or the limit could be a fixed number.

> 
> Nonetheless, there is a master list of candidates (for instance, on a poster and in a booklet available at the voting site), and any voter may vote for any candidate. That is, the ballot listings are purely a formality. New parties may choose their own N for the purposes of assigning districts in this manner, using the "default" districts of N.
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> I'm agnostic about voting format. It could be rated, ranked, or even some form of limited voting. 
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> A proportional system is used to allocate number of seats to each party. Some simple plurality-based or semi-proportional system is used to choose the winners within each party. Then candidates are assigned to seats through some simple satisfaction metric. Any seats above the planned district division for a party which had had more than 3 seats previously are nationwide. Any seats below the planned district division leave a "gap" in the districts; voters for that party who live in the "gap" would naturally go to one of the neighboring district representatives for that party when they needed to contact "their" representative. The map of who corresponds to whom could be formalized in that case.

One approach could be to make the N districts approach a bit softer by using two layers. In that case the district of each candidate would twice as large and each AVA would be part of two districts (or maybe we could be flexible here and allow variation in the number of AVA).

> 
> It could happen in this system that two representatives from the same party from the same district would be elected, and none from another district, although the ballot design would discourage this. In that case, the satisfaction metric would assign one of the two to represent a district where they didn't live. This would be rare and tolerable.

I guess regions with no strong candidates would attract new candidates to start campaigning in that area. And I hope flexible borders in campaigning would also help when some "empty" region has to be covered by the neighbouring regions (that will move and make space somewhere else for a new region).

After reading all the comments my topmost thought is to allow some flexibility in campaigning in the form of wider and overlapping campaign areas.

