I've just been looking through old threads and found this one.

@nevinbr said in Least-bad Single-winner Ranking Method?:

Objectively, the answer is Game Theory Voting. However, it is basically impossible to explain to, well, anyone.

This method was also discussed at greater length on the old CES Google Group here. But the point is that while it is optimal in the sense that you might want to optimise this one particular thing, you might not want to optimise that one particular thing, so it would be wrong to say that it's objectively the best method.

In fact, when you look at what it is trying to achieve, it becomes quite clear that it's really just a bit of game theory fun rather than a method seriously trying to optimise something that a human would want to optimise. And you can see that by an example that you gave in the CES thread.

To expand on that last point, consider the following election with 3 candidates and 100 voters:

49 ABC

48 CAB

3 BCA

This has a Condorcet cycle:

A beats B by 94

B beats C by 4

C beats A by 2

At first glance, we notice that A has the largest victory and the smallest defeat, as well as the highest Borda total. However, the GT method elects A just 4% of the time.

Can that really be optimal?

Let’s think about it.

Okay, B gets crushed by A and barely squeaks by C. We don’t want to get crushed because that is bad for our long-term average, so B probably should not win. And if B loses (or didn’t run at all) then C defeats A.

It seems that A’s victory over B is mostly ephemeral. As much as we would like to score that +94 to improve our long-term average, the only way it happens is if we pick A and the system we’re up against picks B. But since B shouldn’t win, we expect the other system won’t pick B either.

In particular, if we usually pick A and the other system usually picks C, then we are going to lose frequently. We would rather be that other system and pick C most often, which is exactly what GT does. The optimal distribution is:

A wins 4%

B wins 2%

C wins 94%

Moreover, in any 3-way Condorcet cycle, the probability of each candidate winning is always proportional to the margin of victory between the other two candidates. And this is provably optimal.

In the example ballots, it seems clear that A is the best winner. However, under this method, because B definitely isn't a good winner, other methods won't select B so the A>B pairwise win might as well be ignored. Better concentrate on A v C instead and since C wins that, C is the overall best pick.

So what this method does is not pick the candidate that is somehow judged to be best for society, but the candidate that has the best average margin of victory against a candidate picked by another method playing this same game. And this method would never lose on average against another method (though obviously might tie - e.g. against itself). I don't see how this optimality relates to real life at all and why it would be good for us to adopt it.

To make this clear, the ranked pairs method is a Condorcet method that a lot of people like. But I could devise a method that elects a candidate that pairwise beats the ranked pairs winner whenever one exists. Otherwise elect the ranked pairs winner. According the metric used here, this method is better than ranked pairs - when these two methods are viewed as the only choices at least. But is this method better tban ranked pairs by any reasonable measure? Of course not.

An interesting academic exercise, but nothing more. Certainly not objectively the best single-winner voting method.

@jack-waugh You can also draw parallels to referendums or judge elections where you can vote for or against each item, or abstain.

@brozai right there can be, but there isn't always. When there isn't a single Condorcet winner or Copeland winner, as often as not there are three that are tied.

And me. No CPU, No Photocell, that's what I wanted to post about.

@brozai Received!

Reminder -- these happen every Tuesday.

@andy-dienes Thanks this is good, I like your groupings. I'd also like to hold votes that are more specific, such as "for a condorcet method, what is your preferred tiebreaker approach?" With possible answers combining ballot type (ranked, ranked allowing duplicates, rated 0-100, rated 0-5) and tiebreak tabulation method (irv, plurality, borda, score)

I don't want to do anything that requires a different log in or cookie or whatever, I'd like to know where the votes are coming from, and discourage people from voting more than once or voting if they don't even introduce themselves or participate in the community otherwise. So I'd prefer just collect the ballots manually for now, from posts and signatures here, and maybe posts on reddit's EndFPTP forum. There's also the election methods mailing list....

Remember that we can do a new one at any time, and anyone in the group can post one. I'll happily tabulate them and show pretty results and share my work on a forkable codepen , at least to get people started. Anyone is free to retabulate.

I was hoping to collect high-resolution cardinal ballots. I'd suggest rate on a scale of 0-10, decimal places allowed e.g. 5.76. If anyone wants to use a different scale, such as 0 to a million, fine, whatever...it will just be normalized anyway. And then we'll show results in a bunch of different methods. People can supply an approval threshold, if none supplied it defaults to 5. So mine might look like:

Copeland/IRV [10], Ranked Robin[9.5], Any Condorcet [9], Copeland/Normalized Score [8.7], Copeland/Score [8.5], Cardinal Baldwin [8], IRV [6], STAR [5], Approval [3], Score [2], Borda[1], FPTP [0] ApprovalThreshold: 4

(that's using what is in my signature, but some of the groupings don't make sense for a real poll, especially "any condorcet")

I'll show some ideas for the pretty results display (hopefully with some interactivity or ability to animate or whatnot) soon. You may have seen some of my work in this direction....here's a some of it: (the Sankey diagram for IRV in the upper left isn't mine but it is uses an open source library to generate them)screenvoting.png

@rob said in An idea to increase activity at this forum:

That said, in the perfect world, yes there would be a nice voting widget.

