SP Voting: Explanatory Video

cfrank

@andy-dienes I am considering the median in the same sense as Rob, as he and I have discussed this before in some detail. I am talking about the “median candidate,” which in the sense of SP Voting happens to be a candidate who achieves a fitness metric of approximately 1/2. Such a candidate would achieve a typical profile in terms of the distributions chosen for the system, which can be driven by relevant data.

However, I don’t believe I am using an L-estimator for SP Voting.

Also, Arend Lijphart is definitely talking firstly about governments that are responsive to supermajorities rather than slim majorities or pluralities, which is what motivates the balancing principle of SP Voting that majority power should be tempered against broader consensus.

cfrank

@andy-dienes I am aware of the game theoretic and computational complexity literature on voting methods. Publicity in this context is relative to the voting theory community, and I was in no way intimating that publicity has somehow contributed to the fact that Condorcet methods are game theoretically stable. I was saying that Condorcet methods have more support in significant part because they are well-known and well-studied.

If you take a survey of various voting systems, you will notice a triangular spectrum of behavior between (1) game theoretical stability, (2) consensuality in the sense of Lijphart, and (3) computational simplicity. Each of these three properties seems to be somewhat at odds with the other two. In order to be game theoretically stable, systems tend to restrict ballot expressions and reduce the information that can be utilized from the electorate, which reduces the ability to come to a broad and relevant consensus. To build broader consensus, more information from the electorate is necessary, which reduces both stability and simplicity since voters will have more avenues for expression and therefore for tactical voting. Since stability and consensus building are at odds, a system will become more complicated as it attempts to reconcile the two.

@cfrank said in SP Voting: Explanatory Video:

(1) game theoretically stability, (2) consensuality in the sense of Lijphart, and (3) computational simplicity. Each of these three properties seems to be somewhat at odds with the other two.

I think we're unlikely to agree regarding this statement. A rule like Minimax is both strategically stable and extremely simple, and I would certainly "consent" to using Minimax for political elections. Unfortunately I cannot say the same about SP voting.

cfrank

@andy-dienes that is not the meaning of consensualism in the sense of Arend Lijphart. The voting method must be responsive to a broad supermajority. Minimax is still a Condorcet method, which is explicitly majoritarian.

@cfrank Every Condorcet method is responsive to a supermajority. On the other hand SP is not necessarily, depending on the exact weighting parameters you use. So I will admit I do not see the point you are trying to make.

cfrank

@andy-dienes no, Condorcet methods are responsive to a slim majority. That is what it means to be majoritarian. SP Voting with the weighting I proposed, which is a geometric weighting with common ratio 1/2, is by construction responsive to a supermajority whenever possible, and the strength of the supermajority necessary for a divisive candidate to win will increase with the level of broad support available from among other candidates in the election.

@cfrank
From wikipedia:

In this book, Lijphart defines a consociational democracy in terms of four characteristics: (1) "government by grand coalition of the political leaders of all significant segments of the plural society," (2) "the mutual veto", (3) proportionality, and (4) "a high degree of autonomy of each segment to run its own internal affairs."[10]

In contrast to majoritarian democracies, consensus democracies have multiparty systems, parliamentarism with oversized (and therefore inclusive) cabinet coalitions, proportional electoral systems, corporatist (hierarchical) interest group structures, federal structures, bicameralism, rigid constitutions protected by judicial review, and independent central banks. These institutions ensure, firstly, that only a broad supermajority can control policy and, secondly, that once a coalition takes power, its ability to infringe on minority rights is limited.

These definitions are focused around the design of the democratic institutions as a whole, not individual voting rules. Note that even in this definition properties of a consensual democracy are stated in terms of outcomes e.g. a diverse coalition of leaders and proportionality. These are things that can only be achieved by looking at the structural design at a much higher level than a voting algorithm and I again encourage you to stop letting misapplied philosophy have such a heavy hand in what should be a mathematical problem.

Moreover, of of the main tenets of a Lijphart consensual democracy is the protection of minority interests. Even if you want to effect this in the voting rule itself it needs to be defined and proven much more rigorously; there is far too much handwaving for my taste speculating how SP maybe could or should behave.