Juho


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> JQ 
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> 2011/7/30 Juho Laatu <juho4880 at yahoo.co.uk>
> To make the proposals in my earlier mail more concrete, here's one simple (as much as possible) example of a politically proportional, geographically proportional and local representative oriented method. I'll also estimate how well this method meets Jameson Quinn's criteria.
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> - voters write the numbers of three candidates (of one party) in three empty boxes of a ballot (= ranked vote A>B>C)
> - the (proportional) number of candidates of each party is counted at country level (based on the total number of votes to each party) (using e.g. largest remainder)
> - each representative will represent a region that consists of a set of atomic voting areas
> - there will be exactly one representative of each party (that got seats) in each atomic voting area
> - regions of one party shall be about equal in size (measured in votes to this party), so that no region is bigger than any other region of that party if one atomic voting area is taken away from it
> - a slate is a complete set of regions and their representatives (can be computed separately for each party)
> - the region that contains the atomic voting area of a voter (= voter's own region) may be geographically different in different slates
> - a voter is considered to prefer slate1 to slate2 if the voter prefers the representative of region1 (voter's own region in slate1) to the representative of region2
> - a Condorcet method (e.g. minmax(margins)) is used to pick the best slate from a limited set of best found candidate slates (not a complete search because of computational complexity)
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> I hope that description is clear enough. Then let's see how this method would meet the criteria set by Jameson Quinn (for multi-party methods for current two-party countries).
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>> 1. Truly proportional (of course). I would be willing to support a not-truly-proportional system, but I'm not everyone. Egregious compromises on this issue will simply reduce the activist base, to no benefit.
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> - provides exact country wide party based proportionality
> - party internal proportionality is provided in some sense but it is mixed with geographic proportionality and local representation (the latter two have maybe higher priority in this method)
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>> 2. Includes a geographical aspect. People are attached to the "local representation" feature of FPTP, whether that's rational or not.
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> - this method offers one type of local representation (that has been made as local as possible since all parties have exactly one representative per region)
> - better than current two-party systems in the sense that all voters (not only those of the winning party) will have their own local representative of their own party
> - less local in the sense that regions are larger than traditional single-seat districts (for a party with only one representative the region is the whole country, for larger parties with n representatives there will be n regions)
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>> 3. No "closed list". A party should not be able to completely shield any member from the voters. In general, voter power is preferable to party power, insofar as it's compatible with the next criterion.
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> - allows whatever number of candidates (if one uses the ballot format described above) (not only small sets accepted by each party) (having large number of candidates is beneficial to a party)
> - voters (and voters alone) will determine which candidates will be elected (= no predetermined preference order, all candidates treated equally)
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>> 4. Simple ballots. A reasonably-thorough voter should not have to mark more than, say, 5 candidates or options, and an average ballot should not list more than 20 candidates or options. Those are extreme limits; simpler is better, all the way down to around 7 options (of which only around half will be salient and/or viable).
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> - the three boxes approach is very simple (not as simple as one box only, but maybe simple enough and expressive enough at the same time)
> - three boxes (candidates) with "inheritance" to the party in the case that the ballot is "exhausted" may be safer from exhaustion point of view than having five candidates and no inheritance after exhaustion
> - there could be more than 20 candidates from each of the 20 parties (= ballot format and size does not limit the number of candidates)
> - marking three numbers (taken from a poster that lists all candidates with their numbers) in the boxes is simple, but it is a new thing to learn if the old system is based on "ticking names" or ticking one name or party
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>> 5. Ideally, the smoothest transition possible. If existing single-winner districts can be used unchanged, all the better.
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> - existing single-winner districts could be used in this proposal as atomic voting areas (also smaller areas are possible)
> - transition from two parties to multiple parties and full proportional representation can not be very smooth by definition, but this approach that tries to preserve (and in some sense even improve) local representation may be considered smooth in some sense
> - if full proportionality is too much to accept, one approach could be to reduce the level of proportionality, maybe by dividing the country into smaller independent "districts" that each are proportional, but less so because of the smaller number of representatives per "district" and resulting smaller number of parties
> - if full proportionality is too much to accept, one could in addition use also cutoffs and/or a seat allocation algorithm that favours large parties to some extent at country (or "district") level (e.g. D'Hondt tends to give the very last fragment seats to large parties) and/or even disproportional seat distribution algorithms
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>> 6. Insofar as it's compatible with the criteria above, greater freedom in voting is better. For instance, if ballots are printed with only in-district candidates, a system which allows out-of-district write-ins is better than one which doesn't, all other things being equal.
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> - this method allows the voter to vote for any of the candidates, but it makes sense to include candidates that have reasonable chances to become elected from voter's own atomic voting area
> - in the described method the voter was limited to marking candidates of one party only (but this condition could be relaxed if needed, leading to more freedom, but possibly also to some strategic concerns)
> - ballots need not be printed with candidate names, they are standard ballots with three empty boxes
> - write-in candidates (and late additions) should be nominated as candidates of one party and given a number, but after that they will be treated just like any other candidate
> - one could have also traditional pure write-ins with only someone's name written in the box (such write-in candidates would not belong to any party but would form a party of their own)
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> Here are also some pictures that visualize the intended behaviour of the method.
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> In these example simulations there are 8 atomic voting areas (see the first figure). Those areas were determined as 8 random points and areas around them based on shortest distance to the "polling station". The polling stations are visible in the first figure. There are 30 random voters. Voters have been allocated to the atomic voting area where they reside. Voters are shown in the first figure as smaller dots.
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> https://picasaweb.google.com/juho.laatu/July292011#5635013871220667442
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> Then there are three simulations. These figures describe the results of one party only. In the first simulation the figure shows the outcome of the election assuming that this party got 2 representatives. The second simulation assumes 3 representatives, and the third simulation assumes 4 representatives. There are 6 candidates. They are shown as coloured dots. Their colours correspond to colours in the winning areas (= regions of the winning slate).
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> Voters will vote for their nearest candidates (three closest ones since we limited the number of ratings to three). In these simulations political opinions and geographical location are described in the same 2D space. That means that the political opinions are geographical, and as a result the formed regions will be quite compact geographical districts. The described method allows however regions that consist of disjoint parts (e.g. two separate industrial towns that both like an "industrial" candidate x) since there was no criterion that would force the regions to be more compact.
