Election Committee

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Patroklus Murakami
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Election Committee

Post by Patroklus Murakami »

The election committee, chaired by RA member Beathan Vale and advertised here and here, has been running for some time now. Unfortunately, I've been unable to attend these meetings so I've put together some thoughts to post here.

As I've said elsewhere I consider our electoral system to be badly flawed and in need of reform. One of the prime motivations for the reform the RA agreed last term was to allow voters to vote 'No' on a faction they didn't agree with by eliminating that faction from their ballot. As it turned out, this wasn't thought through properly - we discovered after the fact that those voters who eliminated other factions made their vote count for more; those who eliminated all other factions bar their first choice made their votes count the most. The RA reversed that electoral reform so we're back to the situation we had before; we still don't really get to choose between the factions because we're forced to rank all of them. In fact, this combination of ranking and proportional representation produces perverse results because it massively over-represents minority factions; the citizens' voting pattern is rendered largely irrelevant, it's the number of factions contesting an election that really counts. As some have pointed out, our current electoral system can be gamed. If a faction with sizable support in the CDS, such as the CSDF, were to split into 2 or even 3 sub-factions, it could artificially inflate the number of seats won if its voters could be persuaded to vote in an organised fashion for the sub-factions. I think the case for further reform remains.

There are several options open to us and I want to outline a few of them later in this post; we discussed these at our regular CSDF meeting yesterday. First I'd like to consider what kind of principles we might want our electoral system to embody. These mostly come from discussions the community has held in the past and are not meant to be definitive. I'm sure others will have other principles that they will want to play into the discussion.

  • 1. Platforms not personalities. The Constitution says the Representative Assembly is a body of factions, not individuals. It makes sense that we try to focus on ideas rather than personalities in electing RA members. The RA has never ended up with the same people at the end of a term as at the start. People leave for all sorts of reasons during the term and need to be replaced. Electing factions rather than individuals means that voters can be clear they're voting primarily for policies rather than the people who are on the slate. This idea has been challenged recently but this is still a principle many of us subscribe to

    2. Comprehensibility. Our electoral system isn't too difficult to follow. You rank the factions, you rank the candidates in your first choice faction and then, through the mysteries of the Borda count and the Saint Lague method the result is delivered! It's not as straightforward (or as unfair) as first-past-the-post, plurality elections but it's a system I feel I could explain to a layman.

    3. Voter choice. We currently force voters to rank all the factions whether they agree with them or not. That denies voters the power to exercise their choice to vote 'No' by crossing factions they don't agree with off the ballot paper.

    4. Fairness. This a principle I think our current system fails because it does not deliver an RA which represents the views of the CDS citizens in rough proportion to their presence in the electorate. A system where parties gaining 23 and 4 first preferences respectively end up with the same number of seats in the RA is not fair. A system where a faction gaining roughly 50% of the first preferences ends up with 2 out of 7 seats is not fair. This is another principle I'd like to see electoral reform address.

Here are some options we could consider:

  • i) Retain the status quo. This is unattractive for the many reasons outlined above and in previous debates about electoral reform.

    ii) Switch to a system using Single Transferable Vote. The CSDF and CARE both put forward proposals for STV last term but we could not agree on the details. We may be able to do better this term. In terms of the four principles outlined above, it brings personalities more to the fore so could undermine our faction-based system of government to some extent. It scores high on comprehensibility when casting a ballot but understanding how seats are allocated is a little more involved. The count is horrendously complex when you do it manually but there is open source software available to do this for us now. The major advantage of STV is that it allows voters a great deal of choice in casting their ballot - they can rank all candidates of one faction, then another, then another. Or they can rank individuals in order of their perceived ability to do the job regardless of factional label. They can choose to rank only one candidate or all on the ballot or any number in between. And it is fair, few votes are wasted and the resulting RA would truly reflect the choices of the citizens.

    iii). Give citizens one vote to be cast for one faction, keep ranking for that faction's candidates and keep proportional allocation of seats. This retains the faction-based electoral system we're used to and keeps the focus on platforms. It is very easy to understand both in casting a ballot and in working out how the seats get allocated. It could be argued that it limits voter choice in restricting voters to plumping for one preferred faction rather than allowing voters to discriminate between them. I would argue that this is a fake choice if you have no way to avoid voting for factions you disagree with though. It scores highly on the fairness test; seats would be allocated in very close proportion to the distribution of votes.