I'm gradually working toward that. I have experimented with running custom js in this forum and looking for things in posts that I can parse and replace and add interactivity. . (@Jack-Waugh has been trusting enough to allow me privileges so I can do that.... but currently nothing is running) Automatic server-side tabulation and external storage of poll data would come later if people stay interested. It's doable, but not needed to get it started.

Do you know javascript or typescript? 🙂

@rob yup, both those statements are correct!

@rob said in project to make ballot data available:

those who do know how to code can tailor them so non-coders can just paste ballots in

OK. So that's basically collaboration where coders empower non-coders to participate in the research.

Spreadsheets don't have the ability to build on the work of others

Agreed. The don't compose at all. Every spreadsheet is an idiosyncratic work.

@Toby-Pereira I tried to fix this problem, and came up with some formulas to define the quota compliance multiplier using entropy. It’s kind of complicated, but it’s well-defined, and it encourages diverse compromises between parties. It probably now gives more bargaining power to larger parties, and “puppeteering” can still be strategic, but I think those things are in direct conflict unfortunately.

This is a markdown file that defines the formula.

# Proposed Compliance Multiplier Formula This document presents a proposed formula for the compliance multiplier in the proposed system, which compares the observed distribution of ambassador seats with the ideal distribution based solely on voter shares. ## 1. Partition Functions The ideal partition function for a given party \(X\) is defined as: [ Z_P(X) = P(X \sim X) + \sum_{i \neq X} P(X \sim i) + \sum_{j \neq X} P(j \sim X) ] The observed partition function is defined as: [ Z_Q(X) = P(X \sim X) + \sum_{i \neq X} Q(X \sim i) + \sum_{j \neq X} Q(j \sim X) ] *Note: For party consistency, we impose that \(Q(X \sim X) = P(X \sim X)\) for every party \(X\).* ## 2. Entropy–like Quantities The ideal (maximum) entropy is given by: [ E_P(X) = \frac{-P(X \sim X)\ln P(X \sim X) - \sum_{i \neq X} P(X \sim i)\ln P(X \sim i) - \sum_{j \neq X} P(j \sim X)\ln P(j \sim X)}{Z_P(X)} + \ln Z_P(X) ] The observed entropy is given by: [ E_Q(X) = \frac{-P(X \sim X)\ln P(X \sim X) - \sum_{i \neq X} Q(X \sim i)\ln Q(X \sim i) - \sum_{j \neq X} Q(j \sim X)\ln Q(j \sim X)}{Z_Q(X)} + \ln Z_Q(X) ] ## 3. Compliance Multiplier The compliance multiplier for party \(X\) is then defined as: [ \text{Multiplier}(X) = \frac{E_Q(X)}{E_P(X)} ] Since for every off-diagonal entry we have \(Q(X \sim Y) \leq P(X \sim Y)\) (with equality on the diagonal), the normalized observed entropy \(E_Q(X)\) is less than or equal to the ideal entropy \(E_P(X)\). Therefore, it follows that: [ \text{Multiplier}(X) \leq 1. ] This guarantees that a party's compliance multiplier never exceeds 1, reflecting that the observed (normalized) diversity of ambassador nominations cannot surpass the ideal (maximally spread) distribution.

