@rob especially if the state is a swing state, making it more difficult for the large parties to secure voters for their platform I think would be a significant influence forcing large parties and their candidates to more scrutinizingly determine the real interests of voters in those states. It may dilute the interests of less competitive states, but since the competitive states are crucial to obtaining the presidency, the large parties will still have to invest strongly in the interests of voters in those states in order to compete with alternatives (and obviously each other) for the crucial swing points. This may lead to something like an arms race of concessions, which happened in New Zealand in 1996 and led to the national adoption of a PR system, according to Arend Lijphart. Obviously that's quite a leap for the U.S., but maybe a less extreme analogue is not so far-fetched.

Maine is one of the thirteen most competitive states for elections according to a 2016 analysis (Wikipedia: Swing state), so I’m not sure their recent establishment is actually strategically foolish, although it’s possible that it wasn’t fully thought through. I agree it isn't clear.

I think it will definitely be interesting to observe how the current political apparatus responds to Maine--and apparently, more recently, and strangely, Alaska:

https://news.yahoo.com/alaska-is-about-to-try-something-completely-new-in-the-fall-election-193615285.html

Since Alaska is far from competitive, I do think this transition was in fact foolish for the reasoning you stated, but it remains to be seen. If we saw a state like Florida transition to a system like Maine's, it would be very interesting to study the relative differences between federal treatments of Florida, Maine, and Alaska as a case study for how "swingy-ness" might influence the effect of such voting system transitions. If Maine experiences an increase in federal power, it would be a good case for the remaining swing states to make a similar transition. If that occurred, the swing states would become a platform foothold for alternative parties to grow.

@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.

This is a minor attempt to modify Condorcet methods in a simple way to become more responsive to broader consensus and supermajority power. It’s sort of like the reverse of STAR and may already be a system that I don’t know the name of. In my opinion, the majority criterion is not necessarily a good thing in itself, since it enables tyrannical majorities to force highly divisive candidates to win elections, which is why I’ve been trying pretty actively to find some way to escape it.

For the moment I will assume that a Condorcet winner exists in every relevant case, and otherwise defer the replacement to another system.

First, find the Condorcet winner, which will be called the “primary” Condorcet winner. Next, find the “secondary” Condorcet winner, which is the Condorcet winner from the same ballots where the primary Condorcet winner is removed everywhere.

Define the Borda difference from B to A on a ballot as the signed difference in their ranks. For example, the Borda difference from B to A on the ballot A>B>C>D is +1, and on C>B>D>A is -2.

If A and B are the primary and secondary Condorcet winners, respectively, then we tally all of the Borda differences from B to A. If the difference is positive (or above some threshold), then A wins, and if it is negative or zero (or not above the threshold), then B wins.

For example, consider the following election:

A>B>C>D [30%]
A>B>D>C [21%]
C>B>D>A [40%]
D>B>C>A [9%]

In this case, A is a highly divisive majoritarian candidate and is the primary Condorcet winner. B is easily seen to be the secondary Condorcet winner. The net Borda difference from B to A is

(0.3+0.21)-2(0.4+0.09)<0

Therefore B would be chosen as the winner in this case.

Some notes about this method:
It certainly does not satisfy the Condorcet criterion, nor does it satisfy the majority criterion. These are both necessarily sacrificed in an attempt to prevent highly divisive candidates from winning the election. It does reduce to majority rule in the case of two candidates, and it does satisfy the Condorcet loser criterion, as well as monotonicity and is clearly polynomial time. It can also be modified to use some other metric in the runoff based on the ballot-wise Borda differences.

Continuing with the above example, suppose that the divisive majority attempts to bury B, which is the top competitor to A.
This will change the ballots to something like

A>C>D>B [30%]
A>D>C>B [21%]
C>B>D>A [40%]
D>B>C>A [9%]

And if the described mechanism is used in this case, we will find instead that C is elected. So burial has backfired if B is "honestly" preferred over C by the divisive majority, and they would have been better off indicating their honest preference and electing B.

