Is there a place which lists the moderators, admins and such for https://www.votingtheory.org/? It would be good to have transparency about the people who helped to make this and their relevant affiliations.

@Jack-Waugh What STAR does is it renormalizes everybodies vote weight to give them the same impact. This is an attempt to reduce the amount of strategy needed. I do not think that it would outperform somebody who used optimal strategy with score. The point is that most people do not or cannot use optimal strategy. STAR then puts people bad at strategy on a closer level to those who are good at strategy. So I do not think you are wrong in what you say. If all people where fully informed, rational and strategic then score would likely be better. However, people are not any of those things in general. I do not think your like of argument will hold up under this consideration.

An example of where score produces a better outcome than score is

40% = A:5 B:0 C:0
31% = A:0 B:5 C:1
29% = A:0 B:1 C:5

Score give A and STAR gives B. This is an engineered and somewhat extreme example to illustrate the issue. Is 5 infinitely more than 0 or just 5. Is 5 weighted as 4 more than 1 or 5 times. There is no universal metric and different people will choose different metrics. STAR normalizes it all away and compares the two most favoured with full weight to each voter.

STAR is a simplified version of Baldwin's Method. When you think about it that way you see the intent.

Things like utility variance or fraction of electorate with/without a winner among their top choices work to a point, but do not seem particularly theoretically motivated.

If you look at some of the metrics I used in this simulation from the last Equal Vote Committee you will see that I used such metrics. This may be a non-solvable problem for 3 reasons:

• First if there was a metric to maximize we could just make a system that tried all permutations and take the one which maximised the metric. Warren Smith attempted to find such a method here but gave up.
• Secondly, PR has historically been about representing parties fairly not representing people fairly. Even if you came up with a good metric people would fight you on it.
• Lastly, there are theories for the party list case what show that you cant have it all. For example the Balinski–Young theorem. Winner set stability is likely the best definition of PR but it does not always have a solution. There may literally be no answer.

. I could be interested in contributing. Would that look like more simulations or trying to axiomatically characterize these methods or both?

Honestly, since it would be all volunteer it up to you. The mandate last time was to come up with a PR system for Equal Vote to endorse. We ended up with Allocated Score but some of the reasons for that are not 100% proven. Any evidence towards the goal of justifying what the best system is would be great. If you are not a coder or a mathematician there is still lots to do. I would love somebody to write up some of the results for publication.

Simulations can be great tools but one thing I've found is that they frequently have so many tuneable parameters that just by changing a few numbers you can benefit one voting rule or another...

Agreed. There are ways around that but in the end simulations never represent reality. Actual mathematical proofs are better but tend to lack applicability.

Anyway, if you are interested write to Sara (sara@equal.vote) and I(keith@equal.vote).

@jack-waugh This appears to be the Venetian system
https://www.rangevoting.org/VenHist.html

I would make the same suggestion. Add this example to the score voting page.
https://electowiki.org/wiki/Score_voting

A common tactic of the rank voting supporters is to say that cardinal system are not used anywhere.

@cfrank said in Quadratic Voting:

Social choice theory is a subfield of economics, Kenneth Arrow was an economist.

It is a specialized field. Thomas Hare was a political scientist. I am a physicist. Warren Smith is a com Sci person. It is its own field.

I would like to hear more about what you have said in the past about why this system is not at all reasonable.

There was a discussion I started about Quadratic voting on the now decommissioned CES forum a few years ago. It is now archived on the here
https://www.votingtheory.org/archive/posts?where={"topic_id"%3A541}

I'm not sure what is so terrible about it, especially in a multi-winner context.

It has vote splitting and gives low PR. It is not "terrible" but it is not worth considering given that you have simpler systems which do not have vote splitting and give high PR.

Hi @marylander,

In a chat with @Andy-Dienes the other day we came up with a new idea which is somewhat like what sequentially Shrinking Quotas does. There are are least two ways to implement it but the way I like best is as follows:

• It is the same as SSS except if there is a shortfall in reaching a quota to spend

• In that case you ADD some amount of "Ballot Weight" such that the "weighted Ballot" when summed for the winner is exactly a quota

It is doing the same thing as SSQ except that instead of changing the quota size to achieve the goal it it changes every bodies amount of ballot to spend. This gives voting power to those who will elect a candidate in subsequent steps but also to those who are already exhausted. Voters can come back from exhaustion. It gives the same result as SSS in most cases. I can give code if you would like.