And here are some examples

# Four-Party Examples of Compliance Multipliers This document presents computed examples for a 4-party system under different scenarios. We consider four parties—A, B, C, and D—with the following voter shares: - **Party A:** 0.4 - **Party B:** 0.3 - **Party C:** 0.2 - **Party D:** 0.1 The ideal ambassador seat allocation is given by: [ P(X \sim Y)=P(X) \times P(Y) ] Thus, the **ideal matrix** \(P\) is: | From \(\backslash\) To | A | B | C | D | |------------------------|------|------|------|------| | **A** | 0.16 | 0.12 | 0.08 | 0.04 | | **B** | 0.12 | 0.09 | 0.06 | 0.03 | | **C** | 0.08 | 0.06 | 0.04 | 0.02 | | **D** | 0.04 | 0.03 | 0.02 | 0.01 | For each party \(X\), we define the **partition functions** as follows: - **Ideal:** [ Z_P(X)=P(X\sim X)+\sum_{Y\neq X}P(X\sim Y)+\sum_{Y\neq X}P(Y\sim X) ] - **Observed:** [ Z_Q(X)=P(X\sim X)+\sum_{Y\neq X}Q(X\sim Y)+\sum_{Y\neq X}Q(Y\sim X) ] with the assumption that for all parties, \(Q(X \sim X)=P(X \sim X)\). We then define the **entropy–like quantities**: [ E_P(X)=\frac{-\sum_Y P(X\sim Y)\ln P(X\sim Y)}{Z_P(X)}+\ln Z_P(X) ] [ E_Q(X)=\frac{-\sum_Y Q(X\sim Y)\ln Q(X\sim Y)}{Z_Q(X)}+\ln Z_Q(X) ] and the **compliance multiplier** is given by: [ \text{Multiplier}(X)=\frac{E_Q(X)}{E_P(X)}. ] Under the condition that for every off-diagonal entry \(Q(X\sim Y)\leq P(X\sim Y)\), the normalized observed entropy cannot exceed the ideal one—so \(\text{Multiplier}(X)\leq 1\). --- ## Scenario 1: Full Compliance **Situation:** Every party fills its ambassador seats exactly as in the ideal, so for all \(X, Y\): [ Q(X\sim Y)=P(X\sim Y). ] **Results:** - **Party A:** Multiplier = 1.000 - **Party B:** Multiplier = 1.000 - **Party C:** Multiplier = 1.000 - **Party D:** Multiplier = 1.000 --- ## Scenario 2: Sabotage by Party B Against Party A **Modification:** Party B refuses to elect any ambassadors from A. In our observed matrix, we set: [ Q(B\sim A)=0 \quad \text{(instead of the ideal }0.12\text{)}. ] All other entries remain ideal. ### Computed Values **For Party A:** - **Ideal Partition Function:** \(Z_P(A)=0.16+ (0.12+0.08+0.04)+(0.12+0.08+0.04)=0.16+0.24+0.24=0.64.\) - **Observed Partition Function:** - Row A remains: \(0.16+0.12+0.08+0.04=0.40.\) - Column A: Instead of \(0.12+0.08+0.04=0.24,\) we have \(0+0.08+0.04=0.12.\) So, \(Z_Q(A)=0.16+0.24+0.12=0.40.\) - **Entropy–like Quantities (Approximate):** - \(E_P(A) \approx 1.840.\) - \(E_Q(A) \approx 1.472.\) - **Compliance Multiplier:** [ \text{Multiplier}(A)\approx \frac{1.472}{1.840}\approx 0.800. ] **For Party B:** - **Ideal Partition Function:** \(Z_P(B)\approx 0.51.\) - **Observed Partition Function:** \(Z_Q(B)\approx 0.27.\) - **Entropy–like Quantities (Approximate):** - \(E_P(B) \approx 1.824.\) - \(E_Q(B) \approx 1.524.\) - **Compliance Multiplier:** [ \text{Multiplier}(B)\approx \frac{1.524}{1.824}\approx 0.834. ] **For Parties C and D:** No sabotage occurs, so: - **Multiplier(C) = 1.000.** - **Multiplier(D) = 1.000.** --- ## Scenario 3: Puppet Scenario – Party D as a Puppet for Party A **Modification:** Party D acts as a puppet for Party A to harm Party B. We set: [ Q(D\sim B)=0 \quad \text{(instead of the ideal }0.03\text{)}. ] All other entries remain ideal. ### Computed Values **For Party A:** - \(Z_Q(A)\) remains nearly ideal, so **Multiplier(A) \(\approx 1.000\).** **For Party B:** - Losing support from D reduces its observed diversity, so **Multiplier(B) \(\approx 0.910\).** **For Party C:** - Fully compliant, so **Multiplier(C) = 1.000.** **For Party D (the puppet):** - Due to its refusal to elect from B, its observed diversity is reduced: **Multiplier(D) \(\approx 0.940\).** ### Effective Representation for the A Coalition If effective main-platform representation is given by the product of voter share and multiplier, then: - **Party A:** \(0.4 \times 1.000 = 0.400.\) - **Party D:** \(0.1 \times 0.940 \approx 0.094.\) Thus, the total effective representation for the A coalition is: [ R(A \text{ coalition}) = 0.400 + 0.094 \approx 0.494. ] This is slightly less than the 0.5 (50%) of the vote they would control if D were fully compliant, reflecting the cost of splitting support. --- ## Summary of Computed Multipliers - **Scenario 1 (Full Compliance):** - A: 1.000 - B: 1.000 - C: 1.000 - D: 1.000 - **Scenario 2 (Sabotage by B Against A):** - A: ≈ 0.800 - B: ≈ 0.834 - C: 1.000 - D: 1.000 - **Scenario 3 (Puppet – D as Puppet for A):** - A: ≈ 1.000 - B: ≈ 0.910 - C: 1.000 - D: ≈ 0.940 --- ## Interpretation - **Full Compliance:** All parties achieve ideal diversity, so their compliance multipliers are 1. - **Sabotage:** When Party B refuses to elect ambassadors from Party A, both A and B see their normalized diversity reduced (multipliers drop to ≈0.800 and ≈0.834, respectively). - **Puppet Scenario:** Using Party D as a puppet to harm Party B, while A remains nearly ideal, both B and D are penalized—the puppet (D) suffers a lower multiplier (≈0.940) and B’s multiplier drops to about 0.910. Moreover, the A coalition's effective representation becomes slightly diluted (≈0.494 instead of 0.500). These examples illustrate that while parties might attempt sabotage or use puppets to undermine competitors, the system’s reliance on normalized diversity ensures that such strategies come at a cost to all parties involved.

