@cfrank said in Ordinal Score Voting, Weighted Variation:

I do think that those things tend to be correlated in voting systems, and that tendency I am referring to as the “rigid/loose” spectrum of voting systems. Do you agree? Does that make sense?

I'm not seeing where rigid and loose come in. What makes a system rigid or loose? Are you saying that Cardinal vs Ordinal ballots is the difference? Otherwise I'm not sure how those terms apply.

Or are you speaking of things that aren't game theoretically stable (i.e. hall of mirrors) as being loose?

You also use the terms elastic and flexible, which I don't know what you are referring to. And you continue to use the term consensuality and distinguish it from utilitarian, but again, it is not clearly defined.

@jack-waugh said in Terms for Specific Voting Systems:

I suspect that many self-described "conservatives" would expect that any proposal to change the voting system comes from "liberals" looking for a way to win elections unfairly at the expense of "conservatives".

I think you are right, and therefore is something we should be especially careful about. We shouldn't ever appear to take sides here. Example: when I got frustrated with this community's slow progress (and seemingly conflicting agendas), I posted a bunch of photos of violence on January 6th, showing what happens when people are so polarized that many of them can't accept an outcome they don't like.

But to be clear: I am not blaming this on the right. (well, not here, in this forum) I am blaming it on choose-one voting. If someone looks at those 1/6 photos and sees a bunch of patriots fighting for a noble cause.... fine. They can also be angry at choose-one voting.

So it is a bit of a vicious cycle here. Broken voting causes polarization, polarization prevents us from fixing voting.

@andy-dienes in this example there are more scores than there are candidates. The same problems remains though when there are only three scores for three candidates, and I can see why this is a significant issue. With the method I described, no matter what the majority does with strict rankings, the middle candidate will win, even if the ballots are

A>B>C [99%]
C>B>A [1%]

Which is absurd. And without strict rankings, the majority can guarantee their top candidate’s victory by bullet voting anyway. I don’t like it but it is what it is. I think you’ve convinced me.

@toby-pereira said in Entropy-Statistic-Weighted Approval Voting:

While I don't think it would be a good method in practice

The 2 most popular voting systems in practice are IRV and plurality. Anything is a good method in practice 😄

@marylander Your criticisms are definitely fair and especially I hadn’t considered the midrange score devaluation problem, but I also agree that the calibration of the distributions is probably not an example that would reflect actual use. A winning candidate in this system probably needs to effectively pass thresholds of support of various kinds.

Also, any distribution or class of distributions could be selected as the prior, and more sophisticated methods could be implemented to update the distributions such as Bayesian statistics. It could be that a fixed distribution is chosen, I think the order statistics of uniform variables is not a terrible idea as the initial. But anyway it’s also all somewhat arbitrary, choosing a distribution is the same kind of problem as choosing cardinal score values. Furthermore with relevant updating the midrange support candidate will inform and reinforce the potential for compromise in future elections.

The irrelevant ballot problem can be fixed by simply ignoring or disallowing any ballots where the same score is given to all candidates, or more strictly any ballot that does not make use of both the minimal and maximal scores. I am not sure why right-skewed distributions would be problematic, in fact that is part of the functionality of the system.

A pair of concepts that might have use when we think about cast ballots is "ballot token" and "ballot type". A ballot token then would be an individual ballot and a ballot type would be the equivalence class of all the ballots that say the same thing.

@jack-waugh said in Making Voters Equal in Power:

In principle, this is an infinite recursion.

And hence, "hall of mirrors."

In practice, my iterative vote simulator stops when the ordering of candidates doesn't change between two rounds. Since the ordering is all the "vote caster" algorithm looks at, there is no point continuing because it will always get the same result.

But keep in mind, that doesn't mean it has reached the one and only equilibrium. There can be multiple equilibria.

But again, I'd rather have a method that doesn't encourage this sort of thing. If I did a vote simulator for Condorcet, there would be very little, if any, iterating, since there isn't an obvious way to adjust your ballot even if you know how others will vote.