And again, suppose that the divisive majority decides to bury the top two competitors to A, namely B and C, below D, keeping the order of honest preference between them. We will find

A>D>B>C [30%]
A>D>B>C [21%]
C>B>D>A [40%]
D>B>C>A [9%]

In this case, the secondary Condorcet winner is D, and the mechanism will in fact elect D, again a worse outcome for the tactical voters.

Finally, suppose that they swap the order of honest preference and vote as

A>D>C>B [30%]
A>D>C>B [21%]
C>B>D>A [40%]
D>B>C>A [9%]

Still this elects D.

As a general description, this method will elect the Condorcet winner unless they are too divisive, in which case it will elect the secondary Condorcet winner, which will necessarily be less divisive. I believe that choosing the runoff to be between the primary and secondary Condorcet winners should maintain much of the stability of Condorcet methods, while the Borda runoff punishes burial and simultaneously addresses highly divisive candidates.

@rob thanks. And apologies for being snippy before. You and @Andy-Dienes pretty much convinced me that score voting isn’t going to work.

@toby-pereira I totally agree with you here. And a point to supplement or maybe just reiterate your stance on “benevolent dictators,” there’s a definite survivorship bias there. The business dictators who fail don’t show up in the news, while the ones who succeed are often lauded as geniuses without due regard for the role of pure luck or factors totally unrelated to their supposed acumen. The same goes for stock market investors—many who come out on top end up believing they have a special intuition to “outsmart” the market, but when compared with randomly generated portfolios, their inclinations usually fare no better, and often do worse (due to their relative lack of diversity, they are not as robust against market volatility).

So basically, when uncertainty is involved, failure doesn’t always indicate a poor strategy, not any more than success indicates a good one. This reduces my confidence that business dictatorships actually tend to promote the success of a company.

@rob Good Lord you’re absolutely right. The internet is a bad place to get information, I just saw it attributed to him and didn’t look into it further. I haven’t read much Dostoyevsky, I just thought the quote was potentially relevant in terms of being met with hostility for expressing new ideas that are potentially complicated. But you’re right that I need to find a way to simplify the presentation.

I am not saying people who don’t follow me are imbeciles, I’m not trying to win points. I just don’t understand why there seems to be a general culture here of competition and shooting down ideas instead of cooperation and trying to build them up. It seems like we would all be making a lot more progress working as a team.

Anyway, I’ve already indicated the problems I was trying to solve. Most are the same problems we’ve all been trying to solve:

(1) How to balance the conflict between majoritarianism and consensualism;
(2) How to address the problem of strategic voting;
(3) How to create a system that is simple and meaningful and encourages compromise.

The last one is a pet peeve of mine, which is that (4) the cardinal values assigned to scores are arbitrary. This is in fact what led me to create this system, and why it is called an “ordinal score” system.

I believe I have successfully addressed all of the above things, but the “simple” part I suppose is a point of contention. The concept is simple, but the mathematics makes it look more complicated than it actually is, because it deals with probability distributions. The latest version of the system is just as good as if not superior to STAR, and with minor modifications it can be made even better. I’m not sure what else to say about it to make it appear worth looking into.

If you do watch the video, please excuse my brain fart at the beginning, I made it after a long day. @Jack-Waugh at least did watch it. I’ll definitely take a look into your material.

Here is the link: https://app.vmaker.com/record/SGSydGYcwOW9Vf6d

This is a first draft, what I am currently proposing is an additional weighting modification that directly addresses point (1), and it simultaneously improves (2) and (3) as well. I had actually considered weighted (S,P)-voting systems before, but I didn’t see the utility until @Marylander pointed out that the system is still more majoritarian than desired. The new system is explicitly indifferent between majoritarian and consensual influences in exactly the manner I explained in the first post of this topic, I.e. if half of the electorate scores one candidate the top score, but the whole electorate scores a different candidate the lowest nonzero score, then the system is typically indifferent between the candidates (to the first order of magnitude). Full consensual compromise with everybody mostly unhappy is comparable to half of the electorate happy and everybody else potentially fully disappointed.