I think it is actually doing what the true intent of SSS is better than SSS. That intent is to elect a utilitarian winner then adjust every bodies ballot weight "fairly". I tried to formalized "Fairly" with the concept of Vote Unitarity but I think I originally missed something. I think it is important to only subtract away the amount of influence they used to elect the winner. In the case of surplus the amount is reduced proportionally to that influence. In the case of shortfall I had thought it was fair to just take it all since that was the amount and no other group was going to put up that much for another candidate. However, This short-changes the prior winner and people with overlapping preferences. Since in the case of a shortfall I am effectively giving them ballot weight I need to give that amount to others.

Do you have thoughts on this idea? I can add code of you want.

@Marylander Modern cardinal multiwinner methods. I do not think he has ever looked into even the older ones like RRV. Otherwise why does he never mention them?

Here is another good article

https://psephomancy.medium.com/a-majority-of-voters-1d990a53b089

@Jack-Waugh The word strategy appears several times on that page. I do not now exactly how he coded the different strategies but I figure that could help you on your way to doing research.

I am unaware of any property called "the balance condition" and electowiki does not have such a page. Do you intend to refer to The Test of Balance given here. If so I think what you are saying is that in Nash equilibrium two systems which pass this criteria should behave such that the strategy of different factions cancel each other out and they both produce the same winner. The flaw in that logic is the assumption of an underlying symmetry in the size of groups and how that interacts with compromise/utilitarian or majoritarian winners. As I said above, STAR is majoritarian and Score is Utilitarian. In the absence of strategy these systems will give different winners. So even if all the strategy cancelled you would not expect the same winners.

@frenzed If the goal is exact PR then why even have a threshold. I thought we did not want exact PR.

But more on topic I think you are making 2 assumptions you do not know you are making. You assume at all existing parties are independent and uncorrelated. More mathematically, the assumption is that the parties form an orthogonal basis for a political space. This is quite clearly false and I hope I do not need to explain why.

Secondly, by having all of a voters endorsement put towards one party you are preventing exact PR. In fact I would think that in general this effect is larger than the effect you are brining up here. To do this properly you would need to know the vector representation of each voter in the space defined by the parties. Having that you could calculated exact PR.

@marylander said in Proportionality Guarantees of Allocated Score (approvals):

That would be useful. How do you decide whom to give weight back to? Is it even across the ballots?

I sent you an email. Let me know if you don't get it.

Hi @marylander,

In a chat with @Andy-Dienes the other day we came up with a new idea which is somewhat like what sequentially Shrinking Quotas does. There are are least two ways to implement it but the way I like best is as follows:

• It is the same as SSS except if there is a shortfall in reaching a quota to spend

• In that case you ADD some amount of "Ballot Weight" such that the "weighted Ballot" when summed for the winner is exactly a quota

It is doing the same thing as SSQ except that instead of changing the quota size to achieve the goal it it changes every bodies amount of ballot to spend. This gives voting power to those who will elect a candidate in subsequent steps but also to those who are already exhausted. Voters can come back from exhaustion. It gives the same result as SSS in most cases. I can give code if you would like.

I think it is actually doing what the true intent of SSS is better than SSS. That intent is to elect a utilitarian winner then adjust every bodies ballot weight "fairly". I tried to formalized "Fairly" with the concept of Vote Unitarity but I think I originally missed something. I think it is important to only subtract away the amount of influence they used to elect the winner. In the case of surplus the amount is reduced proportionally to that influence. In the case of shortfall I had thought it was fair to just take it all since that was the amount and no other group was going to put up that much for another candidate. However, This short-changes the prior winner and people with overlapping preferences. Since in the case of a shortfall I am effectively giving them ballot weight I need to give that amount to others.

Do you have thoughts on this idea? I can add code of you want.

I believe an earlier iteration of AS did this same thing, but it led to a monotonicity failure, so that failure was resolved by sorting voters by weighted score.

Correct but not a monotonicity failure on the score. It was more like a vote management vulnerability.

I did notice general patterns like throwing out a lot of score information during the reweighting did not affect quality much and made the rules much more robust to different preference distributions, including ad-hoc strategic ones.

This also implies you get the same results between two situations when there is a nuanced difference in preference. I think this is a tradeoff which would be hard to distinguish between.

To me, one of these score PR variants > STV, but nonetheless STV >>> single winner.

Single winner STAR is better if you care more about local representation than PR. In places like Canada with large sparsely populated areas you could end up with 5 member districts the size of Europe.

While I can prove a proportionality degree of (ℓ - 1)/2 for EPA, the proof relies on equal payments and I do not know how to get the result for AS

But AS could perform the same? Based on the similarity I would expect it to perform similarly.