    iv). Allow voters to rank one or more factions but modify it so that all votes weigh the same. Essentially this means following Jon's analysis of the problems with the elimination system we trialled in January. From the voters' perspective they face the same type of ballot paper as in January and can choose to rank one or more of the factions. The change comes in the counting where the votes are adjusted so there is no artificial advantage gained from eliminating one or more factions. This retains the platform aspect of our electoral system as in alternative iii). One disadvantage is that working out how the votes translate into seats is quite complex so working out how seats are allocated is difficult to explain. It also preserves our current electoral system while providing more voter choice and it makes it harder to game the system through elimination or splitting factions to gain seats. It is fairer in that all voter choices are respected in the outcomes but no one's vote is worth more than another just because of the decision to eliminate one or more competitors.

I can see good arguments for ii), iii) and iv). I lean towards option iii) because I tend to prefer simple solutions and ones that are easy to understand but I can see why some would not like to make that shift. iv) would enact the kind of reform we intended to carry out last term and is probably best from that perspective. I also have a soft spot for STV but I think that with the comings and goings that are inevitable in the RA it might not be right for us.

I hope that these ideas can be fed in to the Election Committee discussions and that others will pick them up and debate them here too.

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Re: Election Committee

Post by Beathan »

Thank you Pat --

Your thoughts are very helpful. I will try to discuss them with you in more detail prior to filing my report (which I expect to do in the next couple of weeks).

Beathan

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Re: Election Committee

Post by Claude Desmoulins »

A couple of quick thoughts:

1. Previously when STV was proposed. it was mentioned that one could do STV with factions instead of individual candidates. This could keep the faction system while improving voter choice.

2. We now have data from several cycles of elections. In many cases we have enough data to explain how a real past election would have turned out using one of the proposed systems. I think this kind of analysis is particularly useful, alongside the theoretical discussion, to help us all understand how these systems work in practice.

Of Pat's proposed changes, I like iv the best as it preserves the faction over person emphasis and keeps our coalition driven system. I sense that's one of the things Pat doesn't especially like, but I've pointed out before that in a voluntary community where people who feel cut off may just pack up and leave, slow muddling to consensus may not be a bad thing.

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Re: Election Committee

Post by Patroklus Murakami »

Claude Desmoulins wrote:

1. Previously when STV was proposed. it was mentioned that one could do STV with factions instead of individual candidates. This could keep the faction system while improving voter choice.

This is an interesting idea. How do you think it could be done in practice? STV is used to elect individuals (who may also be representatives of parties) not factions so it would need some adaptation to make it work. I have no idea how you would do this but perhaps others have some plan in mind.

2. We now have data from several cycles of elections. In many cases we have enough data to explain how a real past election would have turned out using one of the proposed systems. I think this kind of analysis is particularly useful, alongside the theoretical discussion, to help us all understand how these systems work in practice.

This is a great idea. If anyone can point us to the aggregate data we can try some scenarios out. We need more aggregate data than we got for the January 08 election though, we would need to know, of those who put Faction A first, how many voted for Faction B second, Faction C etc.

Of Pat's proposed changes, I like iv the best as it preserves the faction over person emphasis and keeps our coalition driven system. I sense that's one of the things Pat doesn't especially like, but I've pointed out before that in a voluntary community where people who feel cut off may just pack up and leave, slow muddling to consensus may not be a bad thing.

I'm afraid you're mistaken Claude:) I like both our faction over person emphasis and our coalition driven system but I think that fair votes are important. If votes don't lead to roughly proportional representation then the majority are entitled to feel disenfranchised and fed up - though personally, I have no intention of packing up and leaving!

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Re: Election Committee

Post by Patroklus Murakami »

Any further thoughts? I have a draft proposed constitutional amendment just waiting....

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Re: Election Committee

Post by Beathan »

Pat --

Can you send me a copy of the proposed Amendment? I can take a look at it -- and get some discussion on it tomorrow at the meeting.

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Re: Election Committee

Post by Patroklus Murakami »

Beathan wrote:

Pat --

Can you send me a copy of the proposed Amendment? I can take a look at it -- and get some discussion on it tomorrow at the meeting.