@brozai I want to look into that Borda dominance scheme and see if it is different from my proposal. (EDIT: I totally do have access)

PFPP may be equivalent to a positional scoring rule at each election, but the prescription of the particular scoring rule and how it is allowed to change from one election to the next according to informative distributions is what makes PFPP different. For example, a thought I had earlier today was actually that if the distributions are allowed to update, then as fewer people over-use the higher score values, they become more potent when they are used. This can give voters an even stronger incentive against strategic bullet voting, since it will weaken their vote in the future when they may actually feel strongly about a candidate.

I'll read the PDF paper you linked and see if they coincide, if they do then I'll be happy because that means probably more analysis has been done on this system! Otherwise I'll try to illustrate points where I find that they differ. I think already the fact that the winner is called "generalized Condorcet" points to something different, since the methods I am proposing (at least on the surface, I could be wrong) have nothing to do with the Condorcet criterion.

@Jack-Waugh you’re right about For-and-Against, the modification I suggested is much less significant because it requires the pairs to match exactly, whereas For-and-Against counts all the positives and all the negatives. Just another example of how arbitrary the concept of “balance” in this formalism is. I liked your strengthening of the argument, you’re absolutely right about that as well, because it virtually eliminates any level of information voters might have about other ballots.

Maybe there is something more tangible that F-balance is trying to point to, but it isn’t clear what it might be. In my opinion, with respect to the concept of balance, the strengthened construction should by all reason send equal.vote back to the drawing board, especially if they can’t even formalize a valid counter-argument.

Hi Jack, apologies for a late reply here, I believe I responded to you via email. I mentioned a little bit ago that I was concerned about notifications on the site, I don't know how we can address that except it appears that there was something I was missing. Notifications appear to be an "opt in" situation, for example I just changed my status on this topic to "Watching," so hopefully I will get a notification when you or anybody else replies.

I personally think it would be better for notifications to be a more passive, opt-out situation, because I think the site should be as conducive as possible to keeping the public conversations and posts easily available to the whole community, especially more recent updates to discussions. I also think I was just not used to the new format of this site compared to the old forum and I think it probably works great. We will have to see it in action once it goes public.

In my opinion though, the site appears to be virtually complete. The privacy policy and terms of use would be more urgent so that we can get the forum public. I also think inviting more people to the council is a good idea, since many of us will probably go through phases of being busier than usual and we want the train to keep rolling.

Also, can I be made an administrator/moderator?

@rob I like this concept, I was also trying to consider the prospect of interstate pacts. In the case of less competitive states, an alternative voting system pact might be set to go into effect only once a sufficiently "large" group of states enter into the agreement (maybe measured according to their electoral college points as you suggest), which could easily negate the difficulties of diminishing federal influence when competing with a large FPTP block.

I think electors tend to be mostly faithful to the interests of their states (at least as far as can be determined by the gerrymandered districts), especially I think since they have the pressure of public scrutiny to more-or-less rubber stamp the results as they come in, and hopefully they also have some humility in their own decision-making powers and confidence in the larger process. I do think it gets problematic because entrusting electors to distribute their votes according to a less black-and-white indication of state interests does give them significantly more political power and responsibility that they will also need to be held accountable for. Generally I don't mind the concept of electors/representative arbiters as long as the incentives are sorted out. The way I see it all we can hope for is a system that consistently gives results that are good enough for national success, and if such a system does the job that'd be just fine with me.

I also think it’s a good sign that we’re at the point of discussing potential issues with real large-scale implementation.

Hi voting folks. I have a habit of throwing ideas out to see if anybody finds them interesting enough to pursue, some day my hope is not to be too busy to pursue some of them myself. But I recently have been learning about formal ontology, which is a significant problem in biology (for example, how do we define "cell identity" in a robust and functional way?). It has me thinking of various uses for formal ontology, and I think this is an area that could be helpful in describing voting systems in a way that is at least quasi-universal, given that everybody is appealing to the same standards.