Qualitatively, it just seems more fair that voters approving the same winner should all pay the same. This is corroborated by the many nice theoretical properties of MES.

They only differ when there is a surplus. In AS there is a threshold on score given. Above the threshold everybody pays the same (ie their whole ballot). Below the threshold everybody pays 0 even if they scored the winner. The people on the threshold pay an amount to match the quota. This does not seem unfair to me. The middle group pays some amount in the middle. In EPA the difference is that the above threshold group and the threshold group are treated the same, right? There can still be people who scored the winner who pay nothing, right? It does not seem clearly true that one method is more fair than the other as long as the distinction for how much somebody pays is based on their level of endorsement for the winner.

This is also one of the main reasons one might prefer either of EPA/AS over MES/SSS since the latter have an incentive at every point.

@Jameson-Quinn Made this point and it was ultimately why Equal Vote chose to endorse AS over SSS. This argument relies on the fact that a voter will actually be able to do such a calculation successfully. Or at least believe that they can. I am unconvinced. In fact I would argue the opposite. Since AS and EPA have major thresholds and somebody could allocated their whole ballot, they may be incentivised to put all their 1s and 2s to 0. In SSS you could only ever spend 2 on a 2 and 1 on a 1 so you are guarded from over spending. Voters will likely not behave rationally so much of it will come down to messaging anyway. Is it easier to explain to voters why they should vote sincerely in one system based on its mechanics. I would argue the mechanic in SSS does this but I am biased.

The above two intuitions are not just fantasy; I corroborated these experimentally across many preference profile distributions and strategy heuristics.

Can you give more detail? If you are saying that you have accurately simulated strategy then I am not going to believe you.

In fact, experiments were one of the main ways I landed on EPA before looking at theoretical guarantees. Empirically EPA returns better results than AS basically across the board on every metric besides total utility. In particular, the variance of utility tends to be significantly lower on instances where they disagree. While the axiom might be 'equal payments' for mostly qualitative reasons, the experiments suggest that this is a good axiom to take.

This work also included SSS and MES right? The simulations were based on my code from the "wolf Committee" right? Would you like to spend some time going through this on zoom?

variants of STV like Meek's (used in New Zealand) are really heinously complicated. Did you know it relies on iterating an optimization program until an arbitrary tolerance level is reached? Imagine if we could get away with that, I'd have a bunch more methods I'd like to suggest...

I think there needs to be a clean way to explain the system even if it is not 100% accurate to the final implementation. In campaigns, STV advocates rarely even mention surplus handling. To be acceptable a system needs to be able to be explained simply and the justification needs to be intuitive. I think MES could be acceptable if somebody came up with a good way to simply explain the selection mechanism.

Anyway, that's just to say if your main goal is to shift reform effort away from STV, I would not focus on elected outcomes because in my opinion the elected outcomes compared to other PR rules (preference profiles held equal) are fine.

The goal is not to move away from STV just because I hate STV. The goal is to offer a system which is monotonic, has a simple ballot to fill (ie not rank), can express level of endorsement (ie score) and gives something close to justified representation or sable winner sets. STV fails all these. I do not want to remove STV from its position as favourite PR system for any reason other than that it is subpar. I realize that in the majority of cases it does not matter but I think democracy is something where it really matters to be precise.

candidate strategy; right now it seems that parties just throw as many candidates on their list as possible in the hopes that a voter will like one of them and rank the whole list. In something like EPA/SSS/MES/AS, this will backfire for the voter (because they fail later-no-harm), so there will likely not be as much of a clone-positive incentive.

I do not understand this. Score systems are clone proof in the sense that your score for one candidate does not restrict the score for another. Are you saying that a party has incentive to put so many candidates that the candidates from another party are never reached when eliminating? This just points out another issue with STV. While it is technically non-partisan, in practice a bit of partisanship sneaks back in. Furthermore, the complexity of ranking incentivises people to "vote above the line" in Australia which reduces it to Party List. Only score systems allow independents to be free of parties. There are no modern examples of score systems but the theory is that they will lower partisanship via that mechanism.

the voter experience

Scoring is simple and faster than ranking.

STV is basically PR enough. I do not think that we will convince anybody to abandon it because it is not quite as PR as some of the score systems. STV is bad for other reasons. Some are listed above. If we can agree that STV is bad and there are systems which are better in all aspects then the problem becomes choosing between these other systems. This is the problem I am trying to solve. I believe the AS/EPA/SSS/MES area of models is the right one to look in. I do not think Thiele (RRV/SPAV) type systems are.