For an example of what I'm talking about, check out this paper[7] where they define a notion of majority power and veto power for a number of voting rules and then analyze existing rules from that perspective. Unsurprisingly, Condorcet rules have in general a stronger veto power (aka minority protection) than Borda, which, being a positional scoring rule, is probably the most similar method in that paper to SP.

cfrank

@andy-dienes
“These institutions ensure, firstly, that only a broad supermajority can control policy…”
This is the primary purpose of those institutions. This is not possible if representatives themselves are not accountable to broad supermajorities.

SP Voting is very different from Borda scoring, which is a cardinal scoring system, AKA a positional scoring rule with fixed weights assigned to each score, whereas SP Voting is not a positional scoring rule, it is a type of ordinal scoring system, which is different. It isn’t the scores themselves that are being weighted, but the quantiles of the candidate in each scoring category.

I can’t single-handedly construct an entire corpus of mathematical work on SP Voting that is comparable in volume with that of Condorcet methods for obvious reasons, not least of all being that SP Voting is a more complicated method that is more difficult to analyze formally. It has to be, since it attempts to reconcile game theoretic stability with consensualism.

Voting is not just a mathematical problem, it’s primarily a social problem that has significant mathematical aspects. Any hand-waving is based on actually testing the method, which I coded up in Python, in many instances, and observing the results. I’ve also written up a document detailing the reasoning behind the method, but I think the video provides visual diagrams that are easier to conceptualize.

rob

@cfrank said in SP Voting: Explanatory Video:

But sure, if you would like to illuminate your perspective as to why you have not convinced me specifically, please be my guest.

I think I said I didn't want to speculate on that, obviously I don't know the answer. It's probably not appropriate to attempt to psychoanalyze you, even with your invitation.

But since you ask, I will say that engaging with you feels like engaging with someone who has invented an spectacularly complicated energy producing machine, complete with pages of mathematical equations, but studiously avoids any attempts to establish a baseline, such as agreeing that the law of conservation of energy is true.

I'm not so much saying you are wrong, as I am saying you have unrealistic expectations as to how much time people are going to be willing to spend looking at the details of what you are trying to sell, given the lack of a simple abstract or summary.

Obviously there is nobody else currently “sold” on SP Voting, Rob.

Well you asked why I haven't convinced everyone of my own views. I think the core concepts don't need me to convince people, since my views are pretty mainstream. But there will always be iconoclasts.

And you are right that Condorcet methods can be shown to have strategic vulnerabilities, which I would characterize as very subtle, just as almost every real world solution to anything has imperfections. Again, that's why I go to the simplest possible examples (voting for a one dimensional numerical value being my favorite) to demonstrate a point and establish a baseline. Another baseline is a simple two candidate election: as Andy notes yours -- like Score -- doesn't seem to distill down to simply electing the majority winner in that case, while I would argue that majority winner is in all senses the correct choice in a binary election. But if we can't agree on that, I don't see why we should waste time trying to agree on something that takes a 47 minute video to explain how it works.

cfrank

@rob the method is not that complicated, and 47 minutes is not very long. It takes upwards of two hours to explain to a typical student how to apply almost any new concept, which is why that’s how long lectures typically last. You just aren’t willing to invest the effort needed to engage with the idea, nor it seems generally with ideas that don’t come flagged with a guarantee to conform with your own mental picture of how things are for whatever reason required to work.

I’ve also given pretty comprehensible reasons, arguments and examples for my opinions about majority rule even in cases of two candidates. Instead of addressing those arguments, you appeal to the stone. That doesn’t make me an iconoclast. If the situation is so clean cut, you should be able to support your point of view with logic.

How my proposal is akin to a perpetual motion machine is well beyond my powers to recognize. You’re just deciding it’s that way without actually looking at it.

rob

@cfrank said in SP Voting: Explanatory Video:

You just aren’t willing to invest the effort needed to engage with the idea

I've spent a lot more time than most people seem willing to spend.

Yes, 47 minutes is long, in my view. This is not a college class, you aren't my professor, and your video does not come with a single recommendation from anyone else but you.

And it has no straightforward summary, and it mixes philosophy, vaguely defined words (that you seem to assume we all agree on their meanings), and hard math in a way that I personally find quite off-putting and frustrating, to be honest.