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> In the 2 representative simulation blue candidate and red candidate are the winners. Red candidate will represent the upper right part of the voters. Blue candidate will represent the lower left part. In the other simulations all the parameters are the same, except that the number of representatives changes. These simulations are all exhaustive, i.e. the Condorcet comparison was between all acceptable (= balanced enough) sets of regions and all region winner / region combinations (more than 2000 of them in the largest simulations).
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> https://picasaweb.google.com/juho.laatu/July292011#5635014056975392002
> https://picasaweb.google.com/juho.laatu/July292011#5635014135807700258
> https://picasaweb.google.com/juho.laatu/July292011#5635014276333092642
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> Note that in the last simulation with 4 representatives the red area is disjoint. Note also that the red candidate is in the yellow region and the yellow candidate is in the red region. I can't tell exactly why the algorithm picked the red and yellow candidates this way and not the other way around, or why the regions are not organized otherwise. If red and yellow candidates would swap the 5 and 6 member atomic voting areas ("ava") between themselves (the rightmost ava has 6 members although only 5 of them are visible in the figure), that would make the 5+1 region so small that the algorithm would would force it to be made bigger, e.g. by joining the other 1 member ava into it. That would obviously give a worse result in the Condorcet comparison. In this simulation the size differences of different avas were quite big (7, 7, 6, 5, 3, 1, 1), so the smallest avas often have to move to make the balance good. Although the method makes its decisions on the winners based on regions that are forced to be the same size, one could also report the popularity of each candidate in each ava. In this last simulation the most popular elected representative is not always the technical representative of each ava. It is also obvious that the "interest area" of each representative is more flexible than the technical winning region only. In the last simulation yellow and red candidates would naturally both try to "represent" the atomic voting areas of the upper left corner. They are likely to take that approach also to guarantee maximum number of votes also in the next election. So, what we learn from this is that the technical regions are used to force fair geographical representation, but in real life all candidates will represent areas where they got lots of votes (or plan to get more votes in the next election).
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> One more observation. I run these simulation also with full rankings (instead of truncating the opinions in three ranks). The outcome was exactly the same except that in the 2 representative simulation green got the seat than went to blue in the 3 box simulation. Further simulations needed to properly estimate how this method behaves in larger and more real life like simulations (that would be also optimization based, not exhaustive brute force based simulations like these).
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> Juho
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> On 25.7.2011, at 1.16, Juho Laatu wrote:
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>> One feature of single-winner district based political systems is that voters will have a clearly named "own" representative that is as local as possible. In a PR context with multiple parties one could redefine this idea so that people should have a known representative that represents them in the assembly. A two-party / single-winner district system has the problem that often the local representative is from the "wrong" party. The requirement could be modified so that the idea is to have a local representative of one's *own* party. With that approach we will lose some of the locality, but on the other hand we may get more natural local representatives.
>> 
>> This kind of methods could work for example so that first the number of seats that each party gets will be determined at national level (to provide perfect proportionality between parties). The country is divided in small voting areas. We know the number of votes from each voting area to each party and the location of each voting area. (Votes are summed up in voting areas instead of using individual votes directly in order to guarantee voter privacy.) Also candidates have a location. That location could be approximate and it could be used only to indicate that the intention of the candidate is to represent certain region. Voters will then vote for the candidates. The system could allow only bullet votes or one could user ranked or rated ballots too.
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>> Then we need an algorithm that takes the votes to some party and their geographical distribution, and the geographical distribution of the votes to different candidates of the party into account. The whole country will be divided in (party specific) regions, and one candidate (of this party) will be elected in each region. Now all supporters of this party will have a single "own" representative of their own party. The size of the regions should reflect the density (or sparseness) of votes from that region. The size of each district would be about the same in terms of votes received from that region. One could allow also disjoint regions, but if one wants the regions not to be too fragmented, one could add some parameter that favours compact regions. One should form such a set of regions and set of representatives in them that the overall happiness of the voters (of this party) is maximized (= local representatives having local support etc.).
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>> One could develop also systems with no party structure (with ranked or rated ballots). In such systems each geographical spot could have exactly one representative. Or alternatively one could agree some (small) number of representatives that each spot should have (= layers). That would allow every voter to have a local representative from their own "wing" at least. Also in this approach different layers could have different regions, and the size of the regions could reflect the popularity distribution of that candidate. (Actually the layers need not be separate layers. It is enough if each representative has a region, and each geographical spot is included in the agreed number of regions.
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>> The end result so far is thus a mixture of strict political and geographical proportionality requirements, leading to electing a fixed number of representatives for each geographic spot. But of course one could still give up the idea of keeping the number of representatives per spot constant :-). One could instead optimize the number of representatives per spot so that it reflects the uniformity of opinion in each location. If some place has only small number of different opinions it could have only a small number of very local representatives, while another place (with similar population density) could have numerous but less local representatives. I guess we will keep the requirement of all representatives having in their regions about equal number of supporters to represent.
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>> One problem of systems without clear district structure and geographic proportionality is that candidates from the capital region and other major cities and television tend to become overrepresented. The discussed system above had no clear fixed district borders (although it could have) and it may allow voters to vote also distant candidates, but it may still maintain regional representation quite well (also without limiting the area where each candidate can collect votes) since individual candidates are more likely to be elected if they get their votes from a "region size" geographical area.
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>> I wrote this mail as a response to the "PR for USA or UK" mail stream, and particularly to the question how to offer good political proportionality, geographic proportionality and local representation at the same time. This model is however not a very concrete and practical proposal for the needs of that mail stream. If one looks for a practical implementations of this approach, maybe the party based approach with one party representative for each spot is closest to being a practical proposal (= one layer per party). The art of districting is anyway already now well known in the two-party countries, so maybe doing that at party level (without fights between political parties (but potentially with some fights between candidates to be elected :-) )) could be an additional positive thing in this proposal.
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>> Juho
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