This is an area that I want to learn more about, but there is a language called Basic Formal Ontology that is an abstraction of the Gene Ontology, and seems to be used in a variety of different fields. I wonder if this would be interesting at all to see if there are any good ontologies of voting systems. My hope in that regard would be that possibly in exploring this general structure, we might be able to come to a stronger consensus across "camps" of what constitutes a "good" system, or at least come to a clearer understanding of the principles guiding the judgments of different groups so that they might be analyzed more formally, kind of like how a philosophical argument should be laid out clearly in premises, arguments, and conclusions.

I ordered a text on this language, and I hope to be able to explore and/or utilize it for my own purposes. I think it would be an interesting project if this doesn't already exist.

https://basic-formal-ontology.org/

This probably already exists but I like the idea. It’s a rank order system based on Tideman’s bottom-2 runoff that proceeds recursively.

Informal description: Eliminates Condorcet losers in steps, each time from the largest possible pool of candidates (which pool of a given size to examine must be addressed).

0. Let N be the number of candidates.

1. From the N candidates with the fewest first-place rankings, determine if a Condorcet loser exists.

2. If no Condorcet loser exists, reduce N by 1 and repeat from step 1.

3. If a Condorcet loser exists, eliminate them from the election, let N be the number of remaining candidates, and repeat from step 1 until a single candidate remains.

Just like Tideman's Bottom-2 Runoff, this system is Condorcet compliant and also satisfies the Condorcet loser criterion. I believe this is due to Smith compliance. Variants can use alternative criteria (as opposed to the number of first-place votes) to determine which subset of candidates to examine. For example, a more general/robust method might only consider Condorcet losers among non-Bucklin winners.

I’m actually not certain whether this system turns out to be equivalent to the bottom-2 runoff. I believe it is generally different, but I haven’t constructed a distinguishing example yet. (1/19/2023)

The only reason for considering such a system is to enhance the robustness of the bottom-2 runoff against Condorcet-cycle induced non-monotonicity.

@rob yes, I do think it's easy to veer into political ideology territory, which is just a small step away, and it should be avoided or approached very cautiously. I do think sometimes an evaluation of the effects that a voting system might have on the quality of representation or government processes is valid, but should be done without asking loaded or aggressive questions, and probably there are other general policies in that regard that we should discuss in this forum. I may be guilty of this kind of rhetoric myself, I have no catalog of past transgressions to exhibit but I won't pretend or claim otherwise. It isn't easy to avoid making ideologically oriented judgments even without realizing. In any case moving forward I personally intend to avoid it, and I think we all should probably do the same and let mistakes be recognized. There are plenty of issues that are less controversial to examine here.

@Jack-Waugh, in my opinion (just having read through this now, and not to scold you) it does seem to me like your implicit claim would warrant more evidence. Anyway, I'll throw my cents in about what may be answers to your original questions. Even if the people of Germany hypothetically were not in charge of their government, it seems like a non-sequitur to conclude therefore that PR and voting rights would be either politically significant or a waste of time. Let's put the topic of Germany entirely aside: PR is used in 40/43 of the European nations.

@mosbrooker Just for future reference it might help to tag us! You can type the "at" symbol and then look for the name of whoever you would like to direct your comments to.

Just to address your comments, I do think there are issues with the way representation is handled in the U.S., but there is also a very thoughtful literature documenting the rationale behind the structure of the federal government. The founders of the U.S. lived in a very different socioeconomic context and, as with anybody, were not capable of predicting all of the challenges that would face the nation in terms of its democratic legitimacy, but they also did consider a lot of important concepts and addressed them in a way that I think would be very difficult to consider anything but extremely successful. After all, the United States has become a globally dominant superpower with a robust economy and an overall incredible standard of living, notwithstanding significant wealth inequality and all the problems that come along with that, among other things (ahem, public education, health care, cough). Surely they did something structurally right. And in fact, they did predict most of the core issues that the nation is struggling with presently.

