Consensualism

[cfrank]

@rob I agree. However, as per our discussion, I do have at least one framework through which to begin to analyze in-group consent: (S,P)-consensuality, which is a construct that can be applied to any rank or score system.

Just to reiterate, if the scores S[k] form a well-ordered set with S[i]<S[j] if and only if i<j, then a candidate C is (S[k],P)-consensual if and only if C was scored at least an S[k] by at least a P-fraction of the electorate.

In this sense, one can take a candidate C and then construct the set

Profile(C):={(S,P) such that C is (S,P)-consensual}

And a single-winner voting system is (S,P)-efficient if

“There is some B different from A with Profile(A) subset of Profile(B)” implies “A does not win.”

(S,P)-efficiency is a crude measure of consent, but using the (S,P)-consensual framework one could try to develop various constructs of consensuality.

[rob]

@cfrank I'll admit I am not able to visualize what all that means. Maybe it is a good example of "a pictures is (or would be) worth a thousand words".

Aside from the description/definition, is there are reason you think that expresses the concept of consensus?

[cfrank]

@rob Yes, I'm sorry it isn't easy to communicate this concept without diagrams, I will try to create a more informative description.

(S,P)-consensuality is a two-dimensional measure of consent. As P is fixed and S increases, as S is fixed and P increases, or as both increase together, the level of consent indicated by (S,P)-consensuality also increases.

As P is fixed and S increases, this means that the same fixed fraction of the electorate has increased their level of approval of the candidate.

As S is fixed and P increases, this means that a larger fraction of the electorate has the same fixed level of approval of the candidate.

As both S and P are increased, this means that a larger fraction of the electorate has a higher level of approval of the candidate.

The issue is about what happens when one is increased and the other is decreased. This is why the (S,P)-profiles of the candidates are interesting, because in some sense they represent the boundary of consent that is achievable with a given candidate, in the same sense as a production possibilities frontier. That's what motivates the definition of (S,P)-efficiency for a voting system.

Any reasonable rank/score system is (S,P)-efficient. However, in general, any formal, finite measure (as in measure theory) over (S,P)-space automatically accomplishes (S,P)-efficiency. For example, a uniform measure over (S,P)-space gives standard score voting. The question is how to establish the measure in a meaningful and productive way that reduces conflicts of interest (which is what causes strategic behavior). In my opinion, a measure that takes into account how the electorate uses the voting system itself and is tuned to accentuate cooperation and compromise over competition would be far superior to a uniform measure. That's what I have tried to propose with SP-Voting and its weighted variants.

[rob]

@cfrank Ok. To me it is still missing a clear description of why you consider this represents the concept of consensuality. I would suggest trying to make some diagrams. It helped when you drew some bar graphs when we were talking, but I'd think if you took the time to draw something up that you can add to your posts , it might be time well spent. GIMP is your friend.

Then again maybe what you've posted sufficiently communicates the concept to other people. Anyone else want to weigh in?

[cfrank]

@rob I already supplied ample materials for anybody who wants to learn about the system to do so, including a detailed explanation and visual aides. I cannot upload my thoughts into your brain, it takes two to tango. If clear English with visual aides is not sufficient I'm not sure what else to do. The photograph I took takes up too much data to upload into this framework, and I don't want to learn a new coding language. If you want to continue to have a discussion about this system with me, please take the time to learn about it. I don't understand how to reconcile that you were willing to have an hour-long private discussion with me, but that an eleven-minute video is too much.

[rob]

@cfrank One thing I've learned in 25-plus years doing UI design is that if the users don't understand or embrace something I make, my first impulse to blame the users for not trying hard enough or not being smart enough is usually misguided.

I've also written some 7500 answers on Quora (https://www.quora.com/profile/Rob-Brown-13), about both technical and non-technical topics, which contributes to my experience with communication and persuasion. Again, I don't tend to blame readers if what I write doesn't resonate with them. Instead I work to improve my approach. I'll admit it is frustrating when I write something that I think is really good but no one even upvotes it, but the best I can do is learn to adjust my approach.

I remain unconvinced that you have explained anywhere why you think the system you propose actually measures "consensus" -- which, by the way, is simply a non-technical English word, and like many such words, has various shades of meaning, does not represent a black and white concept, and is highly subjective. In fact, an argument could be made that "consensus," often defined as "a general agreement" doesn't really have a place in discussing voting methods, since we can't count on there being a general agreement, but we still need to elect someone. I think "reasonable compromise" is a better descriptor of a goal that is actually attainable, much of the time.