Beathan

I've posted the proposed amendment in Legislative Discussion here. Just to be clear, it's my proposal rather than the CSDFs. We have discussed options for electoral reform internally but I think we'd be happy to discuss all the potential options. This is my preferred option and I'm putting it forward to stimulate discussion.

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Individuals vs. Ideas

Post by Gwyneth Llewelyn »

Well, I'll just add the comments I made on the CSDF meetings.

I think we should try to implement things that are adapted to the reality of the CDS, by gently nudging everything into shape (so that we have a bit of required change), instead of starting with the premise of changing things radically just because we are aware the current system doesn't work, and a "clean start" is better.

In the case of the election system, it's clear to everybody that it's flawed, and that the flaw relies mostly on one issue: our system doesn't reflect the number of votes in factions. Simply put, a faction with the majority of the votes never gets more than one or two seats, and factions can even win the elections if they're everybody's second choice (instead of a majority's first choice). While the original purpose was to give minority factions a good chance to get elected, it also means that citizen's votes are strongly "dampened" — the preferences of the majority tend to be less important than, say, tactical voting or the number of factions running for the RA.

There is also a running prejudice against the concept of "factions"; many who post here tend to believe that factions polarise the community, in the sense that because you're in a faction, you're an Evil Antagonist that has to be fought at all costs. Individuals matter less than their affiliation. This is also obviously wrong, thus I understand proposals where the individuals matter more, and the factions much less. Those proposed systems tend to be more humane: they focus on individual's charisma, no matter what their faction is.

On the other hand, we have to keep our feet on solid ground here. Over a period of six months, it's very rare that the RA always has the same members that were voted originally. Like everything else in SL (and even the CDS), people come and go; they become more or less busy, and depending on their availability, a commitment made half a year ago in SL might suddenly drop priority, and they have to leave. There is really no way to avoid this. We can't chain RA members to chairs. "Forcing" them to declare their willingness to serve if elected won't guarantee that they'll stay a whole term in their seats; oaths, campaigns, comments on the forums will be more or less irrelevant to what people's RL lives are going to be in the future. It's a fact of life that we cannot ignore — and we shouldn't "force" reality but accept it as it is.

Over the years, we tried to solve the dilemma by making RA member replacements more easy, and allow things like non-presential voting (eg. the seven-day-vote). We might have hit into some problems here, but the whole issue was to make sure that the RA meets with a quorum, and has enough members to make binding decisions.

On the other hand, it's also clear that people vote for individuals, and that charisma is a strong factor to motivate people to vote (and in a virtual nation where we have already 50% or so citizens abstaining, bringing citizens to the voting booths is indeed important). Thus, Pat's proposal (with STV) tries to place the focus again on people, less on ideology, and give citizens some empowerment in deciding how the "ideal" RA should look like, no matter what factions are actually represented.

In my mind (and I said so publicly) the major issue I have is just one: how can we guarantee to the citizens that the people they've voted on are actually the ones that will stay around, months later, and make decisions?

The short answer is, of course, that we can't. And since citizens know that, why should they bother to vote on a list of people, ordered through STV, if it's impossible to predict that these people will actually be making the decisions some months later? In effect, a faction's strategy would be to simply jot down the names of candidates with high charisma, get a majority of seats, then replace them as time goes by with other members that have more availability. A faction using that strategy might not win the next elections, but it's a good one under a combination of STV and the ability to easily replace any member. Just turn the RA elections into a bikini contest: the most popular will win the seats, which can be replaced later. There is no great glory in being a RA member anyway — it's just tough work, mostly unappreciated...

So how can we balance both extremes? On one hand, it's clear that we need a system where people identify themselves with candidates, and not with the factions; on the other hand, we need a system that deals with replacements in a simple, straightforward manner (because there will always be members leaving the RA mid-term, and we need to have a simple system to replace them) that doesn't defraud citizens' expectations when voting — or the abstaining will just increase, if citizens feel that their vote on candidates is basically useless anyway.

Back to the drawing board. Ultimately, the RA passes legislation (even if it positively adores putting their nose everywhere!). Legislation are basically policies, and they represent the overall idea of what the RA members have of the CDS. Since the RA is usually fragmented (in the sense that all factions get a representation there), and most factions prepare their work beforehand, this means that decisions are mostly made by ideas thrown around, and, based on public opinion, usually "the time for an idea is ripe" and that's what gets voted on the RA. Hardly ever unilateral bills are proposed and voted; usually, it's ideas that we all have, but that we just disagree on minor details, and through voting and discussion, a compromise is met. If the ideas clash too strongly, the bill will not pass; however, if you look at the past, most ideas get passed, even if they get changed in the process.