Meeting scheduled!:
https://www.votingtheory.org/forum/topic/357/attn-forum-council-meeting-scheduled

@cfrank, I don't know how to calculate a probability distribution over a collection of rankings. Maybe someone who knows statistics can understand your proposal and maybe critique it.

In regard to "tragedy", I judge that too broad a word, as it includes accidents, and "past", not fully accurate, because, among other reasons, Mr. Biden is killing children by the minute with US resources.

I ask you to join me in mourning the death of Layan Mohammed Sayed Al-Aker, who was two years old, a girl.

I ask you to join me in spending a minute and a few tears on Samir Mahmoud Hassan Abu Al-Hawa, who was a man, aged 62.

I received the suggestion to "hold space" from an organization, the "US Campaign for Palestinian Rights". Is this organization a grift? Yes, to an extent, they probably are, as indicated by the fact that they have an "executive director", which usually means a person drawing pay out of donations. Nevertheless, I judge the message of this organization more honest than the official story, which "happy Thanksgiving" ties into. This organization suggests for things-taking day, among other practices (which I admit to not having followed):

When you gather with your loved ones, hold space for mourning the mass killing of Indigenous people from Turtle Island to Palestine. Hold a mourning ritual based in your community’s traditions. You may read the names and stories of our beloved people killed by colonial violence (for example, see here).

So I'm endorsing this organization's request, the one that I repeated above, in the context of your having wished me a happy Thanksgiving at this fraught time.

@toby-pereira said in Variable house sizes:

Methods that guarantee core stability are of interest to me (see this thread, which I linked to earlier) even if it's not my priority. From what I've read, I think it's still unproven that it's guaranteed that the core is non-empty. But if you use a stability measure (as suggested in the thread) rather than an all-or-nothing, it could be workable regardless.

BTW, we should probably distinguish different-sized cores—the possibility of an empty Hare core is unknown, but Droop cores can definitely be empty (as the Condorcet paradox proves). What I'm interested in is satisfying the Hare core with high probability and satisfying the anti-Droop core guarantee with certainty; i.e. the share of voters who would prefer some other committee is less than 1 / (seats - 1).

@chocopi said in New voting method: Linear medians:

As part of an experiment to see if it's possible for the Democrats to hate someone more than Trump, or just to set a Guinness World Record for biggest political career implosion?

I didn't say it would be a good idea. As I mentioned, he'd have no hope, since voters are using the primary to settle on an equilibrium. The question is whether Democrats have a gun to their head that would keep them from voting for Buttigieg's third-party, even if Biden looked hopeless.

@chocopi said in New voting method: Linear medians:

I agree more with you that these edge cases can plausibly be disregarded. The very idea of anyone executing a pushover strategy is absurd--you would need exact polling, exact coordination, no counter-strategy, and face a worst-case backfire if you get any of that wrong.

I don't think voters supporting a pushover is where this really falls apart. The problem with Tideman's framework is the strategies he finds are often:

Individually unstable, and therefore couldn't occur with strategic voters. You need voters to do things like betray a favorite, even though that favorite has a good shot at winning. Sometimes they're impossible to pull off with imperfect coordination (improper equilibria, i.e. trembling-hands rule them out). Prosocial or neutral—FPP has lots of opportunities for strategy, which is a good thing, because without strategy it turns into a random lottery. Easily countered by basic defensive strategy.

Every voting system has strategy. The real concern is whether voters playing their optimal strategy creates a bad result, e.g. a turkey winning. After all, in Borda, the Strong Nash equilibrium is still the Condorcet winner, but that doesn't happen in real elections. The reason Borda is bad is because the only proper equilibrium ends up selecting a winner at random.

In Benham's method, optimal strategy looks like a center-squeeze, because whenever you have a center-squeeze setup, the largest faction can bury the Condorcet winner and elect a candidate on the wings. (That's especially true if the wings tend to be overconfident.) By contrast, in cardinal methods, the optimal strategy looks like, well, the Condorcet winner being elected.

I'd like to clarify that I think party strategy does play a huge role in FPP, IRV, or Condorcet elections, because strategy is either too complex for typical voters or there are many equilibria (and voters have to coordinate on just one). In these specific situations, voters have to follow instructions on voting cards issued by their party. In approval or score, any idiot with a pulse can work out that your best strategy is to give as many points as possible to the best frontrunner.