Don't let me just rant, I want to talk about your senator comment. The United States is a federation composed of individual states with distinct laws. The Senate is meant as a body that represents each state on equal footing, independent of population or economic status. The populace of each state is supposed to obtain representation in the House. You may be right that states should have more than 2 senators each, and we probably also need more representatives in the House, since our population is significantly larger than it ever has been! But that is a different way to address the problem. If we essentially do away with the Senate, we won’t really be a federation anymore. As to why that might be a bad idea, you could look to the Federalist Papers. I have my own individual reasons for very much despising the very concept of a large nation, and also large corporations, for that matter. I think each is the suboptimal result of a prisoner’s dilemma.

More than just arguably, election season is mostly toxic due to the "Choose One" voting system, which fuels the competitive and toxic 2-party system that all but disenfranchises moderate voters. This is exactly the problem most of us here want to address by, hopefully, somehow changing the voting system to something that is effective at producing satisfactory representation, and does not suffer from the flaws that induce significant conflicts of interest in voters. European citizens are intrigued to watch U.S. election season like it is a reality TV show. I think they have their own institutional problems as well, but the contrast is at the very least interesting.

Continuous voting has pros and cons, and it's also obviously sensitive to what is considered a "vote." Generally continuous voting would be more sensitive to changes in public opinion, which makes it intrinsically unstable (I'm repeating myself). Maybe you want the status quo to change, but in theory you might want to change it to something. If the system is not stable, whatever you change it to isn't liable to stick around for very long, either. Because it will be unpredictable, it's not easy to preclude it from devolving into something even worse than what it was initially! (Ex: Bolshevik revolution?)

In the end, I don't think we want a revolution. At least as far as what I would like to see, that would be stable and incremental changes that are constructive rather than destructive. I think tearing down the current infrastructure (1) is totally infeasible and (2) would be extremely wasteful anyway. There are many things about our government that work very well, but corruption and institutional issues have eroded its accountability to the public and general welfare.

Benjamin Franklin purportedly said, when asked what the founders had created, “a republic, if you can keep it.” I think the Achilles’ heel of the Constitution was and is the interstate commerce clause, I’m also not alone in this, nor am I by any means an expert. But I also would contest, at the risk of verging on political ideology territory, that movements toward “pure” democracy have been, in my opinion, detrimental, at least in California. I would say that the proposition system has done very little but empower special interest groups to dupe the masses with fine print, and to strip representatives of responsibility without doing the same to their status and power. Anyway, when the masses vote for public goods but also vote not to pay for them, the state is forced to borrow money, and inevitably gets tangled up in all sorts of nonsense, namely internal corruption and crippling debt. Direct democracy does not come structurally equipped with checks and balances. This apology will terminate my rant: sorry.

@mosbrooker all of your examples have been of small groups of people. I already conceded that a system like what you describe is a reasonable solution to delegating executive power and authority in a small tribe, it’s efficient enough and it has historical examples—chiefdoms.

Chiefdoms do not function without oppression when they grow large. The Aztec and Mongolian Empires are sufficient examples. If they aren’t upheld by authoritarian violence, they fragment and crumble, or in any case they generally can’t compete with alternative forms of government without internal violence or oppression. That’s why you don’t see anything like what you describe on a large scale unless you ignore gross oppression. As egalitarian chiefdoms grow larger, they become increasingly unstable.

Also I think the vast majority of people would agree that when fairness of an outcome among alternatives is impossible, an unbiased randomized selection of the alternatives is procedurally fair, and in fact is among the most procedurally fair methods that exist. That’s why coin tosses are used to break two-way ties, neither party can reasonably grumble and say “that’s not fair!” Both had an equal chance, one had to win and the other had to lose. If party #2 wants to flip the table, I don’t think most people would be thrilled to play with them again.

There are ways other than randomness. You could have some contest between the front runners, maybe what, they have a foot race? Wrestling? A game of chess? Fight to the death? It becomes almost just as arbitrary.

I also do not understand how you can consider appointments fair but random selection unfair. Power by appointment is nepotism, bribery and favoritism waiting to happen.