On the other hand, the RA is not the only body of Government. We also have the Executive. Here it's much less about "ideas", but the charisma of the Chancellor that decides. Put into other words, a dynamic Chancellor — no matter what ideas he or she might support — is viewed as a valuable asset, and the members of the RA tend to vote on someone that "gets things done" (or is perceived as being able to do that) because that's what the Executive is supposed to do. So personal charisma, personal skills, attitude, trust, and similar values are quite important to determine who should be the next Chancellor.

So what I see is a place where ideas are put into bills (the RA) and another place where someone, on their own (the Chancellor), gets those ideas into practice. Clearly, those are the strongest traits of Government in the CDS: ideas vs. decision ability and personal charisma.

What I thus suggest is a model that adapts itself to reality, and not to what would be nice to have. Since the RA is about "ideas", and it features a high rotation rate of its members, citizens should vote on what ideas they wish to bring to the RA — and not on the individuals who express those ideas. On the other hand, the Chancellor needs to be an authority figure, with a personality that is able to execute those ideas, and that is universally liked by the citizens. The Chancellor, thus, should be directly elected by the citizens.

RA members should also be easy to replace, while at the same time not defraud citizen's expectations when they vote on the initial composition of the RA. So I propose a very simple system. For the RA, each citizen has just one vote on a faction of their preference (no ranking, no multiple votes, no complexity: one citizen, one vote). Seats are allocated to the factions based on Sainte-Laguë or a modification (depending if we wish to benefit more or less the larger factions). Who will actually be seated is pretty irrelevant (since that might change anyway). There will not be any "ordering" of candidates by the citizens (since the order is irrelevant long-term), although we can require factions to provide an ordered list of candidates just for the purpose of transparency: citizens will know that the RA members will be picked from that list, but have no way to decide which ones will get a seat anyway. All they will decide is on the factions sitting in the RA. The rest will be up to the faction to decide; they can, if they wish, hold internal "primary"-like elections to rank their own candidates, or simply have the faction leader decide who should be a candidate. This reflects precisely how different factions deal with the issue, there is no "one size fits all" model for all the factions in the CDS.

On the other hand, the Chancellor should also be elected directly by the citizens, in a typical "bikini contest": the most popular politician will attract the highest number of votes, and a simple majority system could work. We can always modify the system to have two rounds of voting if the winning candidate has no majority (a system that is employed by so many presidential systems). Chancellors, unlike RA members, tend to stick around for the whole term. They are also loosely connected to factions; in fact, in the past, few factions supported their own candidate, but they tended to vote on other faction's candidates as well. So it's clearly a case where the personality, charisma, and talent/skill far outweights the ideology — and thus a different election model should be used for the Chancellor.

This would mean that every term we would have two simultaneous elections, and each citizen would cast a vote on the faction of their preference (voting for the RA on ideas) and on the Chancellor candidate they like most (voting for the Executive based on charisma and popularity). How factions handle the election campaigns is totally up to them. Some factions might publicly show their candidates, ordered according to what they believe would be the best RA members, and simultaneously promote their own candidate for Chancellor. Other factions might just support a Chancellor and not even run for the RA. A few might never tell who are their members for RA and have no candidate at all for Chancellor. Chancellors can be totally independent of factions, and anyone should be allowed to run for Chancellor if they have been citizens for longer than, say, a term (6 months). Factions' (or candidates for Chancellor's) political strategy should not be controlled or imposed — each faction should decide what they think is best for themselves, and let the citizens decide what they like best — through the vote.

In conclusion:

  • Ideology -> Legislation -> High rotation of members -> electing factions for the RA (using S-L for the seats)

  • Charisma/Skills/Personality -> Decision ability -> Commitment to a job -> electing candidates for the Chancellor (using a simple majority system to decide who wins the election; if none of the candidates get a majority, a second round of voting between the two most voted candidates will decide who becomes Chancellor)

This is much simpler, has no "hidden tricks", allows both faction voting and personality voting, deals with the high rotation of the RA members, makes sure that a majority of votes elects a majority of RA members (or that the Chancellor is effectively elected by a majority of citizens) but giving small factions a chance (plurality of opinions is important at the RA!), and makes sure that each branch of government has actually the kind of composition it needs for its work: Legislation requires ideas; Executive action requires charisma and skills.