@chocopi said in New voting method: Linear medians:

Baldwin's is a ying-yang similarity, a method that is practically only impacted by said esoteric NP-hard strategies. (Simple compromise-burial does almost nothing.) These non-trivial Baldwin strategies are the hardest to calculate of any method, even with perfect [everything]. I think it's a fair and interesting academic question to quantify these, but I'd also raise an eyebrow (or two) at anyone listing them as a point against Baldwin's.

This is a good example of why "NP-hard"ness results are not very useful in practice. What matters is what happens if voters execute their ideal strategy. For Baldwin's method, the strategy is an absolute disaster, just like for Borda: it ends in a turkey winning with high probability.

In practice, elections have 2-5 viable candidates, so even "NP-hard" manipulation is trivial in practice. If you have just 2 candidates and a turkey, Baldwin is Borda-with-runoff, with a simple strategy: bury the leader to make sure they can't make it out of the first round. Does this have a shot of backfiring? Yes. (It has a good shot of picking a turkey, in fact.) But at its core, it's still Borda, and has the same result.

@toby-pereira said in General stuff about approval/cardinal PR:

This project hasn't purely been altruistic - it's been helpful to me by laying everything out for reworking my COWPEA paper!

And the new version can be seen here (as I mentioned in the separate COWPEA thread anyway).

@rob I am now formatting the dates that are associated to the posts.

Topics used to show all the details, including creation date. I no longer show any details for them, just the title of the topic.

I believe there were no other contexts in which dates showed up, just those two.

Of course, post headers themselves show up in three contexts: posts for a topic, a single post, and search results.

@rob no need to feel sorry about my perceptions. I agree that there is not much point in discussing this further with you, much as there is no purpose in asking a question to which you have already decided the answer. The “basic things” we don’t agree on are not basic at all.

I literally explained that those curves represent the distribution of P values attained by each score from past elections, and I explicitly stated that I was NOT calling anybody an imbecile. I have put more than enough effort into explaining the concept clearly and precisely. It is not my fault that certain people apparently concerned with quantity-based systems have not sufficiently developed their education in mathematics…

Guess who were mathematicians:

Condorcet, Arrow, Dodgson, Borda, Black, Copeland, Kemeny, Smith, and Tideman, all giants in Voting Theory.

If you look on the following list, I don’t think you will find a single person not well versed in probability theory:

https://en.m.wikipedia.org/wiki/Category:Voting_theorists

What you are complaining about is absurd. Consider this statement:

“A candidate is called (S,P)-consensual if at least a P-fraction of the electorate scored that candidate at least an S.”

How on Earth could that be made any clearer?

What about this?:

“A candidate’s SP-fitness score is given by the expected value of the number of nodes on that candidate’s profile that will poke out of a randomly-generated candidate profile.”

How would you go about describing that with a glass of water?

If you have a simpler way of explaining the system, be my guest! But it’s very rare that a new idea comes neatly packaged up with a bow, and frankly it’s an absurd requirement to expect, let alone to demand, from anyone.

Directly contrary to your claim, I have definitely suggested a very clear alternative system to “majority rules,” which I believe we had discussed in some detail on the previous forum (perhaps not) and that I alluded to. You seemed to comprehend the concept now, but it seems to be that you’ve also painted over it with unwarranted disdain. It’s quite rude to presume that somebody does not have well-defined justification for their claims or beliefs, and when it is not true such as presently, it is also inefficient and counterproductive.

The reason for making the candidates anonymous except for their score distributions is to eliminate bias among the electorate, and for the electorate to select a candidate who gives a good distribution for the whole rather than having only selfish concern for their own vote. It might be even better to have an impartial human arbiter make the decision, who is also elected and has the responsibility of and incentive to choose a candidate based only on their score profiles. I would propose the opposite question: Why leave it up to a mindless mechanical system when it is totally unnecessary?

But I really don’t see this discussion going anywhere, it feels like pulling teeth.