@mosbrooker I think you are mistaken, as democracy is absolutely not simple at all. Your ideal is good and it would be nice if people were empathetic and universally cooperative, and didn’t bandy together in exclusive groups to exert power and control over others, but unfortunately that isn’t true. People do bandy together in groups to exert power and control over others. If we could stop that from happening, we would hardly need any government at all, and people would just organize their societies spontaneously without any conflict. That doesn’t seem possible in a world where life is short and resources are finite.

A fair successor is one who has “consent to rule by the people.” Defining what it means to have the consent of the people in a way that can be efficiently verified is not easy, so we use the proxy of a vote. I don’t see how your system avoids an oligarchy. What happens if leader A states “if I am not approved, I appoint leader B,” and B states “if I am not approved, I appoint leader A”? This situation is impossible to reconcile with the details you’ve described, and according to it the pair A and B are in power perpetually, which is as close to a dictatorship as you can get without being one.

The only reasonable response to this, unless the dictators are very highly benevolent, is an insurrection by the people to either disregard or overthrow the system. But then there is no need for a leader to begin with, this is just direct democratic rule—which, I agree, is efficient and probably usually good for very small societies.

At the risk of continuing this rant, somebody might try to point to Ancient Greek society as a candidate or example for this kind of democratic system. But the truth is that democracy meant something very different to Ancient Greek people than what it means to us today, and their society was actually highly oligarchical. Something that is historically overlooked quite often is how very new the democratic republic is as a form of government. It was not that long ago that most men simply could not vote. I would recommend reading some of the Federalist and anti-Federalist papers, as well as John Stuart Mill’s “On Liberty.”

@mosbrooker allowing appointments of the successor doesn’t make any sense to me. Don’t take this the wrong way, I think the fantasy doesn’t take into account very real problems that exist with democracy. There are no checks and balances, there’s no constitution, there’s no protection for minorities, and there is no avenue to establish representation, or to create, enforce or validate laws. To me it seems mostly like a vacuous space for something more substantial to fill. What stops the society from devolving into an authoritarian mafia-run police state, or from being destroyed by warlike neighbors who want to take their crops, enslave their men and rape their women?

@mosbrooker the main problem here is how to establish the incentives for representatives to make decisions that are in the interest of the general public. For me, the goal of (real) democracy is to stabilize a society away from the extremes of anarchy and authoritarianism. We may need a better way, but we don’t need the “best” way (especially considering that there is no such thing).

Informal methods like this make sense for small groups where interpersonal social ties and influences are significant, but for large and heterogenous populations those interpersonal social ties become heavily diluted.

Dictators don’t reign primarily by playing whack-a-mole, although they do this as well. The most significant source of dictatorial power is having the seat at the very top of a pyramid, just above an oppressive (and often internally dysfunctional and corrupt) block oligarchy.

A different issue has to do with stability and competency. The whims of the masses are fickle and can be easily swayed by media bias and propaganda, and enabling immediate changing of seats can destroy the coherency of a policy-making apparatus. People are already skeptical about the prospect of term limits being imposed in Congress for that reason. New blood isn’t always a good idea when it means a lack of experience, and direct majoritarian democracy is a bad idea because it enables oppression of minorities without protection or recourse.

What happens in your hypothetical society when competing factions campaign to take control of leadership? In my mind, without a constitution and a formal electoral power structure in place, it devolves into a state of populist demagoguery (and it might do that anyway.) I think just historically that kind of society is only appropriate and stable for a small homogeneous tribe, which is why that’s the only context in which it can be found.

To tie things to current events, the reason Putin hates “The West” (read: liberal democracy) is that it is the single biggest direct threat to his authoritarian regime. All of the culture war nonsense is almost fully pretense or self-deception, and with a psycho-narc vampire like Putin it could go 50/50 either way, at any given time, take your pick.

@toby-pereira @mosbrooker and indeed (as you know) this ping-ponging is exactly the game Putin played with Medvedev and the Russian "presidency."

@mosbrooker this kind of system is only feasibly democratic when the population is very small and homogeneous.