Regardless, I've read what you have written, and watched your video. I am guessing that I have spent more time than anyone else here trying to understand it.

I'll just ask this again, but it is not directed at you: does anyone else get this?

[cfrank]

@rob I am not sure in what sense it is not clear that (S,P)-consensuality measures the degree of consensus. If a candidate is (S,P)-consensual, it means that at least a P fraction of the electorate has agreed that the candidate measures up to their interpretation of whatever level of approval the score of S implies.

If a candidate is (S[max],1)-consensual, for example, then every voter has marked the candidate with the highest possible score. In a score system, aren’t those the two metrics we have for evaluating agreement? The number of people who indicate their approval of a candidate with a particular score?

[rob]

@cfrank Sure ok but then consensus is a two dimensional gray scale thing, rather than something approaching a boolean.

We ultimately need something to unambiguously choose a single candidate, and if your system does that, it isn't clear to me how.

By the way, you said you can't upload a photograph because it is too much data. You should be able to resize it to an appropriate size using various tool available in your operating system or that are free downloads or available online. The diagrams I saw you draw onscreen could be extremely lightweight, datawise. You seem to have a tablet/stylus, so learning a paint program like GIMP seems like it wouldn't be a waste of time.

[cfrank]

@rob if you don’t understand how the system elects a candidate, I have a very hard time believing that you more than cursorily watched the video…

It really is not very pleasant trying to discuss concepts with somebody who is so combative. I’m not sure what you are trying to defend. Why not try to be cooperative? Understanding a concept takes trying to explore its implications on your own. It seems to me that you are continually misrepresenting my point of view with straw dogs rather than actually trying to understand it.

[rob]

@cfrank Sorry you see me as combative. I've watched your video, twice now, and continually had to back up to try to get what you were trying to say, and often gave up. You've used the word "imbecile" to describe people who don't understand what you are saying, while telling us that you are intelligent. In other words, you've blamed us for not understanding, since it can't be your inability to communicate clearly. You say I'm misrepresenting your point of view when I have clearly stated, I don't understand what your point of view is.

Here is one of many sketches and notes I made while trying to grasp your presentation:

Profile for a single candidate. This candidate got 35% of voters giving her a score of at least 2. She is therefore (S2, .35) consensual. She is also (S4,.12) consensual, etc.

If that is incorrect, let me know. If it is correct, I don't understand why you couldn't explain it more straightforwardly than you do.

I don't know that the curves here represent:

As just one more example of where you make it hard to understand, you use the term "probability" and introduce randomness when it is entirely unnecessary. It's as if, instead of saying "the glass is 30% full" you say "there is a 30% probability that a randomly chosen point within a glass is occupied by liquid". Sure, I can understand that, if I go to the effort, but there is a limit to how much time I am going to spend trying to parse and un-convolute that kind of thing.

@Keith-Edmonds, someone who apparently has far more math background than most of us, diplomatically said "I must admit I do not entirely follow your system. Can you give a clear example? Or a step by step procedure." I don't think you've done that. "Watch a 20 minute video where I talk while drawing diagrams on top of a text document" is not that. (why not draw diagrams ahead of time, or, in the case of explaining basics like what a cardinal/scored ballot is, just grab an image from the web? At the very least, draw on a white background maybe? I'm not misrepresenting you when I make such observations about your presentation)

I've offered to help with your attempts to communicate the idea. There are numerous things that show you don't want to go to the effort of making things easily comprehensible, such as explaining some basics up front. You say your system draws data from past elections, so each time you run it it comes up with a different results. That's kind of a big deal, no? While I personally find that bizarre and radical and impractical and unlike any voting system I've seen, maybe if you simply explained why that is necessary we could at least discuss it. And again, if I've misrepresented it, sorry. I don't understand it, and I haven't seen anyone else come on the forum and say they do.

Separately from discussion of this specific proposal, I have attempted to establish common ground, by asking the question about "is a simple majority vote the best way to resolve a 2 candidate election?" Since you couldn't simply answer "yes" (consistent with Arrow, the other people here who answered, and, as far as I know, most everyone else in the world who thinks democracy is a good idea), while proposing no clear alternative other than appealing to people's empathy, clearly we don't have much in the way of common ground. There is probably little point discussing multi-candidate elections, especially ones where it gets into this level of complexity, when we can't agree on such basic things.

[cfrank]

@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.