@cfrank regarding Condorcet methods, some professors I've been in contact with did a series of three works on the methods "Split Cycle" and "Stable Voting" you may like to read.

https://arxiv.org/abs/2004.02350
https://arxiv.org/abs/2008.08451
https://arxiv.org/abs/2108.00542

Regarding multiwinner rules with ranked ballots there is a nice analysis here

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7089675/

One of the main takeaways of that one is that choose-one is actually not too bad when there are multiple winners (although as we know, it is quite bad for a single-winner election).

@jack-waugh I could also see bringing all "viable" candidates to the run off. Viable would be based on total score relative to max to talk score

Red: 10% vote A:5, B:0, C:0, D:1
Yellow: 30% vote A:0, B:5, C:1, D:0
Blue: 30% vote A:0, B:1, C:5, D:0
Green: 30% vote A:0, B:0, C:0, D:5

With regular STLR you would take B and C into the run off and there would be no adjustment to scores

In a version of STLR were you take three into the run off because B,C and D are all "viable". You eliminate A and adjust scores to

Red: 10% vote B:0, C:0, D:5
Yellow: 30% vote B:5, C:1, D:0
Blue: 30% vote B:1, C:5, D:0
Green: 30% vote B:0, C:0, D:5

In this case then D wins.

So basically you want to include all viable candidates in the run off.

@sass Ok well I don't know what you mean by "competitive elections." The elections RCV-Hare have been used in seem quite competitive. I have often used the 2018 San Francisco mayor election as a good example of a competitive election that RCV-Hare did a great job with. irvmayor.png

But you said "3+ competitive factions," which I'm not sure what you mean by that. What qualifies as a faction? In the election above, Mark Leno and Jane Kim campaigned together, and were often "co-endorsed" by newspapers and organizations. To me, that's the sort of thing that should happen. I don't know whether you consider Leno and Kim as a single faction or two factions, or really what you mean. Could you give us a definition of "competitive" or "competitive factions"? For instance, does "competitive" mean "highly polarized, with significant portions of the electorate utterly hating at least one front runner"? Or simply "very close"?
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Hi all,
Sorry for the delay, but this thread was recently brought up again as an example so I'd like to post a comment addressing the Code of Conduct issues raised.

Making the forum welcoming for new (and old) people is important. To that aim, we do have a code of conduct that can be helpful.

It includes this: "Please make an effort to stay on topic and to not waste people's time. Keep in mind that this is a volunteer-driven project, and that time contributed by participants and moderators is appreciated and valued. Try to keep all discussions relevant to voting theory and reform efforts. Avoid sweeping generalizations or assumptions."

I am posting to indicate that I have not abandoned the simulation project; I am gradually trying to progress it. I don't expect a response unless you think I have left something important out or am painting myself into a corner with the design choices I am laying out.

I asked myself: What are we going to read from the file directories and how will what we read figure in during prompting and execution?

At the indicative level, a voting system declares what form of ballot it requires.

Tactics, at the indicative level, will be able to answer given a ballot form, are they capable of generating ballots conforming thereto.

So, when the user selects a voting system, the app will offer the tactics that can produce ballots for that system.

Since tactics will have an indicative level and an executive level, they must comprise at least two files, so it makes sense to use a directory for each tactic.

So there will be one directory containing the subdirectories for the voting systems and one directory containing the subdirectories for the tactics. There is no need for the hierarchy of directories to reflect any kind of categorization of either. So, for example, there will not be a directory of ranking voting systems nor a directory of rating voting systems nor a directory of Condorcet-compliant voting systems, etc.

Example declarations of ballot types:

{ [0]: 'rating', finite: false, /* Continuous -- allows floating-point ratings. */ min: 0, max: 1, } { [0]: 'rating', finite: true, range: [0, 1, 2, 3, 4, 5], /* like STAR */ } { [0]: 'ranking', equal_ranking_allowed: true, }

Here's Approval:

{ [0]: 'rating', finite: true, range: [0, 1], /* Approval */ }

@michaelossipoff said in Ranked Robin Disadvantages -:

River adds a clause to RP, & loses the autodeterence of wv RP & MinMax.

Could you explain more? How does it lose autodeterrence? I was under the impression that River(wv) was effectively minmax with fewer spoilers.