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Re: Election Committee

Post by Beathan »

I very much like Gwyn's observations.

Also -- I definitely dislike the Pat's proposal. which removes the nuance that I consider to be a great element of CDS voting. I think that single faction voting will tend to polarize the CDS and undermine our project. Even the limited single faction voting allowed by faction elimination had this problem -- we should not go down that road.

That said, I think that the complaint that the most popular faction is short-changed by our system is a legitimate complaint. I would rather address that complaint within our system -- so election gurus (Jon, FR) -- how would elections work if we used an geometric progression for vote allocation. That is -- in a four faction election, instead of allocating votes as: first preference = 4; second =3; third =2; fourth = 1; we use first =8; second =4; third =2; fourth = 1. How complicated would this make the calculation? Would this give a fair and proper preference to the top faction while providing for meaningful "second choice" voting to foster and create CDS unity?

Beathan

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Re: Election Committee

Post by cleopatraxigalia »

I think Beathan just wants the most popular factions second votes. And when the "most popular" has a vast majority enough to matter, they in fact do get and extra seat.. i think the debate is ...............how much more matters?

I think a few percentage points over does NOT give them the mandate nor does it mean that they should get some extra power.. If the most popular faction is most popular enough the system DOES indeed work, they get an extra RA seat.. They get the chancellor post.. etc. ... forgive me, but the reason CDSF didnt get chancellor was .........um?? oh yeah !! they didnt have one to run! sorry beathan i disagree.. that argument is sad and weak.

i didnt hear them complaining when they had three seats buddy boy!

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Re: Election Committee

Post by Beathan »

TP --

The point is that it is strange when a faction that has the first-vote support of around 50% of the population ends up with only 2 seats on a 7 seat RA. My faction received the most obvious advantage from this system -- as we only had the first-vote support of around 7 citizens, but we ended up with the same level of representation on the RA as the CSDF. I think that there are real advantages from this system -- so I don't want to throw it out (as Pat does). However, I think that a voting system that appears to diminish the effectiveness of each subsequent vote is one that will alienate large numbers of people -- and I want to avoid that.

It is important to recognize second-choice parties -- as such parties tend to be a moderating force. A STV system would tend to polarize the CDS and reward the extreme parties, which are capable of inspiring passion, at the expense of the moderate parties, which are too steeped in lukewarm reasonableness to do so. However, something must be done to recognize the individual and collective will of the CDS citizens better than we are doing.

Beathan

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Re: Election Committee

Post by Cindy Ecksol »

Beathan wrote:

TP --

The point is that it is strange when a faction that has the first-vote support of around 50% of the population ends up with only 2 seats on a 7 seat RA. My faction received the most obvious advantage from this system -- as we only had the first-vote support of around 7 citizens, but we ended up with the same level of representation on the RA as the CSDF. I think that there are real advantages from this system -- so I don't want to throw it out (as Pat does). However, I think that a voting system that appears to diminish the effectiveness of each subsequent vote is one that will alienate large numbers of people -- and I want to avoid that.

It is important to recognize second-choice parties -- as such parties tend to be a moderating force. A STV system would tend to polarize the CDS and reward the extreme parties, which are capable of inspiring passion, at the expense of the moderate parties, which are too steeped in lukewarm reasonableness to do so. However, something must be done to recognize the individual and collective will of the CDS citizens better than we are doing.

Beathan

I haven't actually worked out the math, Beathan, but my intuition is leading me to think that your suggestion for a geometric progression scoring would have results that were no different from a "winner takes all" scoring.

In any case, I'm still not sure what the fuss is all about with our current system. My hypothesis is that many of us are used to "winner take all" kinds of systems and so think that a system designed to produce consensus is somehow discriminating against the top vote getter. As I've commented before, our system is working exactly as it was designed: it fosters consensus and coalition rather than domination. We COULD change that, but personally I'd like to continue the experiment along those lines and see how it works out over a longer run.