You don't have to take my advice, but that's what it is. Make a good, short presentation. If your idea is too complex to present the gist of it in a minute or two, I don't think it has a chance of spreading widely. You seem good at math, and this is where I'd suggest you, well, do the math.

@cfrank said:

you should be able to support your point of view with logic.

I believe I have. I believe @Andy-Dienes has as well, since I agree with the vast bulk of what he's said above but didn't feel the need to repeat much of it. (I don't disagree with anything, but some of it is outside my area of knowledge. I've copied below things that I especially agree with and think are well stated) The fact that my logic doesn't connect with you is not necessarily all on me.

I'm getting a bit tired of your attacks, and your accusations of my being too lazy to watch the entirety of your (yes, long) presentations. I approached this diplomatically after spending a good bit of time with your video, if not all 47 minutes. I only made the "perpetual motion machine inventor" analogy when you challenged me with demanding to know why I haven't convinced you yet.

An aside:

One thing I have advocated for (and am working on building result visualizers for) is using the voting methods we advocate for to vote for our favorite voting methods. I will run this here and in other forums such as EndFPTP and maybe election methods mailing list. We can run the tabulation in any method we want (since the ballot data will of course be public), so it would be great if you run the tabulation under SP and post the results, if you haven't made an online tabulator so others can.

But since you are asking such questions as "why haven't you convinced everyone?" I think you should be willing to have it on the ballot, so you can see how many people you've convinced of the merits of SP. I'll happily link to whatever presentation you want -- if you think a 47 minute video is best, that's your call. Maybe a lot of people will embrace it, maybe not, I'm not going to make a prediction.

(below are Andy's comments from above that I 100% agree with)

These are things that can only be achieved by looking at the structural design at a much higher level than a voting algorithm and I again encourage you to stop letting misapplied philosophy have such a heavy hand in what should be a mathematical problem.

No, this is neither true nor is it why they are considered game theoretically stable. There are actual mathematical reasons which can be stated and proven quite formally.

I do not think somewhat vague notions like that should be used to decide the exact inner workings of the voting method; instead I would use Lijphart consensus to guide an approach to questions more like "what is the structure of my government" or "which government officials should be publicly elected" or "who gets to vote."

I would still encourage you to try to attach less philosophy to your argument and just treat it like a mechanism design problem. Use the philosophical arguments to decide what you want the mechanism to do, and then just normal math & engineering approachs to design the voting rule to achieve that goal.

Also just very concretely to address the proposed rule at hand: I do not think a rule that does not reduce to majority when there are only two candidates will ever be politically viable (or appropriate). I feel the same way about regular Score as well.

cfrank

@rob I have read and responded in turn to all of Andy’s comments, apparently you have chosen to repeat them. This is a forum for investigating voting theory. You are the audience who is most liable to actually take a look and to gauge the merits and demerits of the system. The video is less than 24 hours old, how on Earth can it be reasonable to demand external recommendation?

You can get as tired as you like with my “attacks,” which are almost nothing else but drawing your attention to logical fallacies. The system is perfectly well-defined, and so are the principles I am referencing.

The “philosophy” I am using is called logical reasoning, and it isn’t “misapplied.”

“Use the philosophical arguments to decide what you want the mechanism to do, and then just normal math & engineering approachs to design the voting rule to achieve that goal.”

The irony of what Andy recommends here is that this is exactly what I have already done, and the reason your logic doesn’t connect with me is that you have not actually addressed my arguments.

Here is your most recent appeal to stone:

“But if you are going to handle it with a vote, and you think there is something better than "everyone pick your favorite temperature, and we'll choose the median," .... yeah, not much point taking the discussion further than that.”

And this is why I intimated that you are being dogmatic, despite the fact that there are logical reasons for people to disagree with your stance, among them being the arguments I have already drawn your attention to before.

rob

@cfrank said in SP Voting: Explanatory Video:

have read and responded in turn to all of Andy’s comments, apparently you have chosen to repeat them.

Of course I did, after you said I didn't support my views with logic (which is frankly a pretty immature thing to say), so I wanted to be clear about the things that I believe are well supported by logic and that I strongly agree with, but hadn't previously stated myself because Andy already had. Not sure what isn't clear about that.