I think with careful consideration, it might be possible to adjust the multiplier so that “puppeteering” actually harms a party in proportion to the harm it could cause to its largest rival. For example, maybe raising the multiplier to some power or passing it through some other function would disincentivize puppeteering more.

When a reform that people think will produce democracy fails to do so, that merits a notice.

Thanks to everyone who came to today's council meeting!

Cliff's Notes:

We had nine people total and three of the four council members present. We were able to get through everything on the agenda, and we added a number of new people to leadership positions! We also made some plans and set some good intentions going forward. This meeting followed the trend of our previous council meetings, and all discussions passed were unanimous (with some abstentions.) We had general consensus to simplify our categories list, but didn't have agreement on a specific proposal, so we decided to continue the discussion here on the forum and then vote when we're ready.

Here's to a great next era of the Voting Theory Forum!

To everyone who RSVPed, attended, volunteered, gave input, or stepped up to serve in a leadership position. Thank you!!!

@cfrank Good question. I'm not sure I can think of one place that gives a good intro to all the stuff. Anything I know I've picked up piecemeal over the years, and there isn't really that much about proportional cardinal methods in general I'd say. The stuff on the Electowiki could probably do with being massively overhauled.

Obviously the Thiele and Phragmén methods have been around for over a century but academic research into this type of method only really picked up again relatively recently, and dry academic papers aren't the best place for a beginner to learn about them anyway.

Edit - Maybe I could start a thread with some basic info. Others can add to it and can also take issue with anything they might disagree with!

@jack-waugh I agree soundly with you. There are many ultimately nihilistic profit seekers who are driving destructive tendencies of the global market, and that’s a full euphemism. It isn’t clear whether that nihilism is actually a value construct (well, it seems if anything to be quite rightly the opposite of one, really) or whether it’s due to a typical lack of awareness or contemplation. But a third alternative is also available, which is a simple (and in enough cases, severe) deficiency in moral character.

Another related topic I consider in this area is the attention economy. You allude essentially to addiction and what I don’t have vocabulary for beyond “post-modernist consumerism.” In my opinion, global attention is a public good that is now being subjected to the tragedy of the commons, and that is all resulting from a de-compartmentalization of access points to attention. It’s also another prisoner’s dilemma. Space and time no longer serve the functional roles of localizing attention to natural social public spheres and communities, and this only drives the lack of awareness and other issues related to mental health (I.e. attention starvation on a global scale, with concomitant depression, I.e. “influencers,” onlyfans, TikTok, etc.). More and more pornographization, commodification and exploitation of human life, even people exploiting themselves.

The only thing I can see that could possibly supplement those barriers is either an artificial enforcement of barriers (a frightening thought) or awareness and personal character. In other words, externally imposed barriers, or barriers of personal choice. Interesting times we live in. Anyway I’m glad at least that others can see this is all more than “just” a moralistic issue.

On a side note, while we’re at the water cooler, I will just mention that I watched a portion of the first Republican candidate debate. I will summarize my thoughts as, “Wow.”

@lime said in "Problematic" Ballot Exhaustion examples - RCV IRV:

Advertisement: a candidate is declared the winner and starts celebrating; then somebody comes up and explains they've found extra votes for the candidate, and the candidate suddenly loses. End with "Last year, Nick Begich lost the Alaska election because voting authorities thought he had too many votes. How could voting for someone make them lose? Don't let it happen here. Vote no on IRV."

New advertisement idea: circle of dictators at a table, bragging about how they took voting rights away from people and laughing. Suddenly, an Alaska politician stands up: "Oh, we did even better. Get this: if too many people vote for a candidate, that guy loses. Pretty great, huh?" Stunned silence. A man in uniform with a thick German accent: "that's too far." "Really?" "Ja, that's illegal in Germany."*

Voiceover: "When even the Germans are calling your system undemocratic, you have a problem. Vote no on IRV."

*Reference to BVerfG ruling on participation failures.

@toby-pereira

Yes, but the big winner, so far, in the burial-deterrence category, is RP(wv), which isn't a new-invention method, but, rather is a traditional, classical, immensely popular & high-prestige method.