The only area where I'd like to improve the potential for a single faction to dominate is with respect to election of the Chancellor. Having the Chancellor elected "at large" and with a strong faction affiliation offers a faction that truly is "the choice of the people" to bolster its position in RA by choosing the Chancellor. With our current system making it difficult for a single faction to get more than two seats, this seems like it would provide a bit more power to that strong party. It also gets rid of the back-room politicking that has accompanied so many Chancellor selections. And of course if we're going to make this change in the way the Chancellor is selected, I'd also like to see the LRA appointed not as the default largest vote-getter in the RA, but chosen by his/her peers in the RA. As I've mentioned before, this puts the proper kind of power where it can be best utilized and would create a better balance (and more accountability) between the various power poles in CDS.

Cindy

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Re: Election Committee

Post by Jon Seattle »

Beathan wrote:

I would rather address that complaint within our system -- so election gurus (Jon, FR) -- how would elections work if we used an geometric progression for vote allocation. That is -- in a four faction election, instead of allocating votes as: first preference = 4; second =3; third =2; fourth = 1; we use first =8; second =4; third =2; fourth = 1. How complicated would this make the calculation?

Under the old system we had point counts 4, 3, 2, 1 with a total of 10 points (I am using one-based Borda for comparison). What matters here is not the absolute point value, but the advantage given to each faction over the average (mean) of the lower ranked factions. For the current system we get the first faction having a (mean) 2 point advantage over the others, the second a 1.5 advantage, and the third a one point advantage:

2, 1.5, 1

In order to compare this with the geometric arrangement, we have to normalize, by dividing by the total number of points (10).

0.20
0.15
0.10

Now to compare the geometric count:

8, 4, 2, 1 (total = 15). The advantages are:

5.66, 2.5, 1

Normalizing we get:

0.377 difference: 0.176 (17.6% of the total points)
0.167 difference: 0.017 (1.7%)
0.067 difference: -0.033 (-3%)

The geometric system actually gives a slight advantage the lowest ranked faction. There is only a mild difference between the two counts (at most a 17.6% advantage). Now testing the geometric version against the last full election is a bit complicated because a geometric progression also makes elimination much more powerful. I did a quick test by eliminating all partial votes.

CSDF (Score = 167, seats = 3)
SP (Score = 102, seats = 2)
NuCARE (Score = 96, seats = 1)
DPU (Score = 85, seats = 1)

This test result disadvantages NuCARE. I strongly suspect that if I "filled in" the eliminated rankings, I would end up with the same 2, 2, 2, 1 split we ended up with last time. I will test this when I have time.

When it comes down to it, a major problem is that under the current system the voter's opinion matter very very little. We might as well not hold elections if all they do is select the "last person out", the one faction that gets only one vote in the RA. The votes going into the system are largely ignored.

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Re: Election Committee

Post by Jon Seattle »

Here is the estimate for the geometric weights. For all partial votes I did the following to estimate the effect of not having elimination:

1. I computed the set of factions that were not ranked in an individual vote
2. I computed the points that would have been assigned to the eliminated positions, for example: [4, 2, 1] and computed the average of these. Note that this average is not always an integer.
3. I added the average number of points of each faction that was not ranked in the individual vote.

CSDF (Score = 232.33, seats = 2)
NuCARE (Score = 154.83, seats = 2)
SP (Score = 145.17, seats = 2)
DPU (Score = 127.67, seats = 1)

As you can see the geometric weights yield the same results as the actual election. In part this is the fault of the Sainte-Laguë method which is very very powerful sandpaper. There is a total of 660 points and 7 seats, so that each seat represents more than 94 points in the total. 94 is 61% of the second highest total, so factions would have to be quite far indeed for there to be any difference in seat allocation. As we grow and have more factions representing diverse interests the effect of this sandpaper will only grow stronger.

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Re: Election Committee

Post by Jon Seattle »

As an experiment I tried a much stronger exponential weighting: 64, 16, 4, 1, total = 85 (that is times 4 on each step). Here are the advantage numbers:

57.0 normalized: 0.67 difference: 0.47
13.5 normalized: 0.16 difference: 0.01
3.0 normalized: 0.04 difference: -0.06

This was, finally, strong enough to counter the Sainte-Laguë sandpaper:

CSDF (Score = 1619.0, seats = 3)
NuCARE (Score = 918.5, seats = 2)
SP (Score = 657.5, seats = 1)
DPU (Score = 545.0, seats = 1)

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