I also think I supported my views with logic myself, but I understand you see otherwise. It appears that you think that anything that doesn't support your invention isn't supported by logic.

cfrank

@rob that’s false. Dismissal without reason is what I consider illogical. If you have a legitimate logical argument against the merits of the system, I would love to hear any of them and would take all warranted criticism of the system.

One variant of SP Voting would be the rank order variant. For whatever distributions you choose, this variant does reduce to majority rule for two candidates. I don’t necessarily think that that’s always a good thing, but that demand can be easily accommodated by the framework.

@cfrank I am beginning to feel that you do not in fact “appreciate [our] feedback and any suggestions” as you say in the initial post.

cfrank

@andy-dienes What I said was, “If you watch it and consider the arguments I make, I would appreciate your feedback and any suggestions.”

I did appreciate your feedback and the resources you referred to, as well as your comprehension of the mechanism. I did not appreciate Rob’s insistence on commenting without hearing the explanation, and instead operating under incorrect assumptions about it.

I do disagree that I am being overly philosophical, and some of the points you made in your response were points I also made myself in the video, such as that “consent” is purely formal and that voters may not have even “consented” to the candidates in the pool in the first place.

rob

@cfrank
You say I was incorrect about something regarding your method, feel free to point out specifically what it was. As far as I can see, the only thing I specifically criticized about your method was that it was complex, and I stand by that one. The rest of the things I said were not about your method per se but about the presentation (long, heavy handed with the philosophy, overuse of the vaguely defined concept of "consensuality", and lacking an easy to find overview or straightforward explanation of how the method is tabulated) as well as about general baseline concepts. Regarding the baseline concepts (such as the importance of game theoretic stability, which implies such basic things as that a two-way race should always elect the one with majority support), I said if we can’t agree on those, there isn’t a whole lot of point in my taking the (unreasonable, in my opinion) time to try to go through your whole video and try to figure out what your method actually does and what benefit it supposedly gets from its complexity.

I don’t expect you to take my advice, but still. You seem to have wildly unrealistic expectations of how much time people are going to spend to take in your ideas, how efficiently your presentations communicate your ideas, and how enamored those people are going to be with them. I'm not stopping anyone else from looking at your idea here, but I also suggest you take the idea to EndFPTP on reddit, or whereever else, and see if anyone there meets your expectations of enthusiasm, open mind and time-on-their-hands.

But again, if you are going to accuse me of being incorrect about something that I assumed about your method and subsequently commented on, please tell us what it was.

(and I should add, unless you want to approach this with a different attitude, which I have no expectation of, I won't say any more....)

cfrank

@rob one of your incorrect assumptions about the system is that it does not reduce to majority judgment in the case of two candidates. It doesn't need to, but it can be easily made to conform to that requirement. Furthermore, until you actually try to engage with how the system works, your notion of it being complex seems pretty well moot to me, frankly. In any case, even if it were to be complex, the system could be used for comparative purposes if nothing more.

I don't expect anybody to be "enamored" by the system without reason. If they actually think about it and like the concept, that's fine. If they actually think about it and don't like the concept, that's also fine. But the baselines you are referring to are circular in this context, since the whole driving principle of this system is that majority power should be tempered against broader consensus, which is not vague at all. The majoritarian principle is precisely the notion under question.

As I mentioned, "consensus" is in the sense of Lijphart, being the principle that representative governments--including their voting systems (how else?)--should be responsive to broad supermajorities rather than primarily to slim majority rule, which can be highly divisive.

Going back to the example of a team lunch with fruit cups and PB&J sandwiches from a long while ago, you mentioned that voters should not be allowed to declare being allergic to a candidate. And certainly, that would be absurd. But what I am trying to touch on is the notion that divisive candidates seem often less preferable to candidates with broader and appeal. Surely there are many ways to try to incorporate a principle to that effect. SP Voting is one of those. If you want to try to understand why it might be a good one, well that's exactly what the video explanation is about.

@cfrank said in SP Voting: Explanatory Video:

As I mentioned, "consensus" is in the sense of Lijphart, being the principle that representative governments--including their voting systems (how else?)--should be responsive to broad supermajorities rather than primarily to slim majority rule, which can be highly divisive.