What Equal Vote did was to to rebrand AS as STAR PR. This way if a tweak like EPA turns out to be better then we can just pivot to that. This is sort of what is done with STV. It is not a single rule but a class of rules.

However, we still need to agree on a specific implementation and be able to justify it to the public.

I think it makes a lot of sense to restrict the space of these rules to those that have good theoretical guarantees on approval ballots, especially since it is a common heuristic that strategic voters will always min-max.

That makes sense to me

chaotic behavior exhibited by Allocated Score

Do you have some examples of this? I have not seen that work.

Not to nitpick, but the utility expressed definitely affects the reweighting! Just, it is converted to a binary value “is above the threshold.” Also note that due to the way skipped ratings are handled, it’s not quite the same as just treating the ballot like a ranked one.

OK, point taken but the point still holds. A lot of the information expressed on the ballot it obscured. I like the MES and SSS handling of score much better.

I agree that this is undesirable, but in the same sense that Perfect Representation is not always achievable, neither is it possible to only exhaust voters for their favourites. The alternative is to sometimes have broad swaths of voter budget go unspent; this is the approach that SSS takes—which has some benefits, most notably that of a more proportional distribution of welfare—but in my view it has also drawbacks in that voters will not pay equal amounts for their winners (aka less proportional distribution of influence),

This is sort of the trade off I was talking about. I am trying to think more in terms of public outreach and referendums. If the choice of "unspent budget" vs "Spend more than you score" translates to welfare proportionality vs influence proportionality that is worth highlighting. The public will only have an opinion on the first tradeoff because the second is too technical.

In the end the goal is to move the reform effort away from STV to a better system. I think any of Allocated Score, EPA, SSS or MES would be preferable to STV but it can be the case that too many options is a problem. If we knew what axioms the public really cared about we could try to come up with a proposal which we could all agree on.

There are many slight variants of Allocated Score. It is very hard for me to know which I like best unless there is a axiom I like which constrains the options to one. So what is the choice being made which turns Allocated score into EPA/

@andy-dienes Right so it is same per voter. When designing SSS I made a specific choice to make it same per score. The 1/2 a quota who scores X a 5 is getting more out of their winning than those who scored a 4 or a 3. It seems unfair to charge them the same amount of weight.

All these tradeoffs seem to be something you are getting your head around very well. Are you taking detailed notes?

The ecosystem of tradeoffs between AS, EPA, SSS and MES is very nuanced. When I talked to Piotr about this he fell back on the fact that MES satisfied Full justified representation. However, he fully admitted that MES and FJR are defined as a pair. One could define a different form of Justified representation such that MES fails and SSS passes based on this choice.

The reason I bring this up is that your EPA system is making a similar assumption to MES. Specifically MES is designed such that somebody who endorses a winner with a score of 1 can spend their whole ballot. My intuition is that this is unfair. Your system, makes as similar assumption but it is even less tied to the score than MES. MES applies their multiplier to the score but yours completely erases all the score data. That is sort of like Allocated Score that takes all people above a threshold. I think the utility expressed by the voter is needs to be accounted for in the reweighting.

To be more scientific and systematic what we should do is document each assumption and follow it to its logical conclusion. That way if the public said we feel that A, B and C are the assumptions we want then we could say which system fits that. Of course some assumptions exclude others so they cannot choose freely but I hope you get my meaning.

I would like to know what assumptions about fairness are being made which lead to MES, EPA and SSS. I tried to document this for SSS in the concept of vote unitarity. I think you are adding a lot with the proofs you are doing because they are more rigorous mathematically. Please tell me you are keeping good notes.

@andy-dienes said in Proportionality Guarantees of Allocated Score (approvals):

2. spending equally from that set of voters.

I do not find this last part specific enough. Say voter A and B support the winner with a score of 1 and 2 respectively. Will A spend half of what B spent on the winner or will they both spend the same. ie spend equally per voter or equally per score?

@andy-dienes I think that it would be best to not refer to this method as a variant of allocated score. Allocated Score is an allocation method by definition as it allocates whole ballots. Your new method does not do that.

This seems closer to MES than AS anyway. What is the difference to MES?

Is there a score variant?

@jack-waugh This appears to be the Venetian system
https://www.rangevoting.org/VenHist.html

I would make the same suggestion. Add this example to the score voting page.
https://electowiki.org/wiki/Score_voting

A common tactic of the rank voting supporters is to say that cardinal system are not used anywhere.

@jack-waugh If you have a citation could you add it to the list here https://electowiki.org/wiki/Approval_voting#Usage