Even just a "slim" majority can still guarantee their candidate a victory in SP voting, so...

I recommend again you stop using relatively vague philosophical notions to instruct your mechanism design; it's fine to have some guiding philosophies but these need to formalized into some rigorous components before they're useful to evaluate voting methods.

rob

@cfrank said in SP Voting: Explanatory Video:

one of your incorrect assumptions about the system is that it does not reduce to majority judgment in the case of two candidates.

I simply noted that Andy said that, if it isn't true, sorry, but that was a very minor side point. Your response certainly implied that it was true ("I’ve also given pretty comprehensible reasons, arguments and examples for my opinions about majority rule even in cases of two candidates") But the real point was that you don't seem to value game theoretic stability, or maybe you don't understand it in the way I do. Regardless I spent far more time on the example of the temperature voting thing to illustrate a similar point but with a bit more generality and because it applies more, given my hope (which I think you share), for there being more than two options so there actually is a middle ground/median. This was to ensure that we were on the same page on whether that was important (given that I still don't know what problem you are really trying to solve). Lijphart certainly seems to favor things that go for middle ground. I spent a bit of time reading his stuff (and about his stuff) and I'm totally on board that sort of approach.

@cfrank said:

Going back to the example of a team lunch with fruit cups and PB&J sandwiches from a long while ago, you mentioned that voters should not be allowed to declare being allergic to a candidate. And certainly, that would be absurd.

I'm not sure what you are saying would be absurd. (ignoring the kid with special requirements, or trying to factor that kind of thing into a way of voting on lunch)

I think it would be rather absurd, in the context of real-world voting, where someone can say "I simply can't accept this candidate, so you must accommodate me because my needs are more important than your simple preferences." In a small group, especially where there is continued interaction, it makes sense that we accommodate people with special requirements such as allergies or disabilities. With larger groups, such as political elections, it should be obvious that such a thing would be abused, so that isn't the kind of thing that voting is intended to handle. It also doesn't really fit with "one person one vote."

To me, voting is about preferences, not absolute requirements.

( The way to accommodate those, actually, is representative democracy. You vote for a person, who you trust to sort out special cases. But you don't get to declare yourself "allergic" to a candidate so you can get your way )

You also, in the context of my example of voting for a thermostat temperature, mentioned a voter who has OCD and doesn't like the number 73. In that case, it just seemed like an attempt to miss the point of a example that is intended to be simple (compared to voting for human candidates) for the purpose of illustration of a concept. Regardless, it doesn't seem like a sincere thing that you think is a likelihood in that scenario. (I have my doubts any real world office would feel the need to accommodate such a person, and also have my doubts that it has ever happened)

Notice that the "capital of Tennessee" example, used widely, elaborates in some detail about such assumptions to keep the example simple (in that case, that everyone would prefer a city closer to themselves, and it actually says that everyone lives in one of the four cities).

As I mentioned, "consensus" is in the sense of Lijphart, being the principle that representative governments--including their voting systems (how else?)--should be responsive to broad supermajorities rather than primarily to slim majority rule, which can be highly divisive.

I don't disagree with that, other than questioning what is meant by majority or supermajority in this context. I am very anti-party, especially when it devolves into two dominant parties (where the concept of majority becomes a real thing because you are left with a binary choice) This is why I keep returning to the concept of median, which is much easier to visualize for me when the thing in question isn't a binary choice but something that essentially lies on a spectrum. Maybe it isn't the best term either because it is hard to define what it means with discrete human candidates, but the temperature voting thing is the best way I can explain what I mean. (since in that case there really is a median, and it is also particularly easy to see the meaninglessness of the term "majority" as the number of potential "candidates" increases and you have options in the middle that have wide appeal even if only a small percentage considers them their first choice)

I don't think I ever got an answer on whether or not you consider this an issue with Condorcet-compliant systems, such as whether you consider Condorcet systems majoritarian. There are internal majorities, yes (between candidates pairwise), but overall they tend to settle on candidates that are near the center and therefore have wide appeal and tend not to be divisive. (as do various other systems like approval and STAR, which just use different approaches to generally elect what would be the Condorcet winner) To me any of those should accomplish your goal, to the best I can understand what your goal actually is.